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Short Report: A simple model to predict the potential abundance of Aedes aegypti mosquitoes a
month in advance
Running Head: A simple model for Aedes aegypti
Authors: Andrew J. Monaghan1*, Mary H. Hayden1, Kirk A. Smith2, M.H. Reiskind3, Ryan
Cabell1, and Kacey C. Ernst4
1National Center for Atmospheric Research, Boulder, CO, USA
2Maricopa County Environmental Services Vector Control Division, Phoenix, AZ, USA
3Department of Entomology, North Carolina State University, Raleigh, NC, USA
4University of Arizona, Mel and Enid Zuckerman College of Public Health, Tucson, AZ, USA
Key words: Aedes aegypti, seasonality, model, prediction, climate
Word count abstract: 150 words max
Word count text: 1500 words max
Number of figures: 2
Number of tables: 1
Supplemental material: Supplemental Figure 1, Supplemental Text 1
* PO Box 3000, Boulder, CO 80307 (USA). monaghan@ucar.edu. 303.497.8424
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Abstract
The mosquito Aedes (Stegomyia) aegypti (L.) is the primary vector of dengue,
chikungunya and Zika viruses in the United States. Surveillance for Ae. aegypti is limited,
hindering understanding of the mosquito’s seasonal patterns and predictions of elevated risk for
autochthonous virus transmission. We developed a simple and intuitive empirical model that
employs readily-available temperature and humidity variables to predict environmental
suitability for low, medium or high abundance of adult Ae. aegypti in a given city one month in
advance. The model correctly predicted the potential abundance of Ae. aegypti in >70% of
months in arid Phoenix, Arizona (over a 10- year period) and humid Miami, Florida (over a 2-
year period). The monthly model predictions can be updated daily, weekly or monthly, and thus
may be applied to forecast suitable conditions for Ae. aegypti to inform vector-control activities
and guide household-level actions to reduce habitat and human exposure.
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Main Text
The mosquito Aedes (Stegomyia) aegypti (L.) is the primary vector of dengue,
chikungunya and Zika viruses in the United States.(Grubaugh et al. 2017) Surveillance for Ae.
aegypti is limited: presence of the species has only been recorded in 291 counties of the 1,443-
2,209 counties deemed environmentally suitable.(Johnson et al. 2017) Most of these records only
note the presence of the mosquito a few times over the past several decades.(Hahn et al. 2016)
Even fewer temporal records of Ae. aegypti presence or abundance exist, hindering
understanding of the seasonal patterns of the mosquito, and the ability to predict periods of
elevated risk for autochthonous virus transmission.(Monaghan et al. 2016)
The seasonal presence and abundance of Ae. aegypti in the U.S. is limited by cool and/or
dry meteorological conditions.(Eisen and Moore 2013) With many of the weather-driven
bionomics of Ae. aegypti known(Morin et al. 2013), it may be possible to address surveillance
gaps using weather-driven dynamic mosquito simulation models(Focks et al. 1993; Morin et al.
2015) to estimate the seasonality of Ae. aegypti abundance across geographic locations.
(Monaghan et al. 2016) However, dynamic models are challenging to implement due to
computational expense, required expertise, and uncertainty in model parameters(Xu et al. 2010).
Here, we describe a simple and intuitive empirical model that employs readily-available
temperature and humidity variables to predict environmental suitability for low, medium or high
abundance of adult Ae. aegypti in a given city one month in advance. The model may be used to
quickly and easily forecast suitable conditions for Ae. aegypti to inform public health and vector-
control activities, and guide resident actions to reduce vector habitat and human exposure.
Two available temporal Ae. aegypti abundance records were used for model fitting and
evaluation. A 10-year (January 2006-December 2015) surveillance record of monthly adult
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abundance from ~750 CDC light traps across Maricopa County (Phoenix, AZ) was collected by
co-author KAS and colleagues. A 2-year (June 2006-June 2008) record of monthly egg
abundance from 30 ovitraps across a 650 km2 area of Palm Beach County (near Miami, FL) was
collected by co-author MHR and colleagues.(Reiskind and Lounibos 2013) The Phoenix record
is longer and draws on more traps, and thus was used for model fitting. The Miami record is
shorter, draws on fewer traps, and measures egg rather than adult abundance, and thus was used
for model evaluation. Both records consist of aggregated counts across all traps by city-month.
