modelling pandemic influenza in the united states timothy c. germann, kai kadau, and catherine a....

Modelling Pandemic Influenza in Modelling Pandemic Influenza in the United Statesthe United States

Timothy C. Germann, Kai Kadau, Timothy C. Germann, Kai Kadau, and Catherine A. Mackenand Catherine A. Macken

Los Alamos National LaboratoryLos Alamos National Laboratory

Ira M. Longini, Jr.Ira M. Longini, Jr.

Fred Hutchinson Cancer Center and Fred Hutchinson Cancer Center and University of Washington, SeattleUniversity of Washington, Seattle

Outline• EpiCast (“Epidemiological Forecasting”)

model design and parameterization

• Simulated pandemics in a fully susceptible population

• Assessment of various mitigation strategies

What is EpiCast? A stochastic agent-based simulation model

of the United States population of 281 million individuals (implemented on modern parallel supercomputers), to predict the nationwide spread of infectious diseases and to assess various mitigation strategies.

T. C. Germann, K. Kadau, I. M. Longini, and C. A. Macken, “Mitigation Strategies for Pandemic Influenza in the United States,”

submitted to Proceedings of the National Academy of Sciences.

Fid

elit

y or

Res

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tion

High(individual, minute-by-

minute)

Low(homogeneously

mixed population)

Moderate (individual, with mixing

groups)

Community City State Nation World

Spatial Scale

EpiSims

Elveback, Longini,Epstein, …

EpiCast

SIR equations (PDE’s)

Oversimplified Perspective of Various Epi-models

S'(t) = -rSII'(t) = rSI - γIR'(t) = γI

ComputationalCost

Supercomputer

Workstation/PC

The four key elements of our model

Community-level transmission between people, Community-level transmission between people, through various contact groups (household, work through various contact groups (household, work group, school, …)group, school, …)

Disease natural history model and parametersDisease natural history model and parameters

U.S. Census demographics (where people live) and U.S. Census demographics (where people live) and workerflow data (where they work), at tract-level workerflow data (where they work), at tract-level resolutionresolution

DOT statistics on long-distance travelDOT statistics on long-distance travel

Person-to-person transmission is described by contact groups within a ~2000-person model community*

*M. E. Halloran *M. E. Halloran et alet al, , ScienceScience 298298, 1428 , 1428 (2002);(2002);

I. M. Longini I. M. Longini et alet al, , ScienceScience 309309, 1083 , 1083 (2005).(2005).

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WG

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WGWG

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WG

WG

WG

WG WG

WG: Work group

Stochastic Transmission

Each susceptible individual (blue) has a Each susceptible individual (blue) has a daily probability of becoming infected, daily probability of becoming infected, based on all of based on all of their potential their potential contacts with contacts with infectious infectious individuals individuals ((redred):):

Stochastic Transmission

P 1 (1 pHHc a )(1 pWG

a a )(1 pComma a )(1 pComm

c a )2

For the susceptible individual shown in blue, the For the susceptible individual shown in blue, the probability of becoming infected is:probability of becoming infected is:

These may be further modified if the infectious and/or susceptible individuals have been vaccinated, are taking antivirals, …

The four key elements of our model Community-level transmission between people, through Community-level transmission between people, through

various contact groups (household, work group, school, various contact groups (household, work group, school, …)…)




Latency

Incubation

Asymptomatic (33%)

0

Probability ofinfecting others

days

Exposure and infection

1.2d

1.9d 4.1d

Natural History for Pandemic Influenza Natural History for Pandemic Influenza

Possibly symptomatic

Symptomatic (67%)

Persons who become ill may self-isolate to

household-only contacts

Case Serial Interval

Time between illness onset times for a case and Time between illness onset times for a case and the person infectedthe person infected Latent, incubation and infectious period lengthsLatent, incubation and infectious period lengths Distribution of infectiousnessDistribution of infectiousness Our model, mean = 3.5 daysOur model, mean = 3.5 days Ferguson, et al. mean = 2.6 daysFerguson, et al. mean = 2.6 days

Determines the speed of the epidemic, but not the Determines the speed of the epidemic, but not the final sizefinal size

Current Avian A(H5N1), seems to have longer Current Avian A(H5N1), seems to have longer serial interval than current human strainsserial interval than current human strains

