Mathematical modelling of trachoma transmission, control and

elimination

Authors

Amy Pinsent*1, Isobel M. Blake||, Maria-Gloria Basáñez†, Manoj Gambhir*

Affiliations* Department of Epidemiology and Preventive Medicine, Monash University, Melbourne, Australia

|| MRC Centre for Outbreak Analysis and Modelling, Department of Infectious Disease Epidemiology, School of Public Health, Faculty of Medicine (St. Mary’s Campus), Imperial College London, London, United Kingdom

† London Centre for Neglected Tropical Disease Research, Department of Infectious Disease Epidemiology, School of Public Health, Faculty of Medicine (St. Mary’s Campus), Imperial College London, London, United Kingdom 1 Corresponding author: E-mail: amy.pinsent@monash.edu

Contents

1. Introduction

1.1 Clinical and epidemiological features

1.2 Trachoma control and elimination

1.3 The role of mathematical models

1.3.1 Deterministic and stochastic modelling

1.3.2 Modelling infection and modelling disease

1.4 Aims and objectives of this review

2. Methods

3. Results

3.1 Characteristics of identified studies

3.2 Deterministic and stochastic models

3.3 Data sets used and model fitting to data

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3.4 Transmission intensity and the basic reproduction number

3.4.1 Estimating the force of infection

3.4.2 Estimating the basic reproduction ratio

3.5 Acquired immunity: recovery rate and infectivity

3.6 Infection and active disease, modelling of disease sequelae

3.7 Simulation of interventions, forecasting infection and disease, and analysis of

their cost effectiveness

4. Discussion

4.1 Using modelling to determine the feasibility of the GET 2020 goals

4.2 Conclusions

Abstract

The World Health Organization has targeted the elimination of blinding trachoma by the

year 2020. To this end, the Global Elimination of blinding Trachoma (GET 2020) alliance

relies on a four-pronged approach, known as the SAFE strategy (S for trichiasis surgery; A for

antibiotic treatment; F for facial cleanliness, and E for environmental improvement). Well-

constructed and parameterised mathematical models provide useful tools that can be used

in policy making and forecasting in order to help control trachoma and understand the

feasibility of this large-scale elimination effort. As we approach this goal, the need to

understand the transmission dynamics of infection within areas of different endemicities, to

optimize available resources, and to identify which strategies are the most cost effective

becomes more pressing. In this study, we conducted a review of the modelling literature for

trachoma and identified 23 articles that included a mechanistic or statistical model of the

transmission, dynamics and/or control of (ocular) Chlamydia trachomatis. Insights into the

dynamics of trachoma transmission have been generated through both deterministic and

stochastic models. A large body of the modelling work conducted to date has shown that, to

varying degrees of effectiveness, antibiotic administration can reduce or interrupt trachoma

transmission. However, very little analysis has been conducted to consider the effect of non-

pharmaceutical interventions (and particularly the F and E components of the SAFE strategy)

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in helping to reduce transmission. Furthermore, very few of the models identified in the

literature review included a structure that permitted tracking of the prevalence of active

disease (in the absence of active infection) and the subsequent progression to disease

sequelae (the morbidity associated with trachoma and ultimately the target of GET 2020

goals). This represents a critical gap in the current trachoma modelling literature, which

makes it difficult to reliably link infection and disease. In addition it hinders the application

of modelling to assist the public health community in understanding whether trachoma

programmes are on track to reach the global elimination of blinding trachoma by 2020.

Another gap identified in this review was that of the 23 articles examined, only 1 considered

the cost effectiveness of the interventions implemented. We conclude that although good

progress has been made towards the development of modelling frameworks for trachoma

transmission, key components of disease sequelae representation and economic evaluation

of interventions are currently missing from the available literature. We recommend that

rapid advances in these areas should be urgently made to ensure that mathematical models

for trachoma transmission can robustly guide elimination efforts and quantify progress

towards GET 2020.

Keywords: Trachoma, Control, Elimination, GET2020, R0, Mathematical modelling

1. Introduction

1.1 Clinical and epidemiological features

Trachoma is one of 17 neglected tropical diseases (NTDs) prioritized by the World Health

Organization (WHO) for control and elimination through preventive chemotherapy or

intensified disease management strategies (WHO, 2015a). NTDs are mostly responsible for

chronic infections/conditions that can cause severe morbidity in affected individuals, leading

to long-term disability, but are deemed to be associated with relatively low mortality in

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comparison to acute, epidemic infectious diseases (WHO, 2015a; Hotez et al., 2014).

Transmission of NTDs is facilitated by living conditions that are associated with poverty, such

as poor housing and sanitation, and limited access to clean water and basic healthcare

(Hotez et al., 2009).

Trachoma is the leading global cause of infectious blindness, and is currently

estimated to affect 84 million people across 51 endemic countries (WHO, 2012). An

estimated 1.8 million people are visually impaired as a result of the disease, of which 0.5

million people are irreversibly blind (WHO, 2012; WHO, 2015b). Active inflammatory disease

—trachomatous follicular and trachomatous inflammatory (TF, TI, according to the WHO

simplified grading scheme (Taylor et al., 2014))—is caused by infection with the bacterium

Chlamydia trachomatis. Repeated infection with the bacteria leads to an

immunopathological response characterized by scarring of the inner part of the eyelid, and

an eventual curling-in of the eyelashes, which abrades the corneal surface. This can lead to

trachomatous trichiasis (TT), corneal opacity (CO) and blindness. Excess mortality is also

reported to be associated with blinding trachoma (Hotez et al., 2014). Estimates of the

Disability-Adjusted Life Years (DALYs) due to trachoma have been variable. The Global

Burden of Disease (GBD) 1990 study estimated the burden of trachoma (all ages) to be

144,000 (95% uncertainty interval (95% UI) 104,000–189,000) DALYs, whereas the GBD 2010

study reported a value of 334,000 (95% UI 243,000–438,000) (Murray et al., 2012). Other

authors have set this figure at least 1 million DALYs (Evans and Ranson, 1995) or as high as

3.6 million, with the highest proportion (72%) contributed by sub-Saharan Africa (Frick et al.,

2003). Among the major causes of blindness in 2010, trachoma represented 5.2% in sub-

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Saharan Africa (Naidoo et al., 2014). An accurate quantitative estimate of the burden of

trachoma remains, however, challenging due to several factors, including scarce data

availability—which limits the ability to estimate accurately the number of people infected—

and an unresolved issue as to whether trichiasis should be considered as a disabling disease

sequela (Burton and Mabey, 2009). The economic impact of trachoma in terms of lost

productivity is estimated to range between US $2.9 and 5.3 billion annually, rising to US $8

billion if trichiasis is included in the estimate (WHO, 2015b).

Countries reported to have the highest prevalence of infection are located in East

Africa and the Sahel belt; however, trachoma is also prevalent in Southeast Asia, the Middle

East, Indian sub-continent and Latin America (Burton and Mabey, 2009), although the

distribution and prevalence of infection are far more heterogeneous in these regions in

comparison to sub-Saharan Africa. While trachoma was previously prevalent in Europe and

North America only one hundred years ago, improvements in sanitary and living conditions

resulted in the gradual disappearance of infection (Burton and Mabey, 2009).

Infection with C. trachomatis is spread through two primary routes. The first is direct

personal contact which could be direct hand contact with an infected individual or through

contact with clothing which has contacted infectious discharge (Burton and Mabey, 2009).

The second route involves eye-seeking flies (e.g. Musca sorbens) which have contacted the

discharge from an infected persons eyes or nose (Emerson et al., 2004). For transmission of

infection to be sustained it must be consistently transmitted from person to person. The

severity of disease experienced by an infected individual varies with age and hence their

duration of exposure to infection (Bailey et al., 1999; Grassly et al., 2008). Infection with C.

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trachomatis becomes shorter in duration and reduced in frequency as individuals age;

therefore, the highest burden of C. trachomatis is observed in young children (Bailey et al.,

1999; Grassly et al., 2008). Repeated infection with age (continuous exposure) leads to

conjunctival scarring, ultimately leading to trachomatous trichiasis (TT), corneal opacity (CO)

and blindness as mentioned above (Burton and Mabey, 2009; West et al., 1991). Several

epidemiological surveys have suggested that severe sequelae in the form of TT and CO

disproportionally affect women in comparison to men, as a result of women having a higher

exposure to the reservoir source of infection, which is reported to be young children

(Courtright and West, 2004; West et al., 1991).

A number of risk factors for trachoma transmission have been identified, including

i) secretions from the eye which other individuals may come into contact with, and which

may also attract flies which help to facilitate transmission (Emerson et al., 2004; Ngondi et

al., 2008); ii) overcrowding within the household, which increases the frequency of contact

between individuals potentially leading to more frequent infection events (Abdou et al.,

2007; Ngondi et al., 2008); iii) limited supplies of clean water resulting in infrequent face

washing, general poor hygiene practice, and lack of easy access to latrines, which can lead

to a buildup of faecal matter in the environment which attracts eye-seeking flies (Emerson

et al., 2004). Transmission intensity of trachoma within a community is classified according

to the prevalence of active disease in 1 – 9 year olds. Communities are considered

hyperendemic if the prevalence of active disease in this age group is > 20%, mesoendemic if

prevalence is >10% but <20%, and hypoendemic if prevalence is <10% (Wright and Taylor,

2005).