The trap records have uncertainty due to issues with species specificity, malfunctions and catch
loss(Sukumaran 2016), and are not directly comparable across locations. We thus focused on
relative abundance across seasons for each city, normalizing the records by setting the maximum
monthly aggregate trap count in each record to 1,000, and proportionally rescaling all other
monthly counts. Next, base 10 logs of the monthly Ae. aegypti counts (“log(aegypti)”) were
computed because the log-transformed values have linear relationships with the meteorological
variables. The logs of values between 1-1,000 conveniently vary between 0-3, allowing
categorization of results into “low” (0-1), “medium” (1-2) and “high” (2-3) potential abundance
categories.
Daily meteorological fields were obtained from version 2 of the 1/8th degree North
American Land Data Assimilation System (NLDAS) forcing dataset.(Cosgrove et al. 2003) Time
series of rainfall, relative humidity, vapor pressure, and temperature (minimum, maximum and
mean) were extracted for the coordinates of Phoenix and Miami for 2006-2015 using bilinear
interpolation. Temperature, humidity and rainfall variables were selected because of their
association with Ae. aegypti suitability in previous models.(Focks et al. 1993) Next, for each
month for which log(aegypti) was to be predicted, the 30-day mean of each meteorological
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variable from the prior month was computed, allowing for a lag of 3 days. For example, to
predict log(aegypti) for a month beginning on 1 July, one would compute the 30-day average
meteorological fields from 29 May – 27 June. This approach accounts for a ~3-day lag in the
availability of the NLDAS fields, enabling users of NLDAS to issue a monthly forecast for
log(aegypti) on the same day the model prediction is made, rather than 3 days later. Note that
the model fit is insensitive to a 3-day versus 0-day lag, so users could simply use monthly
average meteorological variables from, e.g., June to predict July. The choice of 30-day/monthly
average periods to predict log(aegypti) approximates the duration of the combined immature life
stages and adult gonotropic cycle.(Focks et al. 1993)
Six meteorological fields were tested for linear fit by regressing them on log(aegypti) for
Phoenix, precipitation, relative humidity, vapor pressure, average monthly minimum, maximum,
and average daily temperature. Precipitation and relative humidity did not have statistically
significant fits.. Vapor pressure (an absolute measure of humidity) and all three temperature
variables had statistically significant linear fits (p<0.05) (see Supplemental Figure 1). These
robust linear fits motivated the choice to fit a least squares multiple linear regression (MLR)
model to predict log(aegypti). The regression tool in the Data Analysis Toolpack of MS Excel
v15.38 was used. Three MLR models were fit using vapor pressure and each of the three
temperature variables in turn. The model using minimum temperature had the best fit; maximum
and mean temperature were excluded because of their high correlation with minimum
temperature (ρ>0.97).
The best-fit MLR model for log(aegypti) included minimum temperature (Tmin; oC) and
vapor pressure (e; hPa) as explanatory variables:
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log(aegypti) = -0.53968 + 0.07041*Tmin + 0.03829*e [1]
Predicted log(aegypti) is termed “potential abundance” of Ae. aegypti here because it is
essentially an estimate of environmental suitability for levels of Ae. aegypti abundance, rather
than an explicit prediction of abundance. The standard error of regression is 0.40 and the model
explains 74% of the variation in log(aegypti) in Phoenix (Table 1). Observed and predicted year-
to-year monthly and 10-year average monthly variations are shown in Figure 1a and 1b. When
the 10-year average monthly predictions are converted to potential abundance categories (“high”,
“medium” and “low”) they match the observed categories in 11 of 12 months (Figure 1c). Over
the entire 10-year period (n=120; not shown), the predicted categories match those observed in
75% of months, are lower in 16.7% of months, and are higher in 8.3% of months.