Basic Reproductive Number: R0

Number Number of secondary infections due to a of secondary infections due to a singlesingle typicaltypical infected person in a infected person in a totally totally susceptiblesusceptible population population

RR0 0 > 1 for sustained transmission> 1 for sustained transmission

For pandemic influenza: 1< RFor pandemic influenza: 1< R0 0 ≤ 2.4≤ 2.4 A(H3N2) 1968-69, A(H3N2) 1968-69, RR0 0 ≈ 1.7≈ 1.7

A(H1N1) 1918, second wave, A(H1N1) 1918, second wave, RR0 0 ≈ 2≈ 2

Rapid Real Time Evaluation

Important to rapidly estimate key Important to rapidly estimate key parameters of pandemic strainparameters of pandemic strain Pathogenecity, virulence, natural history Pathogenecity, virulence, natural history

parametersparameters Transmissibility parametersTransmissibility parameters

RR00

Serial intervalSerial interval Secondary attack ratesSecondary attack rates OthersOthers

Census tract-level resolutionThe US census tract level provides a finer-scale resolution than counties, with more uniform population sizes that correspond to the 2,000-person community granularity (so that on average, each tract is modeled by two communities):

65,433 U.S. census tracts

Average tract population: 4,300

Constructing the model U.S. population

We use U.S. Census Bureau data on tract-level demographics and worker-flow, and Dept. of Transportation data on irregular long-range travel to assign fixed residential and workplace communities to each individual, in addition to infrequent visits to more distant communities.

1,344 Cook County (IL) census tracts

Census worker flow data

Home CountyHome County Work CountyWork County # # WorkersWorkers

Los Alamos, NMLos Alamos, NM Los Alamos, NMLos Alamos, NM 9,1339,133Santa Fe, NMSanta Fe, NM Los Alamos, NMLos Alamos, NM 4,0294,029Rio Arriba, NMRio Arriba, NM Los Alamos, NMLos Alamos, NM 3,2063,206Sandoval, NMSandoval, NM Los Alamos, NMLos Alamos, NM 606606Bernalillo, NMBernalillo, NM Los Alamos, NMLos Alamos, NM 474474

Taos, NMTaos, NM Los Alamos, NMLos Alamos, NM 242242…… …… ……

Essex, MAEssex, MA Los Alamos, NMLos Alamos, NM 99…… …… ……

Los Alamos, NMLos Alamos, NM Santa Fe, NMSanta Fe, NM 180180

Los Alamos, NMLos Alamos, NM District of District of ColumbiaColumbia 55

…… …… ……

Raw data represents a snapshot at the particular week the survey was carried out; restrict daily commuter

traffic to a “reasonable” distance (e.g., 100 miles):

People go to work according to the distance to work survey data

Long Distance Travel Model*1.1. Trip GenerationTrip Generation: : Which individuals/households make a Which individuals/households make a

long distance trip?long distance trip?Use age-dependent average number of trips per year to determine the daily probability of Use age-dependent average number of trips per year to determine the daily probability of

making a long-distance trip, then roll the dice for each person every day.making a long-distance trip, then roll the dice for each person every day.

2.2. Destination ChoiceDestination Choice: : Where do they go?Where do they go?Simplistic gravity model: choose a random community within the simulation (either a Simplistic gravity model: choose a random community within the simulation (either a

2,000-person residential or a 1,000-person workgroup-only community), without 2,000-person residential or a 1,000-person workgroup-only community), without any distance dependence.any distance dependence.

3.3. Trip DurationTrip Duration: : How long do they stay there?How long do they stay there?Use the national statistics on trip duration to choose a duration from 0-13 nights.Use the national statistics on trip duration to choose a duration from 0-13 nights.

*An advanced model, including household income in step 1, distance and median destination income in step 2, and trip purpose and distance in step 3, has been developed and is currently being implemented.

Capturing long-range (irregular) travel behavior

Use Bureau of Transportation Statistics data on travel frequency and duration (in lieu of detailed city-to-city transportation data):

Influenza in the US: Simulated and Historical Pandemics

Baseline (R0 = 1.9)

Each Census tract is represented by a dot colored according to its Each Census tract is represented by a dot colored according to its prevalence (number of symptomatic cases at any point in time) on prevalence (number of symptomatic cases at any point in time) on a logarithmic color scale, from 0.3-30 cases per 1,000 residents. a logarithmic color scale, from 0.3-30 cases per 1,000 residents.