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1.2 Trachoma control and elimination

The WHO has advocated for the elimination of blinding trachoma by 2020, and the Global

Alliance for the Elimination of Trachoma by 2020 (GET 2020) was established to develop

criteria to help to achieve this goal. These criteria are: 1) to reduce prevalence of TF and TI

(active disease) to <5% in 1–9 year olds across all endemic communities; 2) to reduce the

population prevalence of TT to <1 per 1,000 persons; 3) to enhance the use of the Facial

cleanliness (F) and Environmental improvement (E) components of the SAFE strategy

(Surgery for trichiasis, Antibiotics to combat the infection, Facial cleanliness, and

Environmental improvement) (West, 2003). The GET 2020 goals were developed to

eliminate blinding trachoma by 2020, not completely eliminate infection in the population.

Within the SAFE framework, as the public health burden of trachoma is reduced, infection

will be controlled, but not completely eliminated (hereafter, therefore, any reference to

elimination refers to the elimination of blinding trachoma, unless otherwise specified). The

WHO endorses the implementation of the full SAFE strategy in order to control and treat

trachoma. As mentioned above this comprises of four key components, more specifically

described as: i) surgery in order to correct trichiasis; ii) mass distribution of azithromycin as

the antibiotic of choice used to treat and clear active infection in the community (topical

tetracycline is used in very young children), iii) promotion of facial cleanliness in order to

reduce transmission via eye discharge, and iv) environmental modifications to improve living

conditions, ensuring that the environment no longer helps to facilitate the transmission of

infection (this can be in principle achieved through a number of avenues, such as facilitating

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the provision of clean water, increasing access to well-designed latrines, helping to reduce

the population density of flies, and reducing overcrowding) (West, 2003).

The London Declaration on Neglected Tropical Diseases (NTDs) (Uniting to Combat

NTDs, 2012) has led to a renewed commitment to control and/or eliminate these morbidity-

causing diseases from some of the poorest countries in the world. In addition, it is expected

that the recently established Neglected Tropical Diseases Modelling Consortium

(http://www.ntdmodelling.org/) will help to facilitate the exchange and discussion of ideas

across a range of NTDs and will foster and enhance collaboration between different

mathematical modelling groups. This will help to address many urgent policy issues

concerning the control and elimination of NTDs that can only be answered through the use

of quantitative tools (Basáñez and Anderson, 2015). Models are ideally suited to answering

a wide range of questions relating to the possible impact of various interventions within

populations affected by NTDs, e.g. which interventions to deploy, to whom, how often and

for how long should they be administered.

1.3 The role of mechanistic and statistical models

The epidemiology and dynamics of trachoma infection arise from a complex set of

contributory factors, including the natural history of infection and disease, which is

governed by an individual’s time-varying immunological response to and clearance of

infection. Transmission of trachoma can be altered by the behaviour and social contact

patterns of people within the community. At an even greater scale, the climate and local

ecology, may affect the transmissibility of the causative bacteria of trachoma,

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C. trachomatis. Integrating these effects across several hierarchical scales is a challenge for

any infectious disease.

However, through careful determination of key features of the epidemiology of

infection, models can be formulated as time-dependent mathematical expressions and

solved computationally. These include, but are not limited to, discrete event, agent-based,

or differential equation-based simulations. Equally, a quantitative understanding of data

generating processes can be provided through the development of statistical models.

Statistical models can help to understand the relationship between an outcome of interest

and external variables which may be important within the system, and this can be done

through techniques such as linear or logistic regression. Moreover, epidemiological data

rarely captures observations at every point in the transmission or infection cycle, thus

statistical models such as hidden Markov Models can be used to help provide insights into

the dynamic infection process where certain states of the infection process are not

observed, but the observed epidemiological outcome is dependent on these states.

Mathematical and statistical models, which seek to incorporate key features of the

population biology, demography and ecological covariates (often referred to as mechanistic

models) remain among the only quantitative methods capable of performing this kind of

integration.

1.3.1 Deterministic and stochastic modelling

Mechanistic models of disease transmission are commonly divided into either deterministic

or stochastic. Put simply, results from a deterministic model are fully determined by the

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parameter values chosen and the initial conditions and, therefore, model outputs are the

same every time the model is run (for a given parameter set). In contrast, stochastic models

contain inherent randomness (demographic and/or parametric) and the same parameter

sets (which will have distributions rather than only nominal values) and initial conditions

used will result in a range of output results. Deterministic models describe the average

behaviour of a system and, therefore, the average of many stochastic realisations tends to

approximate the deterministic solution.

The deterministic approach may miss some aspects of disease transmission,

especially in the context of small populations and low infection prevalence, where stochastic

fade-out or take-off may play an important role. However, the simplification gained through

the use of deterministic models allows simpler fitting of models to data to estimate

parameters of interest, a more transparent representation of complex natural histories of

infection, along with realistic population demography. Irrespective of the model structure

used, mathematical models are unlikely to be informative unless they are fitted to or

informed by high quality baseline and follow up surveillance data. The decision to develop a

deterministic or a stochastic model should depend upon the question under investigation.

For example, if data from a small community were analysed and the possibility of

elimination was being explored, a stochastic model would likely be considered more

suitable. However, if one were analysing impacts of different interventions at a population

level, a deterministic model may be more appropriate.

1.3.2 Modelling infection and modelling disease

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The vast majority of data collected from control programmes within endemic communities

have been obtained through clinical diagnosis of active disease or the disease sequelae

(Jimenez et al., 2015). More recently, testing for active infection has been performed in

clinical field studies using polymerase chain reaction (PCR) methods to identify active

infection from conjunctival swabs. However, laboratory tests can suffer from cross-

contamination across numerous stages of the DNA amplification process and the presence

of inhibitors of DNA amplification within samples can also cause amplification problems

(Solomon et al., 2004). Additionally, the collection of individual-level PCR data within a

community is prohibitively expensive, limiting its wide-spread use in surveillance. However,

studies that have been able to collect data on active infection and active disease prevalence

highlight the complex relationship between active infection and disease, whereby

individuals can have detectable active disease but do not have a PCR detectable infection

(Solomon et al., 2004). Hence, active disease can persist much longer than infection (Grassly

et al., 2008; Harding-Esch et al., 2009). This highlights the need for modelling studies to

explicitly account for the period of infection and active disease separately in order to insure

the prevalence of active disease is not underestimated.

The first two GET 2020 goals relate to the specific outcomes of active disease.

Therefore in order to understand if the GET 2020 goals are going to be achieved in different

localities, models of C. trachomatis transmission must also include progression towards

disease sequelae.

1.4 Aims and objectives of this review

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In this review we report previously published mechanistic and statistical mathematical

models that have been developed to provide insight into the transmission, dynamics and

control of trachoma. We compare the different mathematical model structures that have

been published, whether they are stochastic or deterministic and the type of data the

models were fitted to. We consider the availability of data on infection and disease

prevalence, and the estimation of epidemiological parameters such as the basic

reproduction number of the infection, R0. We evaluate how models have been used to

assess the impact of different interventions, and lastly how such models can be used as

disease forecasting tools to help to understand how achievable the GET 2020 goals are. We

then move to a discussion about which of these published studies contain results (or useful

modelling frameworks) pertaining to the GET 2020 goals. Lastly, we address what questions

require further elucidation before critical trachoma control-related questions can be

answered by mathematical models, and provide a perspective on future modelling

directions.

2. Methods

We performed a review of the literature to address and explore the mechanistic and

statistical models of trachoma transmission and control that have been developed to date.

Our search was performed through PubMed on the 24th June, 2015 with no restriction on

the year of publication or language applied. We employed a simple set of broad search

terms pairing the term “trachoma” with the following key words: [model OR modeling OR

modelling], a second search using the keyword [mathematical] was also performed.

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Studies were eligible for inclusion in the literature review if they developed a

mechanistic transmission model or a statistical model which quantified or modelled the

impact of an intervention, through regression analysis or by fitting different statistical

distributions to surveillance data. Statistical models also eligible for inclusion were those

estimating epidemiological parameters and inferring the true dynamics of infection though

Markov models. All study types were eligible if they met these inclusion criteria. Articles

were selected for inclusion by firstly reviewing the full title and abstracts of all studies that

were identified in the initial review searches. Studies that did not meet the inclusion criteria

after this step were excluded from the analysis. The full texts of potentially relevant articles

were then independently examined by AP, and data extracted were independently verified

by MG. MG was consulted by AP on queries relating to the inclusion or exclusion of studies

analysed in the review.

Once a set of eligible articles was established, data from each article were extracted.

