Advertisement
Browse Subject Areas
?

Click through the PLOS taxonomy to find articles in your field.

For more information about PLOS Subject Areas, click here.

  • Loading metrics

ANOSPEX: A Stochastic, Spatially Explicit Model for Studying Anopheles Metapopulation Dynamics

  • Olugbenga O. Oluwagbemi,

    Affiliations W. Harry Feinstone Department of Molecular Microbiology and Immunology and the Johns Hopkins Malaria Research Institute, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland, United States of America, Department of Computer and Information Sciences, College of Science and Technology, School of Natural and Applied Sciences, Covenant University, Ota, Ogun State, Nigeria

  • Christen M. Fornadel,

    Affiliation W. Harry Feinstone Department of Molecular Microbiology and Immunology and the Johns Hopkins Malaria Research Institute, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland, United States of America

  • Ezekiel F. Adebiyi,

    Affiliation Department of Computer and Information Sciences, College of Science and Technology, School of Natural and Applied Sciences, Covenant University, Ota, Ogun State, Nigeria

  • Douglas E. Norris,

    Affiliation W. Harry Feinstone Department of Molecular Microbiology and Immunology and the Johns Hopkins Malaria Research Institute, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland, United States of America

  • Jason L. Rasgon

    jlr54@psu.edu

    Affiliation The Department of Entomology, Center for Infectious Disease Dynamics and Huck Institutes of the Life Sciences, Pennsylvania State University, University Park, Pennsylvania, United States of America

ANOSPEX: A Stochastic, Spatially Explicit Model for Studying Anopheles Metapopulation Dynamics

  • Olugbenga O. Oluwagbemi, 
  • Christen M. Fornadel, 
  • Ezekiel F. Adebiyi, 
  • Douglas E. Norris, 
  • Jason L. Rasgon
PLOS
x

Abstract

Anopheles mosquitoes transmit malaria, a major public health problem among many African countries. One of the most effective methods to control malaria is by controlling the Anopheles mosquito vectors that transmit the parasites. Mathematical models have both predictive and explorative utility to investigate the pros and cons of different malaria control strategies. We have developed a C++ based, stochastic spatially explicit model (ANOSPEX; Anopheles Spatially-Explicit) to simulate Anopheles metapopulation dynamics. The model is biologically rich, parameterized by field data, and driven by field-collected weather data from Macha, Zambia. To preliminarily validate ANOSPEX, simulation results were compared to field mosquito collection data from Macha; simulated and observed dynamics were similar. The ANOSPEX model will be useful in a predictive and exploratory manner to develop, evaluate and implement traditional and novel strategies to control malaria, and for understanding the environmental forces driving Anopheles population dynamics.

Introduction

Human malaria is one of the most important public health problems in many African countries, associated with high rates of mortality and morbidity. The disease presents with a spectrum of systemic complications ranging from mild and self-limiting illness to life-threatening pathology. Malaria incidence has increased in many areas of the African continent due to climate change, insecticide and drug resistance, and social/economic issues [1][4].

As an infectious disease, malaria is transmitted through the bite of infected female Anopheles mosquitoes. Thus, one of the most effective methods to control the disease is by controlling the mosquito vectors. Despite concerted efforts by governmental agencies, public and private non-governmental researchers and other relevant health agencies to offer effective control strategies, malaria still persists in many endemic regions of the world. Thus, there is an urgent need for the development and implementation of existing and novel malaria vector control interventions. Mathematical models are a crucial part of developing and optimizing control techniques, since they are one of the only ways to optimize deployment and conduct risk-assessment prior to an actual intervention attempt [5][7].

Mathematical modeling is crucial to understanding Anopheles population and transmission dynamics for developing strategies for disease control [8]. For over 100 years, models have been developed and applied towards the control of malaria, mosquitoes and mosquito-borne related diseases, ranging from simple models of vectorial capacity to complex predictive models of malaria epidemiology [9][17].

