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Modelling and observing the role of wind in Anopheles population dynamics around a reservoir
© The Author(s) 2018
Received: 14 September 2017
Accepted: 19 January 2018
Published: 25 January 2018
Wind conditions, as well as other environmental conditions, are likely to influence malaria transmission through the behaviours of Anopheles mosquitoes, especially around water-resource reservoirs. Wind-induced waves in a reservoir impose mortality on aquatic-stage mosquitoes. Mosquitoes’ host-seeking activity is also influenced by wind through dispersion of \(CO_2\). However, no malaria transmission model exists to date that simulated those impacts of wind mechanistically.
A modelling framework for simulating the three important effects of wind on the behaviours of mosquito is developed: attraction of adult mosquitoes through dispersion of \(CO_2\) (\(CO_2\) attraction), advection of adult mosquitoes (advection), and aquatic-stage mortality due to wind-induced surface waves (waves). The framework was incorporated in a mechanistic malaria transmission simulator, HYDREMATS. The performance of the extended simulator was compared with the observed population dynamics of the Anopheles mosquitoes at a village adjacent to the Koka Reservoir in Ethiopia.
The observed population dynamics of the Anopheles mosquitoes were reproduced with some reasonable accuracy in HYDREMATS that includes the representation of the wind effects. HYDREMATS without the wind model failed to do so. Offshore wind explained the increase in Anopheles population that cannot be expected from other environmental conditions alone.
Around large water bodies such as reservoirs, the role of wind in the dynamics of Anopheles population, hence in malaria transmission, can be significant. Modelling the impacts of wind on the behaviours of Anopheles mosquitoes aids in reproducing the seasonality of malaria transmission and in estimation of the risk of malaria around reservoirs.
Malaria transmission is an intricate function of environment. Alternation in environment may exacerbate malaria risks, with global warming being an example [1–4], and the construction of dam-related reservoirs and irrigated fields being another [5–13]. Understanding the environmental determinants of malaria transmission helps in predicting the seasonality and the future risks of transmission, and hence in designing efficient control programs.
Wind conditions, as well as many other environmental conditions, are likely to influence malaria transmission through the behaviours of Anopheles mosquitoes—the vectors of malaria. The responses of adult mosquitoes to wind have been poorly understood. Controversy over field observations exists regarding mosquitoes’ flight responses; some suggest mosquitoes fly upwind [14, 15], and others downwind [16, 17]. Results from laboratory experiments support upwind flights, especially in the presence of odour and heat, but also in the absence of them [18–20]. Within some tens of meters from human bait, mosquitoes are generally believed to fly upwind guided by \(CO_2\) plume originating from the humans (upwind flight leads mosquitoes towards higher concentration of \(CO_2\)) [21–24]. Downwind flight behavior may be prominent for long-distance migration [16, 25].
The influence of wind on the population of Anopheles mosquitoes may be especially significant around reservoirs . Aquatic-stage mosquitoes that breed at reservoir shorelines face additional mortality through surface waves in reservoirs. Like turbulence during rainstorms, high waves at a reservoir shoreline provide an unfavourable condition for aquatic-stage mosquitoes [5, 27, 28]. Because surface waves become higher in larger and deeper bodies, the mortality from waves is often unique to large water bodies such as reservoirs, but not to small rain-fed puddles.
This paper aims (1) to model the role of wind in the behaviours of Anopheles mosquitoes based on physics and physiology known to date, and (2) to quantify the role of wind using observations. To the best of the authors’ knowledge, no mechanistic model exists that incorporates the effect of wind on malaria transmission, except for site-to-site deductive correlation-based models. The Anopheles population data come from a village adjacent to the Koka Reservoir in Ethiopia . The impacts of wind on mosquitoes behaviours are incorporated in a malaria transmission model, HYDREMATS—one of the most detailed mechanistic malaria models to date . The role of wind in Anopheles population was analysed combining simulations and observations.
The field campaigns span from Jul. 2012 to Apr. 2015, monitoring environmental and entomological conditions . Detailed information on local wind profile (wind speed and wind direction) were obtained from an in situ weather station at 30-min resolution, as well as other climatological data (Fig. 1a–d). The daily water levels of the Koka Reservoir were obtained from the Ethiopian Electric Power Corporation (EEPCo) (Fig. 1e). Anopheles population dynamics were monitored through weekly or bi-weekly adult sampling surveys using six CDC miniature light traps deployed in Ejersa (Fig. 1f).