The data extracted were as follows: i) the type and structure of the mechanistic or statistical

model applied and/or developed in the study; ii) why the study was performed, and the

data that were used to inform the modelling analysis presented; iii) whether the study

population was classified as a hyper-, meso- or hypoendemic and iv) key findings from the

study and how they related to the existing GET 2020 goals (Table 1). We then assessed if

epidemiological parameters had been reported, and the values estimated or used in the

model were noted. These were: the transmission rate or transmission coefficient (commonly

known as the beta parameter), the age-specific duration of infection (or its reciprocal, the

recovery rate), and the basic reproduction number R0. If R0 was not explicitly calculated, we

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used data on the transmission rate (parameter beta) and the recovery rate (denoted as

parameter gamma in this review) to estimate a crude R0 (where R0 is defined as the ratio

between these latter two parameters) (Ray et al., 2009) (Table 2).

Table 1 approximately here

3. Results

3.1 Characteristics of identified studies

Our initial two searches yielded 172 publications, with 18 publications being repeated across

the two searches. Of the 154 remaining publications, 24 articles were deemed appropriate

after reviewing the title and abstracts of all unique publications. The full text of these

articles was obtained and assessed. After this second screening stage, 23 articles were

deemed to meet the review’s inclusion criteria (Table 1). Twenty of these publications

presented mechanistic transmission models and 4 presented statistical models.

Of the 20 articles identified as describing transmission dynamics of trachoma, 9 used

a deterministic framework (including 4 catalytic models) and 9 used stochastic models, and

1 used both frameworks. One of the statistical models used linear and logistic regression, 2

used a latent/hidden Markov model and 1 fitted different statistical distributions to

surveillance data. We identified 11 studies that attempted to estimate the force of infection

(FOI) (the per susceptible incidence rate), the transmission rate parameter and/or the

recovery rate from infection. While only 5 calculated R0 explicitly, it was possible to calculate

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an approximate value of R0 from the data presented in 2 other studies (Table 2). Only 5

studies incorporated any form of acquired immunity as a result of successive infections. We

identified only 1 study that used serological data to make inferences on historical patterns

of transmission. All 23 studies had conclusions that could provide insight into the

achievability of the GET 2020 goals within the endemic locality analysed. However, we only

identified 1 study that fitted the model to epidemiological data collected before, during and

after an intervention had been implemented.

Table 2 approximately here

3.2 Deterministic and stochastic models

Two main research groups were identified who have developed mechanistic models of

trachoma, one group based at the University of California San Francisco’s (UCSF) Francis

Proctor Foundation and the second at Imperial College London (ICL). The mechanistic

models developed by the UCSF group have largely been stochastic, although their earlier

work was deterministic (Lee et al., 2005; Lietman et al., 1999). In these studies a single state

variable, P, representing the overall prevalence of infection in the community (or in a single

constant sized age group, commonly 0-5 year olds) is modelled (Lee et al., 2005; Ray et al.,

2007). The hazard of infection (also referred to as the force of infection (FOI), commonly

denoted by parameter lambda) for those who are uninfected is proportional to the current

prevalence of infection in the population, which is multiplied by a composite parameter

containing the contact rate and the probability of transmission upon contact with an

15

infected person; this is often referred to as the transmission rate parameter beta mentioned

above. Many of the group’s studies set up a stochastic equation which permits determining

analytically the equilibrium distribution of villages with a given prevalence level, or

determining numerically the likely trajectory of the prevalence of infection for a given village

over time. These stochastic models capture and demonstrate the variability in prevalence

trajectories over time, given close baseline values and (antibiotic) treatment coverage levels

within small communities. In the context of the studies, designed by the UCSF group, these

small communities are often villages in Ethiopia. The prevalence levels of infection,

measured by the group’s field studies, can be represented by the stochastic model-

generated trajectories, with the mean prevalence calculated across several villages

appearing similar to a deterministic trajectory.

The mechanistic models developed at ICL have used primarily deterministic

frameworks (Gambhir et al., 2007; Gambhir et al., 2009; Gambhir et al., 2010), and have

focused on developing age-structured models which capture the age-specific profiles of

infection observed within communities of different endemicities. A backbone of these

models is a ladder of susceptible–infected–susceptible (SIS) infection (Figure 1a) to account

for key epidemiological features that change with age with each successive infection (Figure

1b). However, studies investigating the relative contribution of household and community

transmission lend themselves to be more naturally simulated stochastically (Figure 1c)

(Blake et al., 2009; Blake et al., 2010). We also identified a number of catalytic models

reported in the literature, the use of the catalytic model for epidemiological purposes was

initially presented by (Muench., 1934). These catalytic models explore the change in age-

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specific prevalence of infection, here the force of infection (FOI) can be estimated in a

population from age-specific disease prevalence data, or serological data. In these models

individuals experience an FOI as susceptible, they then progress into the diseased class

where they will stay until they recover or die (Figure 1 d).

3.3 Data sets used and model fitting to data

The availability and collection of routine high quality baseline (prior to intervention),

monitoring and evaluation (during the control programme), and (post-intervention)

surveillance infection data to inform mathematical modelling studies which aim to help and

advice control programmes has been extremely limited. Consequently, the data analysed by

modelling groups in the studies identified here have either been collected by the modelling

groups themselves (Lietman et al., 2011; Liu et al., 2013; Liu et al., 2014; Ray et al., 2007), or

through the careful development and management of collaborations with other research

groups who have conducted field studies (Blake et al., 2009; Gambhir et al., 2009; Gambhir

et al., 2010). Given the large range of settings around the world where trachoma is endemic

(with respect to climatic, ecological and social differences), it does not seem appropriate

that models parameterized primarily with data from Africa be used to make accurate and

informative projections about the transmission dynamics of infection occurring in other

endemic regions such as Southeast Asia or Latin America (where infection is also endemic)

(Figure 2). We identified 8 countries for which any modelling work had been conducted.

Datasets collected from Tanzania have been used in eleven studies analysed here. Datasets

from The Gambia have been used in six studies, from Ethiopia in 5 studies, Taiwan twice (no

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longer an endemic region), Egypt, Tunisia (no longer an endemic region), Malawi and

Australia and India just once each. However, the same dataset has repeatedly been used

across a number of studies. Data from Tanzania has come from 4 key regions: Morogoro,

Dodoma, Singida and Arusha. In The Gambia data has come from Jali, Berenday and Upper

Saloum. In Ethiopia, datasets have been analysed from the regions of Amhara and Gurage in

Ethiopia. Therefore, given the wide geographic distribution of trachoma (Figure 2) and the

considerable within-country heterogeneity in transmission http://www.trachomaatlas.org/), a

greater number of modelling studies should be looking to understand the dynamics of

infection at a more global scale, along with trying to gain insight into the spatial

heterogeneity in transmission that exists within the same country . However, current

progress remains limited given the scarce availability of data from regions outside of a few

key transmission areas, primarily in sub-Saharan Africa, where research (rather than

routine) studies have been conducted. Moreover, modelling is often the final activity

performed in such a partnership, and constitutes a secondary analysis of the data, following

a primary analysis that includes the evaluation of risk factors for disease, and a pre- and

post-intervention description of infection and disease prevalence. This has meant that

modelling and quantitative analysis have not been systematically used as an integrated part

of trachoma control programmes.

The datasets that have primarily been used for model calibration and model-based

analysis have come from long-term epidemiological studies in Upper Saloum district in The

Gambia (Burton et al., 2005), Rombo district in Tanzania (Solomon et al., 2003; Solomon et

al., 2004), Kongwa district in Tanzania (Burton et al., 2005), and Gurage zone of Ethiopia

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(Lietman et al., 2011; Lietman et al., 2015; Liu et al., 2013; Liu et al., 2014; Ray et al., 2007;

Ray et al., 2009). These data include longitudinal measurements of infection, clinical disease,

and associated risk factors. As most of these studies were begun at baselines where control

interventions had not yet been implemented, an ecological ‘steady-state’ (or endemic

equilibrium) constitutes an appropriate initial condition for modelling analyses.

Nevertheless, the vast majority of articles identified in this review estimate parameters

explicitly from a very small number of data sources. Studies for which infection, active

disease and disease sequelae status were all collected should be collated and shared in the

future in order to allow models to be simultaneously fitted to all of these (infection and

morbidity) data sources. In this study we only identified one article that explicitly attempted

to estimate the age-specific duration of active disease (Grassly et al., 2008) through a

hidden Markov model.

We identified one statistical study that used a substantial amount of programmatic

clinical disease data, from a wide time and geographical range collected by the International

Trachoma Initiative (ITI) (Jimenez et al., 2015). This large dataset included data on active

infection (through PCR data), prevalence data on active trachoma disease (TF or TF/TI) and

TT (Table 1). These data were used to investigate the conditions under which control

programmes have been successful. The importance of this study lies not only in its analysis

of a large dataset to draw its conclusions, but also in its presentation of these conclusions as

a ‘decision tree’, which is conceptually similar to the way in which the WHO presents its

recommendations for disease control policy.

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Mathematical models that are successfully fitted to epidemiological data (be it PCR

(infection) prevalence data or data on active disease prevalence), endeavour to estimate

just a few key epidemiological parameters. These are most commonly the transmission rate

(β), the basic reproduction number (R0), and the duration of an individual’s infectious period

(the reciprocal of the recovery rate, gamma). Whether the methodology applied to estimate

these parameters is approached through Maximum Likelihood Estimation (MLE) (Blake et

al., 2009; Gambhir et al., 2009) or a combination of MLE and Markov Chain Monte Carlo

(MCMC) methods (Lietman et al., 2011), the aim of these studies remains the same, which

is, to understand the intensity of transmission and the amount of effort required in order to

control infection.