The most detailed individual-based models of mosquito populations have been developed for Aedes aegypti. Focks and colleagues developed the Container Inhabiting Mosquito Simulation Model (CIMSiM), a deterministic simulation model that is driven by empirical weather data and incorporates very detailed aspects of mosquito biology [18][19]. Although CIMSiM has shown utility in predicting mosquito dynamics in nature [20], it has several limitations: (1) it ignores stocasticity in the data, (2) it assumes a single panmictic mosquito population, and (3) it is written in VisualBasic which is not easily compilable on newer computers [21]. To address these issues, Magori and colleagues developed the SkeeterBuster model. SkeeterBuster shares many algorithms with CIMSiM (and in fact can recapitulate it exactly) but it is written C++, is stochastic and spatially explicit [21]. SkeeterBuster operates at the scale of individual water-filled containers for immature stages and individual properties (houses) for adults. SkeeterBuster also incorporates mosquito genetics [21].

Multiple simulation models of Anopheles population dynamics have been developed [22][28]. However, these models have their limitations. For instance, the Anopheles model developed by Depinay and colleagues [23] does not explicitly incorporate mating between male and female Anopheles gambiae mosquitoes and was not validated against field data. The models developed by Eckhoff [27] and White et al [28] did not present spatially explicit simulations. Arifin and colleagues [29] developed a detailed spatial agent-based model to show the influence of resources on mosquito populations. However, this model was not driven by empirical weather data, nor was it validated against field observations.

To address some of these issues, we developed a stochastic, spatially explicit model of Anopheles metapopulation dynamics. We call this model ANOSPEX, for “Anopheles Spatially-Explicit”. ANOSPEX is biologically rich, driven by empirical weather data, and parameterized by field data to simulate Anopheles metapopulation dynamics. Simulation results from ANOSPEX were preliminarily validated post-hoc using empirical Anopheles adult female collection data from Macha, Zambia.

Methods

ANOSPEX Overview

ANOSPEX was written in C++ and Visual C++ programming languages on an Intel Pentium i5 Computing system running Windows 7. The ANOSPEX codes are a combination of new codes and codes implemented from Skeeterbuster. Parameters used in ANOSPEX were derived from literature whenever possible (Table S1). We modeled stochasticity in the same way as SkeeterBuster [18]; ANOSPEX is not deterministic. Also like SkeeterBuster, ANOSPEX is weather-driven. Hourly weather data (2009–2011) were obtained from the Malaria Institute at Macha (MIAM), Zambia. Weather parameters used in the model were maximum temperature, minimum temperature, average temperature, precipitation, saturation deficit and relative humidity. ANOSPEX does not include mosquito genetics, only mosquito metapopulation dynamics. ANOSPEX is implemented as a grid representation of residential properties, where each property has one house and two larval habitats for mosquitoes to develop in. Adult mosquitoes can move from one property to another property as described below. For simulations, breeding habitats were initially seeded with 25 eggs. References for parameter values are available as supplementary material.

Model Development and Metapopulation Dynamics of Immature and Adult Anopheles Mosquitoes

The diagram in Figure 1 shows the schematic container model of Anopheles lifecycle and development for ANOSPEX.

Egg Phase

An important aspect of the African Anopheles ecology is the egg phase [21]. Important factors that affect the hatching and survival of Anopheles eggs include predation, water and air temperatures, sun exposure, and water depth of the breeding containers [21], [24], [30][32]. The prominent role temperature plays in Anopheles egg development cannot be over-emphasized [31], [37][41]. All malaria vectors are poikilothermic in nature [33]. In ANOSPEX, we applied the enzyme kinetics model derived by Sharpe and DeMichele [34], which is based on the absolute rate of reaction of enzymes for temperature-dependent developmental rates [18], [21], [36], [42][43].

In ANOSPEX, for Anopheles eggs to successfully hatch, the average water temperature has to be above 21°C and eggs have to be consistently immersed in water [31]. If the water within the container is below the average hatching temperature or the eggs are not immersed they will not hatch [44]. If eggs are mature and immersed, eggs hatch [35] according to the enzyme kinetics model (eq. 1) [18], [21], [34], [36]. The fundamental assumption is that a single control enzyme regulates poikilothermic development and the reaction rate of this enzyme affects and determines the rate of development of the organism (here, Anopheles) [34], [36], [45], [46].(1)

r(T) is the rate of development per hour at temperature T(°K). is the developmental rate per hour at 25°C. represents the enthalpy of activation of the reaction catalyzed by the enzyme (cal·mol-1); is the low temperature inactivation enthalpy change associated with the enzyme (cal·mol-1); represents the temperature in °K where 50% of the enzyme is inactivated by low temperature. is the high temperature inactivation enthalpy change associated with the enzyme (cal·mol-1); is the temperature in °K where 50% of the enzyme is inactivated by high temperature. R is the universal gas constant, with a value of (1.987cal·mol-1) [18], [21], [34], [36], [47]. The set of parameter values obtained from [21] was applied to the egg phase modeling within ANOSPEX:  = 0.0413;  = 1.0000;  = −170644;  = 288.8;  = 1000000; and  = 313.3.