This area experiences three climatological seasons: a main rainy season from June to September, locally known as Kiremt; a dry season from October to February, Bega; and a secondary rainy season from March to May, Belg (Fig. 1b). During the main rainy season, the temperature becomes lower than the other two seasons (Fig. 1a). Wind profile also shifts between the rainy seasons and the dry season (Fig. 1c, d). The reservoir water levels have the lowest and highest peaks around the beginning and the end of the main rainy seasons (Fig. 1e). The Anopheles population peaks once or twice a year (Fig. 1f). A large increase in population occurs during Sep.–Dec. (hereafter the major mosquito season). A small increase may or may not occur during May.–June (hereafter the minor mosquito season). How the Anopheles population is influenced by the environmental conditions in Ejersa is described in Endo and Eltahir .
Modelling mosquitoes’ flight behaviours
Modelling the role of wind
Three important effects of wind on the behaviours of mosquitoes are modelled: attraction of adult mosquitoes through dispersion of \(CO_2\) (hereafter, \(CO_2\) attraction), advection of adult mosquitoes (hereafter, advection), and aquatic-stage mortality due to wind-induced surface waves (hereafter, waves).
The height of the emission plume (h) was set at 1 m, roughly the level of beds, and the height at which mosquitoes sense the plume (z) at the same height (1 m). The source emission of \(CO_2\) exhaled is set at 275 ml min−1 per human and 3925 ml min−1 per cow . Based on field surveys, it is assumed every household compound contains five humans and one cow. The concentration of \(CO_2\) at each time step in the model domain is calculated as the sum of the contributions of all exhaling members of the community.
The Gaussian model is a well-established time-averaged model of plume dispersion; however, mosquitoes are known to respond to the instantaneous high concentration of \(CO_2\) that is maintained in a pocket of air due to turbulence, rather than the mean concentrations of \(CO_2\) [21, 22]. Because of turbulence, a \(CO_2\) plume is unevenly distributed in the air with some small eddies containing high concentrations of \(CO_2\). Studies with high-resolution measurements observed many-fold higher than mean concentration of \(CO_2\) at a frequency of 0.1 to a few seconds [21, 22]. Simulating this small-scale structure of \(CO_2\) plumes is computationally expensive. Instead, it is assumed that there exist pockets of \(CO_2\) plume with concentration as high as 10 times the concentration simulated in the Gaussian model, and that mosquitoes can respond to the instantaneous burst of \(CO_2\).
As the Gaussian dispersion equation demonstrates, the concentration of \(CO_2\) depends on the source load of \(CO_2\), distance to the source, wind speed, and wind direction. Assuming that Anopheles can sense elevated levels of \(CO_2\) above 40 ppm (simulated mean concentration of 4 ppm), the maximum range over which Anopheles is activated was simulated to be about 100, 50, 30 and 15 m downwind of a house (with five inhabitants and one cow) under 0.5, 1, 2, and 5 m/s of wind, respectively. The effective range of \(CO_2\) activation is believed to be within some tens of meters around a host [21, 34–36]. Considering that the ranges simulated are for a house with multiple hosts, simulated ranges agree with literature values.
Expected wave height at shorelines of the Koka Reservoir is shown in Fig. 2 for u = 0.5 (blue), 1 (red), and 2 m/s (green) and various angles of wind (x-axis). The in situ wind sentry recorded that the daily wind speed in Ejersa varied between 0.5 and 2 m/s in a year. The observed wave heights at the centimetres, which is in good agreement with the predicted results.
Malaria transmission simulator
The role of wind in shaping the behaviours of Anopheles mosquitoes was incorporated in HYDREMATS [26, 32] to test the accuracy of the model, comparing with observations. HYDREMATS is a village-scale malaria transmission model that features explicit representation of evironmental conditions and behaviours of Anopheles mosquitoes in space and time. Its agent-based approach is suitable for employing the role of wind described above. HYDREMATS was tailored for Ejersa (hereafter, Ejersa model) .
In order to examine the role of wind in the dynamics of Anopheles population, the Ejersa model was also forced with fixed wind speed (fixed wspd model) or with random wind direction (random wdir model) instead of respective observational values. In the fixed wspd model, the observed mean wind speed (0.884 m/s) was employed for every timestep (1 h) throughout the simulation period. The impact of wind speed and direction can be understood by the deviation between the Ejersa model and the respective simulation.