3.4 Transmission intensity and the basic reproduction number

3.4.1 Estimating the force of infection

Intensity of transmission and hence the FOI experienced by a community can be estimated

through the careful collection of data on prevalence or through serological data in the form

of seroprevalence age profiles (Hens et al., 2012).

A study in the former category was reported by Sundaresan and Assad (1973) using

data from Taiwan collected in the 1960s. These authors applied deterministic FOI (catalytic)

modelling to provide insight into the changes in age-specific prevalence of trachoma over

time, and infer past patterns of transmission in the country. Using survey data from 1960–

1961—before the institution of a control, school-based programme with tetracycline

treatment (Assad et al., 1966)—trachoma prevalence increased with age in a fashion

compatible with the operation of a constant FOI (42/1,000 per year). However, using survey

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data from 1968–1969 revealed that the 0–9 year olds had experienced a substantial

decrease in the FOI (11/1,000 per year) (Sundaresan and Assaad, 1973).

The use of serological data to gain insight into the dynamics of transmission has

been a valuable tool across a number of infectious diseases (Badu et al., 2015; Hens et al.,

2010; Mladonicky et al., 2009; Wong et al., 2014; Williams and Keystone, 2012; Yildiz Zeyrek

et al., 2011). Analysis of serological data has also been particularly useful in post-elimination

or low transmission settings (Bousema et al., 2010; Corran et al., 2007; Oguttu et al., 2014).

However, our review only identified one article (a study conducted in Kongwa district,

Tanzania) that used a (reversible catalytic) model fitted to serological data to understand

how interventions may affect the serological status of a community (Figure 1d) (Martin et

al., 2015) (Table 1), and how these data can be used to shed light into the rate of acquisition

of infection and antibodies to infection. Reversible catalytic models (as illustrated by the

first two compartments of Figure 1 d) model seroprevalence in the population over time.

These models have two key parameters, the first is the seroconversion rate λ (Figure 1d),

the second is the seroreversion rate, denoted δ in Figure 1 d, which models the rate at

which immunity in the population is lost, hence the rate at which people serorevert. It is

therefore akin to the SIS model structure shown in Figure 1 a, however in this instance the

acquisition and loss of antibodies are modelled instead of the process of infection and

recovery. Martin et al. (Martin et al., 2015) were able to identify a change in the intensity of

transmission from serological data between 10 and 15 years prior, which was shown to

coincide with a mass antibiotic administration programme that had run between 2000 and

2002. While Martin et al. (Martin et al., 2015) were able to estimate a seroconversion rate,

21

they were not able to estimate a seroreversion rate as they did not identify any individuals

in the dataset who seroreverted. As with other infectious diseases, a mounting evidence

base for serological testing, that is both sensitive and specific to trachoma infection, has the

potential to be used as a rich new data source for understanding the changing patterns of

transmission dynamics of trachoma (Martin et al., 2015).

3.4.2 Estimating the basic reproduction ratio

The most commonly-used parameter to summarize the transmission potential of an

infectious disease is the basic reproduction ratio or number, R0 (the average number of

secondary infectious cases that arise from an index case in a wholly susceptible population).

R0 was calculated (by the authors of the papers) in only 4 of the trachoma modelling studies

identified in this review, despite the fact that it could have been estimated in several of the

remaining models as the ratio of the transmission coefficient and the recovery rate from

infection (beta/gamma). This has been done by us and the results are presented in Table 2.

For the more complicated published models, involving age-structure and functional forms

for an individual’s acquired immunity and infectivity, the calculation of R0 is more involved

and can most easily be performed using the Next Generation Matrix method (Diekmann et

al., 2010). The acquisition and waning of immunity complicates the calculation of the

reproduction number, since R0’s definition refers to the beginning of an epidemic, i.e. in a

fully susceptible population (hence individuals have no prior immunity to infection). In these

circumstances, while the calculation process remains essentially the same, the parameter

22

that is being calculated is correctly referred to as the effective reproduction number (Re); in

this review we identified only one study that estimated Re (Liu et al., 2014).

As evidenced by the total number of studies that explicitly calculated R0 in this

review, analysis and calculation of R0 in the trachoma modelling community has remained

very limited. However, recent work by Liu et al. (Liu et al., 2013) used a mechanistic model

to perform a statistical analysis of infection control and rebound data from several Ethiopian

villages to determine whether there was a change in the value of the reproduction number

following each round of mass antibiotic administration. Changes in the reproduction

number over time could potentially be caused by the decreasing efficacy of the antibiotic

drug over time, or the loss of short-term immunity in the population, as the stimulus of

exposure to C. trachomatis diminishes. Liu et al. (Liu et al., 2013) found no statistically

significant change in the reproduction number in the Ethiopian data set analysed and

therefore, these authors concluded that changes in drug efficacy or in immunity were not

operating at an appreciable level in the epidemiological settings evaluated in their study.

Comparing across the small number of studies that have attempted to calculate a

value of R0 or Re (or published values from which estimates could be obtained), we observed

limited heterogeneity in the range of estimates from communities classified as having the

same level of endemicity (Table 2). For example, Ray et al. (Ray et al., 2009) estimated R0 to

be 3.14 (95% CI, 2.51–3.77) for 16 hyperendemic communities in Ethiopia; in 2013 Liu et al.

(Liu et al., 2013) estimated an overall R0 of 1.39 (and yearly R0 values of 1.40, 1.38, 1.35)

across 32 communities of Tanzania; Ray et al. (Ray et al., 2007) provided values of beta

(0.047 per week) and gamma (0.017 per week) that yield a figure of 2.59 for the 16 villages

23

mentioned above (which are located in the Gurage region of southern Ethiopia). We

estimated Re using the next generation matrix method (unpublished estimate) using a

previously published model and best fit parameters from another hyperendemic area in

Tanzania, and yielded a value of 3.2 (Gambhir et al., 2009), an estimate similar to that of Ray

et al. (Ray et al., 2009). Therefore, there is some consistency in the literature that values of

R0, even within high transmission settings are likely to be less than 5. These estimates have

been derived using different methodological approaches, suggesting that the estimate is not

specific to the methodology applied. However, it is worth noting that transmission of

trachoma in some regions is reported to be seasonal, and that this source of heterogeneity

has not been incorporated into any of the R0 estimates identified in this review. Therefore,

current estimates of R0 may be pertinent to the particular times the studies were conducted.

Very few studies have collected prevalence data of active trachoma and C. trachomatis

infection at multiple time points throughout consecutive years limiting the inference that

can be made on the role of seasonality on transmission.

24

3.5 Acquired immunity: recovery rate and infectivity

25

Immunity to trachoma with repeated infection is reported to decrease the duration of an

infected individual’s infectious period (Gambhir et al., 2009; Gambhir et al., 2010), and also

reduce the bacterial load harboured by an individual (West et al., 2005). However, in

addition to whether any acquired immunity affecting infectivity and/or recovery rates was

incorporated into the models reviewed here, we observed marked heterogeneity in the

rates of recovery from infection reported and used in the modelling studies analysed. The

models evaluated in this review that were published by the UCSF group did not, in general,

include the development of acquired immunity, with the exception of one study in which

the model assumed that older age groups developed partial immunity to (re)infection either

because of decreased susceptibility to infection, or because of clearing infection faster than

younger individuals (Lietman et al., 1999). In general, these models assume a single value

for the rate of recovery from infection, approximately equivalent to a mean duration of

infection of 6 months although there is some heterogeneity between their studies; in the

study by Lietman et al. (Lietman et al., 1999) duration of infection ranges from 9 to 17

weeks. This is a somewhat slower rate of recovery than that considered by the models of

the ICL group, which suggested that the mean duration of infection/infectivity after an

individual has experienced multiple prior infections was approximately 2.8 months—but

duration of infection for the first episode was 15 months—(Gambhir et al., 2009). Additional

work by the ICL group estimated the duration of infection to be 16–17 weeks (c. 4 months)

using frequent follow-up data from The Gambia (Grassly et al., 2008), which was

subsequently used in a number of other studies (Blake et al., 2009; Gambhir et al., 2010).

However, the assumed duration of infectivity can have substantial implications for the

26

estimation of the feasibility of elimination of infection and the estimation of the

transmission rate β. For models that assume a longer duration of infection, the estimated

value of β is likely to be lower than for those assuming a shorter duration (although both

types of model would yield the same value of R0). From the perspective of trachoma control,

a lower value of β may suggest that the effort required to eliminate infection through

transmission reduction measures is less than that needed when a shorter infectious period

is assumed. However, the assumption of a longer infectious period would increase the

potential for infection to persist within a community, especially if movement of infected

individuals between villages is considered, as this could result in the re-introduction of

infection.