The egg hatch algorithm within sites is shown in Figure S1.

Larval Phase

The development rate and survival of Anopheles larvae is dependent on water temperature [48], implying that the Anopheles larvae phase also depends on the enzyme kinetic equation (eq. 1) for development [21]. The set of parameter values obtained from [21] was applied to the larval phase modeling within ANOSPEX;  = 0.037;  = 15684;  = −229902;  = 286.4;  = 822285; and  = 310.3. Other factors within an African locality context, such as land cover types and topography [49], habitat types [49][53], predators [53][57], food availability [58], competition [59][60] and desiccation [61][65] also affect the development, survival and distribution of Anopheles larvae within their habitats.

In ANOSPEX, there are two conditions that Anopheles larvae must meet before pupating. First, larvae must attain complete physiological maturity. In ANOSPEX, larvae attain physiological maturity if their cumulative development exceeds a threshold value (eq. 2). The second condition is that developed Anopheles larvae attain pupation only if they have attained a sufficient weight worthy of them pupating. Anopheles larvae undergo a developmental cycle based on the enzyme kinetic equation as illustrated in eq.1 until they attain 4th instar [18], [21].

The algorithm governing the development of Anopheles larvae within containers is depicted in the flowchart in Figure S2. For a given cohort of age n at time t, the cumulative physiological development CDt is given by equation 2 [15], [16], [18]:(2)

In ANOSPEX, we assumed that the probability of larval development is a function of the total physiological development. Thus, no larvae matured below a total physiological development of 0.92 and above 1.20 respectively [18]. Setting these conditions allows certain portions of the Anopheles larval cohort to achieve maturity at a lower cumulative development, while rest achieve higher than the mean date of physiological maturation before being developed.

In ANOSPEX, food intake by Anopheles larvae contributes to the increase in individual and collective larval weight. Food intake was based on an average of 3-day food intake plus random food intake by the Anopheles larvae [66][67]. The dynamics of the amount of Anopheles larval food in a breeding site and the larvae cohort weight are governed by equations adapted from CIMSiM [15], [68].

Daily survival rates for Anopheles eggs, larvae, pupae and adults were determined and estimated from the literature (Table S1). Larvae that die are converted into biomass as larval food. We estimated the value of this parameter with a 0.40 conversion factor [58], [69].

Pupation Phase

Anopheles pupation was modeled as in CIMSiM and SkeeterBuster [15][16], [18]. Developing Anopheles larvae have to achieve a specific weight at maturation to successfully transit into the pupae phase. Temperature and the cumulative physiological development of Anopheles larvae are two factors that affect the transit into the pupae phase. The set of parameter values obtained from [21] was applied to the pupae phase modeling within ANOSPEX; the values of  = 0.034;  = 1.0000;  = −154394;  = 313.8;  = 554707; and  = 313.8.

The model flowchart for the pupae phase is shown in Figure S3. Completion of the Anopheles pupae developmental phase occurs as soon as Anopheles pupae attain complete maturation. We assumed that the maturation probability for an Anopheles pupa was a function of its total physiological development. We assumed that no pupa attains maturity below a total physiological development value of 0.92 while all pupae above 1.20 attain maturity. The survival of Anopheles pupae in ANOSPEX model depends on temperature. Dead Anopheles pupae are converted into biomass for food, with a conversion rate of 0.40 [58], [69].

Adult Phase

The emergence of adult Anopheles from their pupal case leads into the adult phase of the Anopheles life cycle. Anopheles pupae that successfully enter into this phase further develop into male and female Anopheles adults. Both male and female Anopheles adult mosquitoes can undergo mortality due to extreme conditions from the local environment.

Female adult Anopheles mosquitoes’ gonotrophic development was also modeled based on the enzyme kinetics equation outlined above [18], [21], [34], [36]. The set of parameter values obtained from [21] was applied to the female adult gonotrophic phase modeling within ANOSPEX; the values of  = 0.02;  = 1000;  = −75371;  = 293.1;  = 388691; and  = 313.4.