Observation of environment and Anopheles population dynamics
Temperature and rainfall are often described as the primary determinants of Anopheles population dynamics [3, 38, 39]; however, in Ejersa, reservoir water levels and wind profile are likely to be more important  (Fig. 1). Around the temperature range in Ejersa (19–24 °C), the expected longevity of Anopheles is not sensitive to temperature [40, 41]. Thus, the influence of temperature on the Anopheles population dynamics is limited. Field observations found a handful of rain-fed puddles in Ejersa, but only a few of them were positive breeding sites. This is because rain-fed puddles rarely persist long enough to support the completion of Anopheles’ aquatic-stage development, which takes around 15–20 days at the cold range of temperature in the field. . The lag in observed Anopheles population dynamics was too large to be explained by the rainfall (Fig. 1b, f). On the other hand, the primary determinant of the Anopheles population was analysed to be the reservoir water levels (Fig. 1e, f), which determine the location of the reservoir shoreline . The shoreline—the main breeding habitat for Anopheles mosquitoes—becomes closer to the village as the reservoir water levels increase, making reproduction more likely.
The observed Anopheles population dynamics during the minor mosquito season (around May, more precisely) were distinctive between 2013 and 2014 (Fig. 1f). The mosquito population increased in 2013 but not in 2014. Neither temperature, rainfall, nor reservoir water level is likely to explain the difference, because the observed data during the same season in the two years were similar. The noticeable differences between the two periods were found only in wind speed and wind direction (Fig. 1c, d, respectively). Whether or not this observational differences in wind profile can explain the observed Anopheles population dynamics during the minor mosquito season are examined mechanistically in the next section.
Simulation of Anopheles population dynamics
The observed Anopheles population increased in May in 2013, but not in 2014 (Fig. 4a, b). This difference was simulated in the Ejersa model, and the simulation results suggest that it is accounted for mostly by the wind direction (Fig. 3). Figure 4 demonstrates that the observed wind direction in the minor mosquito seasons in 2013 worked to enhance mosquito population (c, black) slightly, as compared to an assumed condition with random wind direction (c, blue). The observed wind direction in the minor mosquito season in 2014, on the other hand, worked to suppress mosquito population (d, black), as compared to an assumed condition with random wind direction (d, blue).
The role of wind in mosquito behaviours was modelled based on the physics of \(CO_2\) dispersion and surface waves and on the physiology of mosquitoes. The mosquitoes’ behavioural responses to wind are still not fully understood; however, the model incorporating some of the known effects of wind speed and wind direction was demonstrated to be able to reproduce the observed dynamics of Anopheles population in Ejersa, which was not possible without those wind effects. Thus, the impacts of wind on the mosquitoes’ behavioural responses are believed to be credibly represented in this analysis. Some of the model parameters may still benefit from further calibration. To the best of the authors’ knowledge, HYDREMATS is the only malaria transmission model that mechanistically incorporates the effect of wind.
The effect of wind on the Anopheles population dynamics has received limited attention in the scientific community [20, 21, 23, 24], yet it was shown to have a significant contribution around a reservoir. The importance of wind is expected to be particularly significant around reservoirs for two reasons. The first reason is that the waves created by the wind can become fatal to aquatic-stage mosquitoes at large water bodies. The height of the wave increases with the depth and the fetch (~ surface area) of the reservoir. Thus, waves are more likely to influence Anopheles mosquitoes’ breeding at reservoirs than at small water bodies such as rain-fed pools. The second reason is the heterogeneity in the surrounding environment around reservoirs, where human settlements are located only at one side of the shoreline. Under such environment, the population dynamics of Anopheles mosquitoes are likely to be influenced by the wind direction.
As compared to offshore wind, onshore wind creates larger waves because the fetch is large. Thus, aquatic-stage mosquitoes experience larger mortality, leading to smaller Anopheles populations. In addition, under the onshore wind, a large part of \(CO_2\) plume emanated from the village moves away from the reservoir, which makes mosquitoes emerging at reservoir shorelines less efficient in identifying the direction of the village for host-seeking. Thus, under onshore wind, Anopheles population can further decrease due to limited \(CO_2\) attraction and less efficient host-seeking activity. These two factors conclude that Anopheles populations are generally low under the onshore wind condition.