The model predictions for Miami are also shown in Fig. 1. The 2-year average monthly
predictions match the observed categories in 10 of 12 months (Figure 1f). Over the entire 2-year
period (n=25; not shown), the predicted categories match those observed in 72% of months, are
lower in 16% of months, and higher in 12% of months. Given that Miami is a humid subtropical
environment compared to the arid setting of Phoenix, and the Miami mosquito data was not used
in model fitting, the fact that the Miami categorical predictions nearly as accurate as for Phoenix
suggests the model can be applied more broadly across different environments.
The MLR model was thus used to explore the seasonality of Ae. aegypti across the entire
contiguous U.S. (Figure 2). The 10-year average NLDAS meteorological fields described above
were used as model inputs. Because winter conditions limit the northernmost range of Ae.
aegypti(Eisen et al. 2014) – which the MLR model does not account for – the results were
masked using an observation-constrained map of environmental suitability for Ae. aegypti
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presence.(Johnson et al. 2017) The resulting maps indicate areas of high potential abundance in
the Southeast from July-November. Potential abundance in south Florida and southernmost
Texas, where Aedes-borne viruses have been transmitted locally in the past decade(Monaghan et
al. 2016; Grubaugh et al. 2017), is at least moderate all-year-round. In California, where Ae.
aegypti was initially detected in 2013 and has since spread(Pless et al. 2017), potential
abundance is moderate across large geographic areas of the state from July-October.
Remarkably, the simple MLR model produces nearly identical seasonal patterns of potential
abundance compared to estimates from complex dynamic mosquito simulation models.
(Monaghan et al. 2016)
Users of the MLR model should note several limitations. The model was fit using data
from an arid city that differs from humid environments where Ae. aegypti is most common
studied using traps that are not specific to Ae. aegypti. Rainfall did not emerge as a significant
predictor, though it can be an important source of water for the immature stages of Ae. aegypti.
(Morin et al. 2015) It is possible that vapor pressure, which is correlated with rainfall, is an
adequate proxy of rainfall in the MLR model. Temperatures in Phoenix regularly exceed 40 oC in
summer and are not typical of many environments where Ae. aegypti is present(Eisen et al.
2014). The use of minimum temperature in the MLR partially addresses this difference, as the
greater nighttime cooling in desert cities like Phoenix can lead to average minimum temperatures
comparable to humid cities like Miami. The use of one-month meteorological averages as
predictors may limit the model’s ability to detect fluctuations in Ae. aegypti populations related
to episodic events such as large storms or heatwaves. The model does not account for the effects
of interspecies competition(Reiskind and Lounibos 2013), adaptation(Kearney et al. 2009),
winter egg survival(Brady et al. 2014) or diel temperature fluctuations.(Lambrechts et al. 2011)
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Finally, the model neglects non-climatic factors important for supporting Ae. aegypti such as
presence of humans and availability of container habitats.(Hayden et al. 2015)
Despite its simplicity and limitations, the model produces seasonal estimates of Ae.
aegypti potential abundance across the U.S. consistent with complex dynamic model
simulations(Monaghan et al. 2016) and presence records.(Hahn et al. 2016) Regions where
predicted Ae. aegypti potential abundance is moderate or high nearly year-round coincide with
areas of recent arbovirus transmission.(Monaghan et al. 2016; Grubaugh et al. 2017) We
demonstrate that the model is useful for understanding the general seasonality of Ae. aegypti
mosquitoes in the U.S. The model was designed for easy, rapid, low-cost implementation using
readily available meteorological data (see Supplemental Text 1 for step-by-step instructions). It
may be most beneficial for ‘real time’ applications, such as forecasting suitable conditions for
Ae. aegypti a month in advance for local action, including informing timing of surveillance
activities in areas without a current program, triggering mobilization of vector control activities,
and initiation of educational campaigns to the public to prepare their yards for the season.
Acknowledgements
We thank Rebecca Eisen and Tammi Johnson of CDC for providing their habitat
suitability model results.(Johnson et al. 2017)
Financial Support
This work was funded by NASA Grant NNX16AO98G. The National Center for
Atmospheric Research is sponsored by the National Science Foundation.
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References
1. Grubaugh ND et al., 2017. Genomic epidemiology reveals multiple introductions of Zika virus into the United States. Nature 546: 401–405.
