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.

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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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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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