Wind direction in Ejersa shifts from about 90° north in the dry season to about 220° north in the main rainy season. A gradual shift of wind direction is experienced during the secondary rainy season. The wind from 90° and 220° north corresponds to onshore wind and near-offshore wind for Ejersa. As a results, part of the increase in the Anopheles population during the main rainy season (beginning of the main mosquito season, more specifically) can be explained by the wind blowing from near-offshore (Fig. 3). The difference in the Anopheles population dynamics during the minor rainy season (which almost corresponds to the secondary mosquito season) between 2013 and 2014 can also be explained by the wind direction. In 2013, the shift in wind direction during the minor rainy seasons occurred earlier than in 2014 (Fig. 1), explaining the observed and simulated difference in the Anopheles population dynamics.
The model that replaced the observed wind speed with the averaged wind speed (fixed wind model) consistently simulated smaller Anopheles population than the model with observed wind speed (Ejersa model) throughout a year. This unexpected result can be explained by the fact that Anopheles mosquitoes are modelled to be active only during the night time, and the “average” wind speed averages the observed profile not only over the seasons but also over day and night. The day-time wind speed (~ 1.0 m/s) was larger than the night-time wind speed (~ 0.65 m/s). Thus, the average wind speed was larger than the night-time wind speed. Larger wind speed enhances waves and does not deliver high concentration of \(CO_2\) plume far enough—both mechanisms contribute to decrease the Anopheles population. Thus, the fixed wspd model resulted in consistently smaller Anopheles population than the Ejersa model throughout the simulation period.
Around large water bodies such as reservoirs, the role of wind in Anopheles population dynamics, hence in malaria transmission, can be significant. This paper provided a framework to model the effects of wind in the behaviours of Anopheles mosquitoes. The effects important for Anopheles behaviours include: attraction of adult mosquitoes through dispersion of \(CO_2\), advection of adult mosquitoes, and aquatic-stage mortality due to wind-induced surface waves. Combining simulation studies and observational data of Anopheles population dynamics collected around the Koka Reservoir in Ethiopia, this study demonstrates a substantial role of wind in Anopheles population dynamics—hence the dynamics of malaria transmission. It is suggested that malaria is generally suppressed when wind blows from a reservoir to a village.
NE conceived and conducted the study. EABE supervised the research. NE wrote the manuscript. NE and EABE edited the manuscript. Both authors read and approved the final manuscript.
This work was supported by the U.S. National Science Foundation and by the Cooperative Agreement between the Masdar Institute of Science and Technology (Masdar Institute), Abu Dhabi, UAE and the Massachusetts Institute of Technology (MIT), Cambridge, MA.
The authors declare that they have no competing interests.
Availability of data and materials
All the data used in this study are available upon request.
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Ethics approval and consent to participate
This work was funded by the U.S. National Science Foundation grant EAR-0946280 and by the Cooperative Agreement between the Masdar Institute of Science and Technology (Masdar Institute), Abu Dhabi, UAE and the Massachusetts Institute of Technology (MIT), Cambridge, MA, USA—Reference 02/MI/MI/CP/11/07633/GEN/G/00.