2. Johnson TL et al., 2017. Modeling the Environmental Suitability for Aedes (Stegomyia) aegypti and Aedes (Stegomyia) albopictus (Diptera: Culicidae) in the Contiguous United States. J Med Entomol tjx163.
3. Hahn MB, Eisen RJ, Eisen L, Boegler KA, Moore CG, McAllister J, Savage HM, Mutebi J-P, 2016. Reported Distribution of Aedes ( Stegomyia ) aegypti and Aedes ( Stegomyia ) albopictus in the United States, 1995-2016 (Diptera: Culicidae). J Med Entomol 53: 1169–1175.
4. Monaghan AJ et al., 2016. On the Seasonal Occurrence and Abundance of the Zika Virus Vector Mosquito Aedes Aegypti in the Contiguous United States. PLoS Curr 8: ecurrents.outbreaks.50dfc7f46798675fc63e7d7da563da76.
5. Eisen L, Moore CG, 2013. Aedes (Stegomyia) aegypti in the continental United States: a vector at the cool margin of its geographic range. J Med Entomol 50: 467–478.
6. Morin CW, Comrie AC, Ernst K, 2013. Climate and Dengue Transmission: Evidence and Implications. Environ Health Perspect 121: 1264–1272.
7. Focks DA, Haile DG, Daniels E, Mount GA, 1993. Dynamic Life Table Model for Aedes aegypti (Diptera: Culicidae): Analysis of the Literature and Model Development. J Med Entomol 30: 1003–1017.
8. Morin CW, Monaghan AJ, Hayden MH, Barrera R, Ernst K, 2015. Meteorologically Driven Simulations of Dengue Epidemics in San Juan, PR. PLoS Negl Trop Dis 9: e0004002.
9. Xu C, Legros M, Gould F, Lloyd AL, 2010. Understanding Uncertainties in Model-Based Predictions of Aedes aegypti Population Dynamics. PLoS Negl Trop Dis 4: e830.
10. Reiskind MH, Lounibos LP, 2013. Spatial and temporal patterns of abundance of Aedes aegypti L. (Stegomyia aegypti) and Aedes albopictus (Skuse) [Stegomyia albopictus (Skuse)] in southern Florida. Med Vet Entomol 27: 421–429.
11. Sukumaran D, 2016. A review on use of attractants and traps for host seeking Aedes aegypti mosquitoes. Indian J Nat Prod Resour IJNPR Former Nat Prod Radiance NPR 7: 207–214.
12. Cosgrove BA et al., 2003. Real-time and retrospective forcing in the North American Land Data Assimilation System (NLDAS) project. J Geophys Res Atmospheres 108: 8842.
13. Eisen L, Monaghan AJ, Lozano-Fuentes S, Steinhoff DF, Hayden MH, Bieringer PE, 2014. The Impact of Temperature on the Bionomics of Aedes (Stegomyia) Aegypti, with Special Reference to the Cool Geographic Range Margins. J Med Entomol 51: 496–516.
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14. Pless E, Gloria-Soria A, Evans BR, Kramer V, Bolling BG, Tabachnick WJ, Powell JR, 2017. Multiple introductions of the dengue vector, Aedes aegypti, into California. PLoS Negl Trop Dis 11: e0005718.
15. Kearney M, Porter WP, Williams C, Ritchie S, Hoffmann AA, 2009. Integrating biophysical models and evolutionary theory to predict climatic impacts on species’ ranges: the dengue mosquito Aedes aegypti in Australia. Funct Ecol 23: 528–538.
16. Brady OJ et al., 2014. Global temperature constraints on Aedes aegypti and Ae. albopictus persistence and competence for dengue virus transmission. Parasit Vectors 7: 338.
17. Lambrechts L, Paaijmans KP, Fansiri T, Carrington LB, Kramer LD, Thomas MB, Scott TW, 2011. Impact of daily temperature fluctuations on dengue virus transmission by Aedes aegypti. Proc Natl Acad Sci 108: 7460–7465.