QuickTime™ and aMPEG-4 Video decompressor

are needed to see this picture.

Baselinesimulatedpandemics

Most of the epidemic activity is in a 2-3 month period, starting

1-2 months after introduction

Asian Influenza A(H2N2) 1957-1958*

July 1957, sporadic cases, West Coast and July 1957, sporadic cases, West Coast and LouisianaLouisiana

Aug. 1957, local small epidemics beginAug. 1957, local small epidemics begin Sept. 1957 – Oct. 1957, peaks occurSept. 1957 – Oct. 1957, peaks occur

Most epidemic activity over this 60 day periodMost epidemic activity over this 60 day period

*Source: Kilbourne (1975)

Hong Kong Influenza A(H3N2) 1968-1969*

July 1968, sporadic cases, West CoastJuly 1968, sporadic cases, West Coast Oct. 1968, local epidemics beginOct. 1968, local epidemics begin Dec. 1968 – Jan. 1969, peaks occurDec. 1968 – Jan. 1969, peaks occur

Most epidemic activity over this 60 day periodMost epidemic activity over this 60 day period March. 1968, end of epidemic activityMarch. 1968, end of epidemic activity

*Source: WHO (1968-1970), Rvachev and Longini (1985)

Day 60

Day 80

Day 100

Day 120

Introduction of 40 infecteds on day 0, either in NY or LA,

with and without nationwide travel

restrictions

Assessment of Mitigation Strategies

Assessment of Mitigation Strategies (single or in combination)

In the following, we assume (and simulation results confirm) In the following, we assume (and simulation results confirm) that disease spread is so rapid that all interventions are that disease spread is so rapid that all interventions are done on a nationwide basis simultaneously; however, a done on a nationwide basis simultaneously; however, a state-by-state (or more local, down to tract-by-tract) staged state-by-state (or more local, down to tract-by-tract) staged response can also be studied with our model.response can also be studied with our model.

• Vaccination (with a fixed rate of production and distribution)Vaccination (with a fixed rate of production and distribution)

• Targeted antiviral prophylaxis (from a limited national stockpile)Targeted antiviral prophylaxis (from a limited national stockpile)

• School closureSchool closure

• Social distancing, either a voluntary response to an ongoing Social distancing, either a voluntary response to an ongoing pandemic, or as the result of an imposed quarantine or travel pandemic, or as the result of an imposed quarantine or travel restrictionsrestrictions

•Production capacity 4/10/20M doses per week•Dose (and efficacy) of vaccine - 1 vs. 2 doses•Timing of vaccination - relative to start of pandemic

Zoonoses Pandemic spread Pandemic in U.S.

Time

Low efficacyLow efficacy - one doseHigh efficacy - two doses

Simulated protection by vaccination

30d60d

-60d

Dynamic Vaccination Options

Dynamic VaccinationDistribute the available supply of vaccine (with a specified starting date, rate, and limit for Distribute the available supply of vaccine (with a specified starting date, rate, and limit for

production and distribution) to the eligible population (neither sick nor previously vaccinated) production and distribution) to the eligible population (neither sick nor previously vaccinated) using two strategies:using two strategies:

• Random distribution to the entire (eligible) populationRandom distribution to the entire (eligible) population

• Distribute preferentially to children first, then any remaining supply to the adult populationDistribute preferentially to children first, then any remaining supply to the adult population

Also consider two different scenarios:Also consider two different scenarios:

• The early production of a low-efficacy, single-dose vaccine, with:The early production of a low-efficacy, single-dose vaccine, with: Vaccine efficacy for susceptibility VEs = 0.30Vaccine efficacy for susceptibility VEs = 0.30 Vaccine efficacy for infectiousness VEi = 0.50Vaccine efficacy for infectiousness VEi = 0.50

• The delayed production of a higher-effficacy, 2-dose vaccine, with:The delayed production of a higher-effficacy, 2-dose vaccine, with: Vaccine efficacy for susceptibility VEs = 0.70Vaccine efficacy for susceptibility VEs = 0.70