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- Patz JA, Campbell-Lendrum D, Holloway T, Foley JA. Impact of regional climate change on human health. Nature. 2005;438:311–7.View ArticleGoogle Scholar
- Patz JA, Hulme M, Rosenzweig C, Mitchell TD, Goldberg RA, Githeko AK, et al. Climate change: regional warming and malaria resurgence. Nature. 2002;420:627–8.View ArticlePubMedGoogle Scholar
- Yamana TK, Bomblies A, Eltahir EAB. Climate change unlikely to increase malaria burden in West Africa. Nat Clim Chang. 2016;6:1009–13.View ArticleGoogle Scholar
- Zhou G, Minakawa N, Githeko AK, Yan G. Association between climate variability and malaria epidemics in the East African highlands. Proc Natl Acad Sci USA. 2004;101:2375–80.View ArticlePubMedPubMed CentralGoogle Scholar
- U.S. Public Health Service Tennessee Valley Authority. Malaria control on impounded waters. Hawaii: University Press of the Pacific; 1949.Google Scholar
- Jobin W. Dams and diseases: ecological design and health impacts of large dams, canals and irrigation system. London: E & FN Spoon Press; 1999.View ArticleGoogle Scholar
- Sow S, de Vlas SJ, Engels D, Gryseels B. Water-related disease patterns before and after the construction of the Diama dam in northern Senegal. Ann Trop Med Parasitol. 2002;96:575–86.View ArticlePubMedGoogle Scholar
- Keiser J, de Castro MC, Maltese MF, Bos R, Tanner M, Singer BH, Utzinger J. Effect of irrigation and large dams on the burden of malaria on a global and regional scale. Am J Trop Med Hyg. 2005;72:392–406.PubMedGoogle Scholar
- Kibret S, McCartney M, Lautze J, Jayasinghe G. Malaria transmission in the vicinity of impounded water: evidence from the Koka reservoir, Ethiopia. IWMI Research Report 132; 2009.Google Scholar
- Yewhalaw D, Legesse W, van Bortel W, Gebre-Selassie S, Kloos H, Duchateau L, Speybroeck N. Malaria and water resource development: the case of Gilgel-Gibe hydroelectric dam in Ethiopia. Malar J. 2009;8:21.View ArticlePubMedPubMed CentralGoogle Scholar
- Kibret S, Lautze J, McCartney M, Wilson GG, Nhamo L. Malaria impact of large dams in sub-Saharan Africa: maps, estimates and predictions. Malar J. 2015;14:339.View ArticlePubMedPubMed CentralGoogle Scholar
- Castellanos A, Chaparro-Narvàez P, Morales-Plaza CD, Alzate A, Padilla J, Arèvalo M, Herrera S. Malaria in gold-mining areas in Colombia. Memorias do Instituto Oswaldo Cruz. 2016;111:59–66.View ArticlePubMedPubMed CentralGoogle Scholar
- Pommier de Santi V, Girod R, Mura M, Dia A, Briolant S, Djossou F, et al. Epidemiological and entomological studies of a malaria outbreak among French armed forces deployed at illegal gold mining sites reveal new aspects of the disease’s transmission in French Guiana. Malar J. 2016;15:35.View ArticlePubMedGoogle Scholar
- Midega JT, Smith DL, Olotu A, Mwangangi JM, Nzovu JG, Wambua J, et al. Wind direction and proximity to larval sites determines malaria risk in Kilifi District in Kenya. Nat Commun. 2012;3:674.View ArticlePubMedPubMed CentralGoogle Scholar
- Lindsay SW, Armstrong Schellenberg JRM, Zeiler HA, Daly RJ, Salum FM, Wilkins HA. Exposure of Gambian children to Anopheles gambiae malaria vectors in an irrigated rice production area. Med Vet Entomol. 1995;9:50–8.View ArticlePubMedGoogle Scholar
- Gillies MT, Wilkers TJ. Evidence for downwind flights by host-seeking mosquitoes. Nature. 1972;252:388–9.View ArticleGoogle Scholar
- Service MW. Mosquito (Diptera: Culicidae) dispersal—the long and short of it. J Med Entomol. 1997;34:579–88.View ArticlePubMedGoogle Scholar
- Spitzen J, Spoor CW, Grieco F, ter Braak C, Beeuwkes J, van Brugge SP, et al. A 3D analysis of flight behavior of Anopheles gambiae sensu stricto malaria mosquitoes in response to human odor and heat. PLoS ONE. 2013;8:e62995. https://doi.org/10.1371/journal.pone.0062995.View ArticlePubMedPubMed CentralGoogle Scholar
- Dekker T, Carde RT. Moment-to-moment flight manoeuvres of the female yellow fever mosquito (Aedes aegypti L.) in response to plumes of carbon dioxide and human skin odour. J Exp Biol. 2011;214:3480–94.View ArticlePubMedGoogle Scholar
- Healy TP, Copland MJ. Activation of Anopheles gambiae mosquitoes by carbon dioxide and human breath. Med Vet Entomol. 1955;9:331–6.View ArticleGoogle Scholar