18. Hayden MH, Cavanaugh JL, Tittel C, Butterworth M, Haenchen S, Dickinson K, Monaghan AJ, Ernst KC, 2015. Post Outbreak Review: Dengue Preparedness and Response in Key West, Florida. Am J Trop Med Hyg 93: 397–400.
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PHOENIX MIAMI
Figure 1. Phoenix (left) and Miami (right) observed vs. predicted: a,d) log(aegypti) by year and month; b,e) multi-year average log(aegypti) by month; and c,f) multi-year average potential abundance categories by month. The multi-year average for Phoenix spans January 2006-December 2015, and for Miami spans June 2006-June 2008. Potential abundance categories are 3 for “high”, 2 for “medium” and 1 for “low”.
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Figure 2. 2006-2015 average monthly log(aegypti) in the U.S., predicted using the average meteorological fields from the prior month per equation (1). For example, average August log(aegypti) is based on average meteorological conditions in July. The log(aegypti) values are color-coded into their respective potential abundance categories including “low” (blue), “medium” (green) and “high” (red).
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Table 1. MLR model fit statistics.
Regression Statistics Multiple R 0.86 R Square 0.74 Adjusted R Square 0.74 Standard Error 0.40 Observations 120
Coefficient
sStandard
ErrorP-
valueLower 95%
Upper 95%
Intercept -0.53968 0.097 0.000 -0.732 -0.348Tmin 0.07041 0.007 0.000 0.056 0.085e 0.03829 0.017 0.029 0.004 0.073
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Supplemental Figure 1
Supplemental Figure 1. Scatter plots showing linear fits of minimum temperature (top panel) and vapor pressure (bottom panel) with log(aegypti) in Phoenix.
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Supplemental Text 1
Step-by-step instructions on use of the MLR model to predict monthly log(aegypti)
1. Compute the 30-day average daily minimum temperature (Tmin) in units of oC for the previous 30 days (with lag of 3). For example, if you are interested in making a prediction for the month beginning on the 1st of July, you would compute the 30-day average of Tmin from May 29 thru June 27. If you wanted to make a prediction for the month beginning on the 8th of July, you would average daily Tmin for June 5 thru July 4. Note that the 30-day-with-3-day-lag method of computing averages is designed specifically for using NLDAS meteorological fields to make predictions for the upcoming month in ‘real time’. For simplicity, since monthly average meteorological fields are readily available, you can achieve similar results using monthly averages as a proxy of 30-day averages.
2. Compute the 30-day (or monthly) average vapor pressure, e, in the same manner. Vapor pressure is an output of datasets such as Daymet V3 and WorldClim V2. However, relative humidity is often a more commonly available variable in climate datasets (e.g., NLDAS), or directly from local weather stations. If you only have access to relative humidity data, vapor pressure can be computed from monthly relative humidity and average temperature data as follows (you can skip to step 3 if you already have computed vapor pressure):
2a. Compute the 30-day (or monthly) average daily temperature (Tavg) in the same manner.
2b. Compute the 30-day (or monthly) average daily relative humidity (RH) in the same manner. (units=%)
2c. Compute the 30-day (or monthly) average vapor pressure (e), in units of hPa, using Tavg and RH, as follows:
2c.1. es =6.11*10^((7.5*Tavg)/(237.3+Tavg))
2c.2. (es-e) =1.33322*(((100-RH)/100)*4.9463*EXP(0.0621*Tavg))
2c.3. e = es - (es-e) ; i.e., subtract the result of 2c.2 from the result of 2c.1
3. Compute log(aegypti) using the 30-day (or monthly) average minimum temperature and vapor pressure using the following equation. The value should be between 0-3 (and can occasionally exceed 3 if conditions are highly suitable).
log(aegypti) =-0.53968+0.07041*Tmin+0.03829*e
For example, if the monthly average temperature is 25.6 oC and the monthly average vapor pressure is 18.7 hPa: log(aegypti) =-0.53968+0.07041*25.6+0.03829*18.7 = 1.98
4. Compute the Aedes aegypti potential abundance category:
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High if log(aegypti) ≥ 2Medium if log(aegypti) ≥ 1 and < 2Low if log(aegypti) < 1
5. This monthly forecast can be updated at any desired time interval (e.g., daily, weekly or monthly).
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