The models of the ICL group explicitly account for the development of immunity to

infection with an increasing number of infections experienced (Gambhir et al., 2009;

Gambhir et al., 2010). Acquired immunity to infection is modelled as a function of the

number of prior infections, i which is described by an exponentially saturating rise in the

recovery rate (or fall in the infectivity). These functions, which have three parameters, are

not the only choice of functional form accounting for acquired immunity; for example, a

logistic function or a Hill function which allow for saturating effects may be more

appropriate (Regoes et al., 2004). However, the available epidemiological data are at

present unlikely to permit distinguishing between these different functional forms. The

importance of this process and its implication for long-term transmission patterns remain

poorly understood.

27

3.6 Infection and active disease, modelling of disease sequelae

Most infectious disease models are based on the idea that contact between

individuals leads to the transmission of a pathogen from one individual to another with a

given probability; they are, therefore, infection- and not disease-based. Surveillance for

trachoma control is based upon disease and therefore there is a need to link transmission

models to active trachoma and the later disease sequelae.

Due to the indirect relationship between active disease in trachoma and C.

trachomatis infection, PCR data (rather than data on active disease) have most often been

used to inform the vast majority of the models identified in this review. Trachoma models

have mostly been constructed as infection models, as demonstrated by the large number of

studies identified that have used the classic SIS model structure (Figure 1 a) (also commonly

used to model genital chlamydia infection). Notwithstanding the ubiquity of the SIS

backbone, we only identified a small number of modelling studies which explicitly included

age structure across the host population (Blake et al., 2010; Gambhir et al., 2009; Gambhir

et al., 2010; Grassly et al., 2008), and hence would have the ability to assess the impact of

infection (and disease) on an individual throughout life, this represents a critical gap in the

current literature. Whereas the infectious load and duration of active infection decreases

with age, repeated infection throughout an individual’s life results in the serious morbidities

associated with trachoma infection. This is particularly important as the first two GET 2020

goals seek to understand the impact of the infection dynamics on the long-term patterns of

active disease and the elimination of blinding trachoma.

28

The successful economic evaluation of the impact of disease and disease-associated

morbidities through trachoma infection relies on accurately quantifying the burden of

disease (Lee et al., 2015). However, the development of mathematical models for trachoma

has remained primarily focused on the use of the SIS model structure, which does not lend

itself to the analysis and understanding of the long-term implications of numerous active

disease episodes with age. This represents a critical gap in the literature. However, we

identified 3 studies which used the ‘force of infection’ (FOI) modelling approach (Assaad and

Maxwell-Lyons, 1966; Parthasarathy, 1967; Sundaresan and Assaad, 1973) to describe age

profiles of total trachoma cases (simple catalytic model, with constant FOI) and of active

disease (two-stage catalytic model) in Taiwan before the institution of control measures in

the early 1960s. In these models individuals become infected and clinically diseased

according to an FOI (which was estimated to be 0.042 year–1); this translated into a

prevalence of trachoma that increased monotonically with age. By contrast, the prevalence

of active disease showed a humped pattern, reaching its maximum at 15–20 years of age

and decreasing afterwards; in this case the two-stage catalytic model estimated a rate of

acquisition and of loss of active disease of 0.050 year–1 and 0.072 year–1, respectively.

Through these models it was possible to gain insight into the dynamic nature of the burden

of active disease with age prior to the implementation of an intervention.

Models which are intended to be used in close conjunction with control programmes

should, therefore, include active disease and disease sequelae components if they are to be

truly useful as tools to support decision-making in the context of the GET 2020 goals. While

infection and active disease are the proximate causes of scarring and the resulting sequelae,

29

the timescales associated with the development of scarring, trichiasis, corneal opacity and

blindness are different from one another, and should be accounted for when forecasting for

control programmes aiming to achieve the GET 2020 goals (Gambhir et al., 2009; Gambhir et

al., 2010; Gambhir et al., 2015; Shattock et al., 2015). To date, very few models have done

so. Gambhir et al. (Gambhir et al., 2010) illustrated a first attempt at adding active disease

to a simple age-structured infection-based model (Figure 3). The model used a series of

partial differential equations (PDEs) to explore the impact of treatment on active disease,

having previously fitted the model to disease sequelae data. The authors identified that in

their model the prevalence of active disease was always higher than the prevalence of

infection, and that following mass antibiotic treatment the decline in prevalence of active

disease lagged behind the immediate drop in infection prevalence (Gambhir et al., 2010).

The mechanistic model of Shattock et al. (Shattock et al., 2015) took this concept further by

developing a stochastic agent-based model to create a complex representation of the

natural history of infection (Figure 1e) and disease for every individual within a defined

community, and by then fitting this model to active disease data from multiple Australian

Aboriginal communities. Therefore, models which can be fitted to active disease data are

needed if we are to understand whether the GET 2020 goals are being achieved. Modelling

analysis of additional active disease datasets is a pressing need in order to disentangle the

complex relationship between the dynamics of infection across different transmission

settings and the prevalence of active disease/disease sequelae, and to help the public health

community to understand the feasibility of achieving the GET 2020 goals.

30

Here we suggest 5 crucial pieces of data that could be collected and that would help

to ensure more accurate parameterization of subsequent models of trachoma infection and

disease: 1) collection of data that help to inform understanding of the age-specific duration

of active disease (TI/TF) following infection with C. trachomatis; 2) data on the duration of

overlap between active infection and active disease by age; 3) data on the age-specific

duration of infection alone; 4) data on how the bacterial load harboured with age varies

across different transmission settings; 5) data on how immunity to trachoma wanes in the

absence of frequent exposure.

3.7 Simulation of interventions, forecasting infection and disease, and

analysis of their cost effectiveness

Mechanistic modelling in the context of control interventions was explored in 13 of the 23

articles identified in this review, all of which examined the A (antibiotics) component of the

SAFE strategy. Lietman et al. (Lietman et al., 1999) showed that annual MDA was not

sufficient to eliminate infectious trachoma from hyperendemic communities and that the

frequency of treatment required depends on the initial doubling time of a re-introduced

epidemic; the latter does not decrease as prevalence of infection decreases during a

treatment programme. In order for the doubling time of a re-introduced epidemic to be

reduced, changes in the community must occur, such as the implementation of hygiene

measures (F and E components), that can help to reduce the overall level of transmission.

This study also highlighted the need for biannual mass antibiotic treatment in hyperendemic

communities. Gambhir et al. (Gambhir et al., 2010) demonstrated a similar finding. Ray et al.

31

(Ray et al., 2007) investigated the impact of annual and biannual rounds of mass antibiotic

treatment and showed that 5 years of biannual treatment could be sufficient to eliminate

infection in 95% of the hyperendemic Ethiopian villages simulated in the study. In a follow

up paper, Ray et al. (Ray et al., 2009) used the same model—fitted to data from three

different transmission settings: Ethiopian (hyperendemic), Tanzanian (mesoendemic), and

Gambian (hypoendemic)—to demonstrate that an adjusted mass treatment strategy, in

which mass antibiotic administration was withheld from specific communities whose

infection prevalence levels fell below 5% (in children aged 1 – 5 years), had a comparable

impact to that of the WHO-endorsed strategy, and saved a considerable number of

antibiotic doses. However, the logistics and costs associated with testing infection at the

community level instead of the district level (outside of specific trial, research settings) can

be both expensive and challenging, making the practical implications of these findings

difficult to implement on a much wider, routine scale. To overcome these difficulties, Ray et

al. (2009) suggested that pooled PCR sampling for entire communities could be performed,

leading to substantial cost savings. However, a specific cost breakdown for the

implementation of such an approach would be useful for understanding whether it would

be feasible from a programmatic perspective and for modelling its cost effectiveness.

An important factor which can impact the effectiveness of antibiotic treatment is the

level of coverage that can be achieved within a community. If the level of coverage is poor

few people will get treated, therefore the impact on transmission going to be less than if the

level of coverage achieved was high. Within a trial setting, where much of the

epidemiological data about the success of MDA is collected the level of coverage achieved

32

can be extremely high (>90%) (Lakew et al., 2009). However, outside of a trial setting the

level of coverage achieved is likely to be much lower, suggesting that the findings identified

in trials may not be fully reflective of the outcomes observed during routine rounds of MDA.

We did not identify any studies that assessed the sensitivity of their findings to the level of

MDA coverage achieved. This represents an important gap in the modelling literature that

needs to be explored more thoroughly in future studies if we are to make realistic forecasts

about the prospective impact of MDA.

One of the first questions public health workers ask disease modellers relates to the

forecasting of future disease levels. However, the majority of trachoma modelling work has

been conducted to improve the understanding of trachoma epidemiology, and not

specifically to forecast disease levels. Nevertheless, a well-parameterised mechanistic or

statistical model is often capable of being run forward in time, forecasting disease and

uncertainty bounds. Indeed, we identified 3 published studies that have been formulated in

order to make forecasts in the context of control interventions; these were the studies by

Gambhir et al. (Gambhir et al., 2015); Ray et al. (Ray et al., 2009) and Shattock et al.