(VEs = 0.50 for elderly)(VEs = 0.50 for elderly) Vaccine efficacy for infectiousness VEi = 0.80Vaccine efficacy for infectiousness VEi = 0.80

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cina

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Random vaccination, RRandom vaccination, R00 = 1.6 = 1.6

CONTACTSHouseholdHousehold clusterPreschool/daycareSchoolWorkplace

TAP: Targeted antiviral prophylaxisTAP: Targeted antiviral prophylaxisusing neuraminidase inhibitors (oseltamivir/relenza)using neuraminidase inhibitors (oseltamivir/relenza)

60% ascertainment

100% household + HH cluster

100% preschool

60% school

60% workplace

Targeted Antiviral Prophylaxis (TAP)• Close contacts of symptomatic individuals are treated Close contacts of symptomatic individuals are treated

prophylactically, until the national stockpile is exhaustedprophylactically, until the national stockpile is exhausted• Assume X% of symptomatic cases can be identified, then:Assume X% of symptomatic cases can be identified, then:

100% of household, household cluster, and preschool / playgroup 100% of household, household cluster, and preschool / playgroup contacts are treatedcontacts are treated

Y% of workgroup and school contacts are treatedY% of workgroup and school contacts are treated We will focus on two cases: X = Y = 60% or 80%We will focus on two cases: X = Y = 60% or 80%

• Each course consists of 10 tablets, 2/day for treatment of Each course consists of 10 tablets, 2/day for treatment of symptomatic cases and 1/day for prophylaxissymptomatic cases and 1/day for prophylaxis

• Antiviral treatment reduces the sick period by 1 dayAntiviral treatment reduces the sick period by 1 day• 5% of patients stop taking antiviral after 1 day5% of patients stop taking antiviral after 1 day• Antiviral efficacy for susceptibility AVEs = 0.30Antiviral efficacy for susceptibility AVEs = 0.30• Antiviral efficacy for infectiousness AVEi = 0.62Antiviral efficacy for infectiousness AVEi = 0.62• Antiviral efficacy for illness given infectionAntiviral efficacy for illness given infection

AVEd = 0.60AVEd = 0.60

TA

P (

20M

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)

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Rapid intervention can preserve the limited antiviral stockpile and reduce the attack rate:

Pandemic virus arrives in U.S. Pandemic alert

60% TAPR0 = 1.9

U.S. Strategic National Stockpile of

Tamiflu® Now: 2.3M courses

Planned: 20M courses

School closure

We assume that once schools are closed, they remain closed We assume that once schools are closed, they remain closed for the duration of the epidemic. School closure includes:for the duration of the epidemic. School closure includes:

• High schoolsHigh schools

• Middle schoolsMiddle schools

• Elementary schoolsElementary schools

• PreschoolsPreschools

• Regular preschool-age playgroupsRegular preschool-age playgroups

Social distancing / quarantineAs a result of either a formal quarantine program, or voluntary As a result of either a formal quarantine program, or voluntary

changes in social and hygienic behavior in the event of a changes in social and hygienic behavior in the event of a widespread pandemic, we assume that:widespread pandemic, we assume that:

• School, preschool, and playgroup contact rates are cut in half.School, preschool, and playgroup contact rates are cut in half.

• Workgroup contact rates are cut in half.Workgroup contact rates are cut in half.

• Household contact rates double.Household contact rates double.

• Household cluster contact rates remain unchanged.Household cluster contact rates remain unchanged.

Once initiated, this alteration in normal behavior is assumed to last Once initiated, this alteration in normal behavior is assumed to last throughout the remainder of the epidemic.throughout the remainder of the epidemic.

Travel restrictions

The random long-range travel frequency can be reduced at The random long-range travel frequency can be reduced at any time, either due to imposed travel restrictions or any time, either due to imposed travel restrictions or behavioral changes (as occurred during the SARS scare).behavioral changes (as occurred during the SARS scare).

While by itself this can only slow the spread, it can While by itself this can only slow the spread, it can potentially be useful to buy time for other interventions.potentially be useful to buy time for other interventions.