- Cardé RT, Willis MA. Navigational strategies used by insects to find distant, wind-borne sources of odor. J Chem Ecol. 2008;34:854–66.View ArticlePubMedGoogle Scholar
- Murlis J, Elkinton JS, Cardé RT, et al. Odor plumes and how insects use them. Ann Rev Entomol. 1992;37:505–32.View ArticleGoogle Scholar
- Sutcliffe JF. Distance orientation of biting ies to their hosts. Insect Sci Its Appl. 1987;8:611–6.Google Scholar
- Takken W, Knols BGJ. Odor-mediated behavior of afrotropical malaria mosquitoes. Ann Rev Entomol. 1999;44:131–57.View ArticleGoogle Scholar
- Lehmann T, Dao A, Yaro AS, Huestis DL, Diallo M, Timbiné S, et al. Phenotypic divergence among the members of the African malaria mosquitoes and strategies of persistence throughout the dry season. Malar J. 2014;13:2.View ArticleGoogle Scholar
- Endo N. Malaria transmission around the Koka Reservoir in Ethiopia: field observations, model predictions, and strategies for prevention. Ph.D. thesis, Massachusetts Institute of Technology. 2017.Google Scholar
- Russell PF, West LS, Manwell RD, Maxwell RD RD, et al. Practical malariology. Oxford: Oxford University Press; 1946.Google Scholar
- Paaijmans KP, Wandago MO, Githeko AK, Takken W. Unexpected high losses of Anopheles gambiae larvae due to rainfall. PLoS ONE. 2007;2:e1146. https://doi.org/10.1371/journal.pone.0001146.View ArticlePubMedPubMed CentralGoogle Scholar
- Reiner RC, Perkins TA, Barker CM, Niu T, Chaves LF, Ellis AM, et al. A systematic review of mathematical models of mosquito-borne pathogen transmission: 1970–2010. Interface J R Soc. 2013;10(81):20120921.View ArticleGoogle Scholar
- Smith M. Recommended guide for the prediction of the dispersion of airborne effluents. New York City: American Society for Mechanical Engineers; 1968.Google Scholar
- Grant AJ, Aghajanian JG, O’Connell RJ, Wigton BE. Electrophysiological responses of receptor neurons in mosquito maxillary palp sensilla to carbon dioxide. J Comp Physiol A. 1995;177:389–96.View ArticlePubMedGoogle Scholar
- Bomblies A, Duchemin J-B, Eltahir EAB. Hydrology of malaria: model development and application to a Sahelian village. Water Resour Res. 2008;44:12445.View ArticleGoogle Scholar
- Kinsman R, Sauer FD, Jackson HA, Wolynetz MS. Methane and carbon dioxide emissions from dairy cows in full lactation monitored over a six-month period. J Dairy Sci. 1995;78:2760–6.View ArticlePubMedGoogle Scholar
- Cardé RT, Gibson G. Host finding by female mosquitoes: mechanisms of orientation to host odours and other cues. In: Takken W, Knols BGJ, editors. Olfaction in vector–host interactions. Ecology and control of vector-borne diseases. Wageningen: Wageningen Academic Publishers; 2010. p. 115–41.Google Scholar
- van Breugel F, Riffell J, Fairhall A, Dickinson MH. Mosquitoes use vision to associate odor plumes with thermal targets. Curr Biol. 2015;25:2123–9.View ArticlePubMedPubMed CentralGoogle Scholar
- Gillies MT. The role of carbon dioxide in host-finding by mosquitoes (Diptera: Culicidae): a review. Bull Entomol Res. 1980;70:525–32.View ArticleGoogle Scholar
- US Army Corps of Engineers, Coastal Engineering Research Center. Shore protection manual: volume I. Technical report. 1984.Google Scholar
- Craig M, Le Sueur D, Snow B. A climate-based distribution model of malaria transmission in sub-Saharan Africa. Parasitol Today. 1999;15:105–11.View ArticlePubMedGoogle Scholar
- Ermert V, Fink AH, Jones AE, Morse AP. Development of a new version of the Liverpool Malaria Model. I. Refining the parameter settings and mathematical formulation of basic processes based on a literature review. Malar J. 2011;10:35.View ArticlePubMedPubMed CentralGoogle Scholar
- Martens WJ. Health impacts of climate change and ozone depletion: an ecoepidemiologic modeling approach. Ph.D. thesis, Maastricht University, Maastricht, Netherland. 1997.Google Scholar
- Parham PE, Pople D, Christiansen-Jucht C, Lindsay S, Hinsley W, Michael E. Modeling the role of environmental variables on the population dynamics of the malaria vector Anopheles gambiae sensu stricto. Malar J. 2012;11:271.View ArticlePubMedPubMed CentralGoogle Scholar