(Shattock et al., 2015). Each of these 3 studies forecasts the prevalence of infection and/or

disease following various interventions (see section 3.7 Simulation of interventions and

analysis of their cost effectiveness). Shattock et al. (Shattock et al., 2015) fitted their

individual-based model to clinical disease prevalence surveillance data from 67 Australian

Aboriginal communities, and then investigated the possible future impact of different

treatment combinations on the long-term prevalence of trachoma infection. The authors

identified that under the current intervention strategies, control of infection within these

33

communities would not be achieved by 2020. Ray et al. (Ray et al., 2009) used a stochastic

differential equation model to evaluate an antibiotic-sparing strategy that halted treatment

when community infection prevalence dropped below 5%, following the WHO

recommended 3 annual rounds of antibiotic administration. This was shown to be effective

in meso and hypoendemic communities (supported with evidence from trial data from

Tanzania (Solomon et al., 2008)). However, the feasibility of lowering the prevalence of

infection in hyperendemic communities was much lower. Gambhir et al. (Gambhir et al.,

2015) performed forecasts for a variety of treatment interventions within the SAFE strategy,

individually and in concert with one another, with the specific aim of determining whether

the GET 2020 goals could be met within the next 5, 10 or 20 years (as of 2015). These

studies highlight how modelling can be used to provide information and insightful

projections of public health importance in the context of the GET 2020 goals.

In a modified approach to the classic SIS models previously discussed, Blake et al.

(Blake et al., 2010) developed a model that incorporated both household and community

transmission which was used to explore cost-effective means of distributing antibiotics,

whereby treatment was tied to clinical disease diagnosis at the household level. The

modelling analysis by Blake et al. (Blake et al., 2010) is the only study that features a health

economics component, an area that is clearly in need of attention as rationales for budgets

to address blinding disease elimination are made in the future. Research groups working on

several of the other NTDs have integrated health economics evaluations of control

interventions, largely pharmaceutical, into mechanistic modelling frameworks resulting in

studies that can immediately feed into policy (e.g. onchocerciasis (Turner et al., 2014;

34

Turner et al., 2015), lymphatic filariasis (Goldman et al., 2007), soil-transmitted

helminthiases (Turner et al., 2015), and schistosomiasis (Brooker et al., 2008; Guyatt et al.,

1994)). For a review outlining the use of mathematical modelling in economic evaluations of

interventions against the NTDs included in the London Declaration see Turner et al. (Turner

et al., 2014), and for a review of economic evaluation approaches and studies for the NTDs

see Lee et al. (Lee et al, 2015). Such approaches should also be taken forward in trachoma.

In principle, the results of the statistical modelling paper by Jimenez et al. (Jimenez

et al., 2015) could be used to understand the effectiveness of control interventions for a

variety of trachoma-endemic settings, whose previous intervention history varies from none

to the implementation of the full WHO recommended SAFE strategy over time. The

drawbacks of their statistical approach are that it only allows for a small number of location-

specific covariates to be defined for each community, and that while the results are often

intuitive (Table 1), the model is expressed as a set of correlations, without explicitly

accounting for the biological and epidemiological mechanisms underlying their community

classifications.

The majority of the modelling work identified in this review has sought to

understand and project the impact of antibiotic administration, whether in the modality of

mass treatment or through assessing the impact of targeted treatment strategies to only

those who present with active infection, or specific age groups (Blake et al., 2009; Gambhir

et al., 2010; Lakew et al., 2009; Lietman et al., 2011; Liu et al., 2014; Ray et al., 2007; Ray et

al., 2009).

35

However, antibiotics represent only one arm of the SAFE strategy. As such, there is a

pressing need for research to determine how best to incorporate non-pharmaceutical

intervention (NPI) into mathematical models of trachoma. In this review we identified only

one study that explicitly assessed the impact of both MDA and NPIs within communities

(Shattock et al., 2015). Indeed, the third GET 2020 goal states that the F and E components

of the SAFE strategy should be enhanced. However, accurate quantification of the impact of

these interventions in helping to reduce trachoma transmission and incidence remains

limited and poorly understood, making it difficult to model accurately their potential impact.

Ejere et al. (Ejere et al., 2012) conducted a review of face washing promotion for the

prevention of active trachoma and concluded that although there is some evidence that

face washing combined with topical tetracycline can be effective in reducing severe

trachoma and increasing the prevalence of clean faces, face washing alone or in

combination with topical tetracycline did not significantly reduce active trachoma. Rabiu et

al. (Rabiu et al., 2012) performed a review of environmental interventions for preventing

active trachoma and concluded that insecticides against the mechanical fly carriers may be

effective in reducing trachoma but provision of latrines as a fly control measure did not

significantly reduced trachoma transmission. Generally there is a dearth of data to

determine the effectiveness of all aspects of environmental sanitation in the control of

trachoma.

Currently, the best available resource for understanding the possible impact of NPIs

on trachoma and incorporating these NPIs into trachoma models is the meta-analysis

presented by Stocks et al. (Stocks et al., 2014). This study collated epidemiological evidence

36

for each of the components of water, sanitation, and hygiene (WASH) upon active trachoma

and infection with C. trachomatis. The Odds Ratios (OR) for each WASH component

provided by this article could be translated into modified parameter values to be

incorporated into appropriately defined mechanistic models; many interventions would

essentially alter the reproduction number by an amount directly calculable from the

relevant OR (generally by reducing the value of the reproduction number in a linear

manner).

4. Discussion

4.1 Using modelling to determine the feasibility of the GET 2020 goals

Studies focusing on the epidemiological modelling of trachoma have been steadily published

over the past 40 years. Collectively, they provide a considerable amount of accumulated

insight pertaining to the GET 2020 goals. The World Health Assembly passed resolution

51.11 in the year 1998 outlining the intention to end trachoma as a public health problem.

These goals included the global elimination of blinding trachoma by the year 2020

(GET 2020) (WHO, 2003). However, there has been limited involvement of modellers to help

to understand if and whether these goals are being/will be achieved within the proposed

timeframes.

The GET 2020 annual meeting is organized by the WHO and has taken place since

1997. Prior to the main meeting, a Trachoma Scientific Informal Workshop (TSIW) is held in

which the latest scientific results pertaining to GET 2020 are shared. The results shared by

this group comprise, for example, data from intervention trials of azithromycin antibiotic

distribution in a variety of trachoma-endemic settings (primarily in The Gambia, Tanzania,

37

Ethopia, and more recently Niger (Cromwell., 2014) and Guinea Bissau (Last et al., 2014)),

and rates of success, reversion, and risk factors associated with surgery for trachomatous

trichiasis, among others (WHO, 2015). However, it is only recently that modelling is being

viewed as a tool to help inform policy and infection control strategies (see e.g. WHO 2015).

The vast majority of modelling studies identified in this review have not explicitly

referred to the GET 2020 goals. However, they all contain findings that pertain to the goals

(Table 1). Therefore, despite the high relevance of many of these articles to the questions

posed and goals proposed by GET 2020, modelling groups and their resulting studies have

largely failed to be integrated into the discussions leading to the development of control

programme policy. The body of model-based work that has been produced for trachoma is

not significantly different to that which has been published for the other NTDs. However,

the failure to integrate modelling into understanding the feasibility of achieving the

GET 2020 goals across a range of endemic settings may be due to the fact that trachoma has

previously been perceived as controllable and that the current intervention strategies are

working (House et al., 2007). As such, it may be felt that modelling studies tend only to

confirm intuition or are only taken into account as part of the decision-support apparatus of

public health workers when it is deemed that current interventions are not working.

As described, a wide range of models have been developed to explore a multitude of

hypotheses. However, it could be suggested that many studies seek not only to fit models to

data to support or refute a hypothesis, but also aim to develop and apply innovative

methodologies. This has potentially led to the publication of a wide range of studies that

from a programmatic perspective may all appear quite different, leading to confusion in the

38

trachoma community. However, from the modelling perspective they are still seeking to

understand the same underlying processes. This in itself may be leading to a barrier

between modellers and those who work in the field.

4.2 Conclusions

Having assessed the modelling literature, we outline three key gaps that future modelling

work should address in order to help to understand if and where the GET 2020 goals can be

achieved. First, we would suggest that modellers work to develop mathematical models that

explicitly include an active disease component which accounts for the fact that even if an

individual does not have an active, PCR-detectable infection, they may still have active

disease. Mathematical models that are fitted to infection and active disease data and

validated with baseline and follow-up, longitudinal active disease data will be valuable for

forecasting purposes. Second, we would encourage that a better quantitative understanding

of the impact of the F and E interventions be developed; this will allow NPIs to be included

more accurately into mathematical models, facilitating the long-term impact of these

interventions to be explored more thoroughly. Finally, we would suggest that health

economic analysis be integrated into scenario analysis, as not only is the understanding of

the feasibility of the GET 2020 goals vital, but so is developing an understanding of the

financial implications of doing so.

Competing interests MG, MGB and IMB declare in accordance with the ICMJE conflict of

interest form that 7 of the articles identified and evaluated in this review articles have been

authored or co-authored by them. AP declares no competing interests.

39

Authors’ contributions

AP and MG designed the study and prepared the first draft. IB and MGB critically review the

draft and contributed with intellectual input. All authors contributed to the writing of the

final version of the manuscript and approved the final, submitted version.