90%

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TAP, vaccination, or school closure can contain an outbreak for R0 ≤ 1.6 (cumulative ill per 100)

Intervention R0 = 1.6 R0 = 1.9 R0 = 2.1 R0 = 2.4

Baseline (no intervention) 32.6 43.5 48.5 53.7

Targeted Antiviral Prophylaxis1

(# of courses)

0.06

(2.8 M)

4.3

(182 M)

12.2

(418 M)

19.3

(530 M)

Dynamic vaccination2 (1-dose regimen) 0.7 17.7 30.1 41.1

Dynamic child-first vaccination2 0.04 2.8 16.3 35.3

Dynamic vaccination3 (2-dose regimen) 12.3 32.3 40.1 48.0

Dynamic child-first vaccination3 1.9 24.7 36.1 46.4

School closure4 1.0 29.3 37.9 46.4

Local social distancing4 25.1 39.2 44.6 50.3

Travel restrictions5 during entire time 32.8 44.0 48.9 54.1160% TAP, 7 days after pandemic alert, unlimited antiviral supply.210 million doses of a low-efficacy vaccine (single-dose regimen) per week for 25 weeks, beginning such that the first persons treated develop an immune response on the date of the first U.S. introduction.310 million doses of a high-efficacy vaccine (2-dose regimen) per week for 25 weeks, beginning such that the first persons treated develop a full immune response 30 days after the first U.S. introduction.4Intervention starting 7 days after pandemic alert.5Reduction in long-distance travel, to 10% of normal frequency.

An aggressive combination of therapeutic and social measures can succeed for R0 ≤ 2.4

Intervention R0 = 1.6 R0 = 1.9 R0 = 2.1 R0 = 2.4

Social distancing & travel restictions4,5 19.6 39.3 44.7 50.5

60% TAP4, school closure5, and social distancing5

0.02

(0.6 M)

0.07

(1.6 M)

0.14

(3.3 M)

2.8*

(20 M)

Dynamic vaccination2, social distancing4, travel restrictions4,5, and

school closure6

0.04 0.2 0.6 4.5

60% TAP4, dynamic vaccination2, social distancing4, travel restrictions4,5, and

school closure6

0.02

(0.3 M)

0.3

(0.7 M)

0.06

(1.4 M)

0.1

(3.0 M)

Dynamic child-first vaccination2, social distancing4, travel restrictions4,5, and

school closure6

0.02 0.2 0.9 7.7

210 million doses of a low-efficacy vaccine (single-dose regimen) per week for 25 weeks, beginning such that the first persons treated develop an immune response on the date of the first U.S. introduction.4Intervention starting 7 days after pandemic alert.5Reduction in long-distance travel, to 10% of normal frequency.6Intervention starting 14 days after pandemic alert.

*Exhausted the available supply of 20M antiviral courses.

Epi curves (note log scale)

Recommendations

For RFor R00 ≥ 1.9, we would need at least 182 million ≥ 1.9, we would need at least 182 million

courses of oseltamivir to have an impact on spreadcourses of oseltamivir to have an impact on spread For For RR00

≤ 1.6, spread can be controlled by dynamic ≤ 1.6, spread can be controlled by dynamic vaccination with low efficacy vaccine (10 million vaccination with low efficacy vaccine (10 million doses per week), school closuredoses per week), school closure

For 1.9 ≤ RFor 1.9 ≤ R0 0 ≤ 2.4, only combinations of TAP, ≤ 2.4, only combinations of TAP, vaccination, social distancing measures and travel vaccination, social distancing measures and travel restrictions are effectiverestrictions are effective

Social distancing and travel restrictions are Social distancing and travel restrictions are notnot effective when used aloneeffective when used alone

Recommendations (cont.)

For limited quantities of vaccineFor limited quantities of vaccine Rapid vaccination of one-dose low efficacy is more Rapid vaccination of one-dose low efficacy is more

effective than two-dose high efficacyeffective than two-dose high efficacy Vaccination of school children first is much better than Vaccination of school children first is much better than

random vaccinationrandom vaccination Vaccination alone requires high vaccination rates and Vaccination alone requires high vaccination rates and

production totalproduction total Rapid use of TAP preserves limited antiviral Rapid use of TAP preserves limited antiviral

stockpilesstockpiles We can effectively divert antivirals and vaccines to the We can effectively divert antivirals and vaccines to the

critical workforce within limitscritical workforce within limits

The End

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modelling pandemic influenza in the united states timothy c. germann, kai kadau, and catherine a....

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