Acknowledgments

AP, MGB and MG gratefully acknowledge funding of the NTD Modelling Consortium by the

Bill and Melinda Gates Foundation in partnership with the Task Force for Global Health. The

views, opinions, assumptions or any other information set out in this article are solely those

of the authors. MG also acknowledges funding from the Australian NHMRC and Monash

University.

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Figure legends

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Figure 1. Diagrammatic overview of the 4 key model structures and state variables that have

been used for modelling trachoma transmission. Here S represents an individual or

individuals who are susceptible to infection and I represents those who are infected with

trachoma. (a) Classic SIS model structure; individuals move into the infected compartment

at a rateλ (the force of infection), and recover at a rate γ (independent of the number of

previous infections), returning to the S compartment. (b) SIS ladder of infection model

(Gambhir et al., 2007); this framework tracks the number of infections (i) that individuals

experience throughout their lifetime as they age. They experience a force of infection

lambda λ λ and move into the I state; however, they recover at a rate γi dependent on the

number of previous infections they have had and move to state Si. Equally, the infectivity of

individuals decreases with each infection experienced. (c) Household model (Blake et al.,

2009; Blake et al., 2010); each oval represents either a household or a community;

transmission of infection is modelled within each household or community as in (a) with

local force of infection λL ; however, each community or household also provides and

experiences a (global) force of infection, λG from all other households or communities). (d)

Catalytic model (Assaad and Maxwell-Lyons, 1966; Parthasarathy, 1967; Sundareasn and

Assaad, 1973; Martin et al., 2015); individuals experience a force of infection (or

seroconversion rate), λ , and move into the infected (seropositive), or diseased state;

however, once they are classified as such they do not serorevert or recover. In the two-

stage catalytic model (Assaad and Maxwell-Lyons, 1968), individual’s progress from S state

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to present with active disease; individuals leave the active disease compartment (and

progress to other disease sequelae states). (E) An extension of the classic SIS model

structure, which explicitly models individuals in the disease state and after a certain period

of recovery allows them to be re-infected while they are still in the partially diseased state.

Figure 2. A map of the global distribution of trachoma endemic communities and those

currently under surveillance. Red indicates countries that are classified as endemic by the

WHO, and yellow indicates those currently under surveillance. Grey dots show a country

where a transmission model of trachoma has been fitted to data from that country,

although Taiwan and Tunisia are no longer classified as endemic regions. The size of the dots

is not proportional to the number of studies. However the total number of datasets

collected and used to inform modelling studies is not equal across all countries. Data

collected from Tanzania has been used in 11 modelling studies identified, data from The

Gambia has been used 6 times in the studies analysed here, data from Ethiopia has been

used 5 times, data from Taiwan has been used twice and data from Egypt, Tunisia, Malawi,

India and Australia have all been used once. Data on endemicity was inferred from

http://apps.who.int/neglected_diseases/ntddata/trachoma/trachoma.html .

Figure 3. Flow diagram of the modelling study that developed the ladder of infection model

(Figure 1b) in order to track and model progress to disease sequelae (Gambhir et al., 2009).

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Progression into TS (trachomatous scarring) and TT (trachomatous trichiasis) is determined

by a threshold number of repeated infections. Once individuals reach a threshold number of

infections they are considered to have TS, they recover from infection and then get re-

infected until they reach the threshold number of infections for TT (dashed arrows), from

here progression to CO (corneal opacity) occurs at a constant rate σ with no further

infections required due to the damaged already incurred by those with TT. Disease sequelae

classes are indicated with a dashed red box.

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Table 1. Studies identified through the literature review that have developed a mechanistic and statistical models of trachoma transmission and/or control

Reference Model type Study purpose Type of data used Levels of endemicity evaluated

Relevance for GET 2020 goals

Assaad and Maxwell-Lyons, 1966

Simple and two-stage catalytic model

Estimate FOI and rates of acquisition and loss of active disease before a control programme

Age prevalence of clinical trachoma cases and active disease in Taiwan (1960–1961)

Hyper Changes in transmission have arisen due to socio-economic change. These can be detected with a catalytic model, which showed a profound impact on transmission.

Parthasarathy, 1967

Catalytic model

Estimate the FOI in the population and elucidate the epidemiological pattern of trachoma in a high endemic area

Data collected from 15 Indian states between 1959 – 1963. Eye examination performed.

Not stated Illustrates catalytic models can be fitted to age-specific disease data. Estimates the FOI and identifies the maximum proportion of the population likely to have been infected, giving insight on the number of rounds of MDA that may be required.

Sundaresan and Assaad, 1973

Catalytic model

Determine how FOI changes after implementation of school-based treatment programme

Age prevalence of trachoma in Taiwan pre-control (1960–1961) and in 1968–1969

Hyper Estimating the FOI may be useful to measure changes in transmission as a result of control

Lietman et al., SIS Explore how frequently Endemic prevalence from Hypo, Meso, Achievable. Mass treat every

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1999 deterministic, partial immunity in older age groups

should mass antibiotic treatment be given for settings with different baseline endemicity levels

Egypt, Malawi, Tanzania, The Gambia and Tunisia

Hyper 12-24 months in hypo, every 6-12 mo. in hyper/meso; 100% coverage

Lee et al., 2005

SIS deterministic & stochastic, only state I (infecteds) is modelled

Investigate whether there are optimal times of the year for mass antibiotic distribution

Model prevalence over time. Rates of transmission, β , and recovery, γ calibrated with data for 24 Ethiopian villages

Hyper Easier to achieve elimination if treatment is delivered after high and before low season, when transmission rates are at their lowest

Gambhir et al., 2007

SIS deterministic, ladder of infection model

Develop a model to explain observed distribution of community infection. Explain heterogeneous response to treatment

Kongwa district, Tanzania Need to consider age infection profiles and different responders (heterogeneity in exposure, predisposition)

Ray et al., 2007

SIS stochastic Investigate how long should treatment be continued in high transmission settings to eliminate infection

16 Ethiopian villages. PCR data in children 1–5 years. Baseline and follow up data after 2, 6, 12, 18 and 24 months after mass drug administration

Hyper Biannual treatment implemented for 5 years will lead to elimination in 95% of villages. Need to consider distribution of infection that leads to hotspots and the role of re-introduction from untreated communities

Grassly et al., 2008

2 & 4 state Markov model. Looking at infected and active disease

Infer parameters on the natural history of infection, and how they relate to demographic and baseline immune

256 people from Gambian villages, Jali and Berending, signs of infection checked every two weeks over 6

Meso Average duration of infection in young children is long. This contributes to persistence of infection after treatment. Young children may need more

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measurements months. Presence of chlamydial lipopolysaccharide antigen tested by ELISA

follow-up.

Gambhir et al., 2009

SIS deterministic, ladder of infection model

Refine model to capture age-specific prevalence of infection and estimate the average number of infections for the development of disease sequelae

Data from The Gambia and Tanzania. Infection by qPCR. For hyperendemic setting age-profiles of infection, infection load (Tanzania) and rate of recovery (The Gambia)

Hypo, Meso, Hyper

Captures age-specific prevalence patterns. Indicates roughly the number of prior infections which are necessary for the development of TS and TT

Blake et al., 2009

SIS stochastic Examine the contribution of transmission between and within households

Cross-sectional data on prevalence of infection (by PCR) from Upper Saloum District and Jali village in The Gambia and Kahe Mpya and Maindi villages in Tanzania

Hypo, Meso, Hyper

Household transmission is an important contributor to incidence and repeat infections. Treatment only may not be sufficient. Not including household transmission can alter the expected result of mass treatment

Ray et al., 2009

SIS stochastic Investigate two different treatment strategies: 3 annual mass treatments in all communities (as per WHO) versus 3 annual mass treatments but

Data from 3 different regions. Collected at baseline, 3 and 6 months after treatment. Upper conjunctiva swab and DNA tested for with PCR.

Hypo, Meso, Hyper

Graduating communities from a programme when infection is reduced below 5% is a reasonable strategy and could reduce the amount of antibiotic distributed in some areas by

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stopping treatment in those communities whose prevalence falls <5%

In The Gambia 1–5 year olds tested; In Tanzania and Ethiopia data from 1–10 year olds are used

more than 2-fold

Blake et al., 2010

SIS stochastic.Differential transmission between children and adults

Investigate whether targeting antibiotics to households that have at least one member with active disease is effective in preventing infection

Calculate the cost effectiveness of targeted household treatment compared with mass antibiotic distribution

West and East Africa (Upper Saloum District and Jali village in The Gambia; Kahe Mpya sub-village and Maindi village in Tanzania). Presence of infection assessed with PCR. In Maindi village, quantitative PCR to indicate presence of infection. Clinical observations also used

Hypo, Meso, Hyper

Household-targeted treatment produces comparable results to mass treatment. Active disease not a 100% sensitive marker of infection. Probability of eliminating infection with 10 years of biannual treatment not very high

Goals not currently achievable

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Gambhir et al., 2010

SIS ladder of infection model, deterministic

Second model to look at a disease only state

Examine the effect of antibiotics on infection and disease, implications on programmes. Usefulness of modelling for control programme impact projections

Same data as in Blake et al., 2009

First model hyper

Second model mixture of endemicities

In low initial endemicity areas 1-2 annual mass treatments may be sufficient for elimination. In hyperendemic areas 3 annual treatments result in no lasting effect on infection or disease sequelae. Hard to achieve goals. Implement full SAFE to reduce transmission

Lietman et al., 2011

SIS stochastic Assess re-introduction of infection following treatment

Prevalence of ocular chlamydial infection by PCR in 24 Ethiopian communities after a single MDA round. Communities were re-treated, by design, after the 24-month survey

Hypo (Nepal), Meso (Tanzania), Hyper (Ethiopia)

Easier to achieve elimination of infection than previously thought when considering positive feedback (the hazard of a susceptible individual becoming infected per infectious case increases with prevalence). Re-introduction is slow enough to detect through surveillance

Koukounari et al., 2013

Latent Markov model

Infer the population prevalence of infection and active disease in addition to the sensitivity and specificity of 3 diagnostic tests

Same as Gambhir et al., 2009, but only use data for children <10 years of age.

Hyper The sensitivity and positive predictive values of clinical examination for infection were low in The Gambia but the sensitivity of TI and positive predictive value of the clinical exam for TF and TI were low in Tanzania. This could result in

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communities experiencing further rounds of treatment when it has been eliminated from communities .

Liu et al., 2013 SIS stochastic Estimate the change in R0 per year following treatment. Assess the evidence that treatment can cause loss of short-term immunity

32 communities cluster- randomized clinical trial in Tanzania. Children 0–5 years examined at baseline, and at 6–36 months after baseline. Swab for the presence of chlamydial DNA. Mass treatment at baseline, 12 and 24 months

Meso The lack of change in R0, small negative linear trend and no evidence of loss of immunity suggest repeated treatment can help to eliminate infection

Liu et al., 2014 SIS stochastic Assess the prevalence of infection within the community following treatment. Calculate the effective field efficacy of azithromycin in clearing ocular Chlamydia

Same data as in Liu et al., 2013

Meso Efficacy = 68% (95% CI: 57–75%); no decrease in efficacy during trial; 89% chance of elimination after 10 years of annual treatment at 95% coverage

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Martin et al., 2015

Catalytic model allowing for change in FOI

Use seroconversion rate to estimate changes in the force of infection after the implementation of mass antibiotic distribution

Tanzania community, Kahe Mpya sub-village, 575 people.Detection of conjunctival swab DNA and eye examination. Prevalence of TF, TI or both, and of TS/TT/CO.

Meso Absence of antibody responses in children born after implementation of mass treatment reflects lack of C. trachomatis transmission. FOI modelling suggests serology could play a role in post-treatment surveillance

Lietman et al., 2015

SIS stochastic Test the hypothesis that a geometric distribution describes the prevalence of infection in different communities where infection is disappearing

Gurage, Ethiopia, and the TANA study in Amhara Ethiopia; from 24 communities monitored for infection. TEF study, 1–5 year old children monitored biannually. TANA study, 0–9 year old children monitored, treated annually or biannually for 42 months. PCR data

Hyper Surveying infection in low transmission settings may be difficult. Community-level cross-sectional prevalence may be approximated by a geometric distribution. Its relatively heavy tail suggests that presence of an occasional high-prevalence community is to be expected, not necessarily reflecting transmission hotspots or programme failure

Jimenez et al., 2015

Linear and logistic regression statistical models

Determine how many annual mass treatments are needed to achieve elimination. Assess factors that affect the success of reaching

283 cross-sectional survey pairs with baseline and follow-up data, mass treatment conducted in 170 districts. Prevalence of

Hypo, Meso, Hyper

Annual treatment alone is insufficient. More information needed on the effects of baseline prevalence, therapeutic coverage and underlying environmental and

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elimination goals active trachoma (TF or TF/TI) and of trachomatous trichiasis (TT)

hygiene conditions. When trachoma prevalence >30%, 7 or more annual treatments may be required

Shattock et al., 2015

Multi-stage infection SIS, stochastic, individual- based model. Household and community transmission

Assess whether past trachoma intervention efforts have been effective. Evaluate what impact can be expected if current intervention strategies are maintained. Investigate whether shifts in strategy or increases in the intensity of its implementation may lead to improved results

67 Australian communities modelled using prevalence data. Data used for all 3 different transmission settings.

Hypo, Meso, Hyper

Current intervention strategy unlikely to achieve 2020 goals. The likelihood of achieving this goal can be significantly increased by large-scale antibiotic distribution programmes accompanied by screening, treatment, facial cleanliness and housing construction

Rahman et al., 2015

Statistical model

Test whether Chlamydia trachomatis prevalence across 75 Tanzanian communities where trachoma has been disappearing was exponentially distributed

75 communities in 8 districts in Tanzania. Survey infection swab and PCR. Pre-school children aged 5 years and under were surveyed

Prevalence in 1999: 17–79%; 2007/2008: 0–28%

Models correctly predict that infection prevalence across communities where trachoma is disappearing can be described by an exponential distribution

Gambhir et al., 2015

SIS deterministic, ladder of infection model

Explore the impact of each of the components of SAFE on disease sequelae. Investigate whether the prevalence

Maindi in Kongwa, Tanzania. Trachoma was assessed according to the WHO simplified grading scheme. Specimens were

Hyper Increased intensity of all interventions will reduce TT prevalence and CO incidence. Surgery against TT alone is a stopgap until transmission is

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of TT can be reduced to 1 in 1,000, and the incidence of CO to 1 in 10,000 per annum

collected for detection of ocular C. trachomatis by real-time PCR

reduced and mass antibiotic distribution is enhanced. Goals are achievable if all interventions are implemented simultaneously. High transmission settings may take 20 years to achieve GET 2020 goals

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Table 2. Values of basic (R0) or effective (Re) reproductive numbers reported in the articles identified in this literature review, or calculated (as beta/gamma) where estimates of the rate of transmission (parameter beta) and of the rate of recovery (parameter gamma) were provided.

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Reference Beta (week–1 unless otherwise specified in original article)(95% CIs)

Gamma (week–1 unless otherwise specified)(95% CIs)

Parameters estimated in this study

Reproduction number (95% CIs)

Country and transmission setting

R0, Re, R*

1

Lee et al., 2005 0.20 month–1 0.10 month–1 Beta: No, fixedRecovery: No, fixed

2.00 Ethiopian (hyper) R02

Ray et al., 2007 0.047 0.017 Beta: Yes, MLERecovery: Yes, MLE

3.16 Ethiopian (hyper) R02

Blake et al., 20093

0.29 (0.16–0.51) 0.76 (0.39–1.40) 1.73 (1.18–2.37) 1.70 (1.15–2.46)

0.058 Beta: YesRecovery: No (1/17.2 weeks)

1.252.811.182.65

The Gambia (meso) The Gambia (hyper) Tanzania (meso) Tanzania (hyper)

R*1

Ray et al., 2009 0.0520.0330.039

0.052 (0.000–0.113) 0.037 (0.001–0.073)0.0123 (0.005–0.02)

Beta: Yes, MLERecovery: Yes, MLE

1.01 (0.50–1.27)0.89 (0.66–1.36)3.14 (2.51–3.77)

The Gambia (hypo) Tanzania (meso) Ethiopia (hyper)

R0

Lietman et al., 2011

0.014 (0.007–0.021)0.019 (0.016–0.052)0.014 (0.007–0.029)0.019 (0.015, 0.037)

0.017 (0.01–0.024)0.017 (0.013–0.041)0.014 (0.009–0.023)0.014 (0.011–0.024)

Beta: Yes, MLERecovery: Yes, MLE

1.151.161.111.84

Ethiopia (prevalence of ocular Chlamydia ranging from 5% to 75%)

R02

Liu et al., 2013 0.233 (0.210–0.258) month–1 0.167 month–1

(1/6 months)Beta: YesRecovery: No4

1.40 (1.26–1.55) R0 for first year, prior to interventions. Tanzania (hyper) at baseline

R0

Liu et al., 2014 0.229 (0.202–0.262) month–1 0.167 month–1

(1/6 months)Beta: YesRecovery: No

1.37 (1.21–1.57) Tanzania (hyper) at baseline of trial

Re

Gambhir et al., 20095

1.8 (1.6–2.1) year–1 2.4 (2.0–2.9) year–1

27.7 (21.8–35.1) or 186 year–1

0.066 (0.043–0.154) mo–1 (first infection, for R0) 0.357 (0.313–0.417) mo–1 (after many infections, Re)

Beta: YesRecovery: Yes, NGMM

1.101.403.206

The Gambia (hypo)Tanzania (meso) Tanzania (hyper)

Re2,5

Re2,5

Re2,5

R0, Basic reproduction number; Re, Effective reproduction number; 1R*, Household basic reproduction number; 2Derived from parameters given in the article but not explicitly

calculated by the authors of the original study; 3values for beta areβG , Global (household/community) transmission coefficient; MLE, maximum likelihood estimation; 4Liu et al. (2013) estimate beta for each year of the study assuming a fixed rate of recovery ; 5values for Re calculated using the next generation matrix method (NGMM) (unpublished calculation) from the best fit parameters estimated in Gambhir et al., 2009.

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