The algorithm governing the development of Anopheles male and female adult development within containers is depicted in the flowcharts of Figures S4 and S5 respectively. We assumed unrestricted access of female adult Anopheles to blood, and the availability and homogeneity of hosts. Female Anopheles adults were assumed to oviposit after the completion of their gonotrophic cycle.

Adult Mosquito Movement

Anopheles mosquito movements were modeled by adapting knowledge gained from cellular automata, by using the Von Neumann neighborhood algorithm [70][72], where for each dispersing adult Anopheles mosquito there is a random selection of one of the possible four directions. Each residential property on the grid is represented by the coordinates . Distance between one residential property and the other is represented by . In ANOSPEX, we estimated that each adult Anopheles has a short-range dispersal probability of 0.35 [73][75]. We also applied the boundary assumptions adopted in the SkeeterBuster model [18].

Field Survey and Preliminary Model Validation

We validated ANOSPEX by comparing predicted numbers of female Anopheles against mosquito capture data from Macha, Zambia. The choice of Macha, Zambia as a study location for our experiment was made because of the availability of hourly weather data from MIAM (Johns Hopkins Malaria Institute at Macha) that was coincident with previously published mosquito collection data (February–April 2009) (CDC traps, cattle-baited traps, and human landing captures [76].

Results

Mosquito Population Dynamics

The total number of adult mosquitoes (males, nulliparous females and parous females) over a 10×10 grid was simulated over a one-year period to evaluate the role of weather in governing mosquito population dynamics. ANOSPEX captures the weather-driven dynamics and shows, unsurprisingly, that mosquito population numbers peak during the rainy season, reach an approximate equilibrium level, then crash during the dry season (Figure 2).

thumbnail
Figure 2. Simulation run results for Anopheles adult dynamics over a 10X10 grid.

Letters represent the first letter of the months of the year.

https://doi.org/10.1371/journal.pone.0068040.g002

Mosquito Dispersal

ANOSPEX simulates mosquito population dynamics across a grid of residential properties. Mosquito numbers within a property are a product of local production (driven by weather) and dispersal of adults into and out of the property. Figure 3 shows an example of this dynamic for female adult Anopheles in a 100-property grid (10×10) from the onset to the peak of the wet season (November – March). Mosquito numbers within and between properties change due to reproduction, death and migration.

thumbnail
Figure 3. Simulation run results for Anopheles female adult dynamics over a 10×10 grid from the onset to the peak of the wet season.

First box represents initial pupal distribution among properties.

https://doi.org/10.1371/journal.pone.0068040.g003

Preliminary Model Validation

Model validation is critical to ascertaining the utility of a predictive model. In order to validate ANOSPEX, we compared model predictions from a 25-property grid (5×5) to empirical adult female Anopheles mosquito collection numbers from the Johns Hopkins Malaria Institute at Macha during the time period of February 1 to April 10, 2009 [76]. ANOSPEX was driven by empirical weather data for this same time period. Since ANOSPEX simulates adult numbers but does not distinguish particular habitats, we pooled data from CDC light traps, cattle-baited traps, and human landing catches (both inside and outside houses).

While the overall number of mosquitoes differed significantly between predicted and empirical results, the trends were similar (Figure 4A). This is to be expected, since ANOSPEX simulates total mosquito numbers, while the collection data represented that fraction of the mosquito population that was captured, and simulations were carried out over a 5×5 grid that may not accurately reflect the geographic size of the natural habitat. Nevertheless, ANOSPEX performed well at capturing the overall mosquito population dynamics, as both the predicted and empirical mosquito numbers change by approximately the same magnitude (Figure 4). The correlation between model predicted and empirical results was highly significant (P<0.0001), with an R2 of 0.53 (Figure 4B).

thumbnail
Figure 4. Preliminary ANOSPEX validation.

A: Predicted numbers of female adult Anopheles arabiensis mosquitoes were compared to empirical mosquito collection data from Macha, Zambia [76]. B: Correlation between predicted and empirical results.

https://doi.org/10.1371/journal.pone.0068040.g004

Discussion

From an applied standpoint, many novel vector control strategies (such as release of genetically modified mosquitoes) cannot be empirically tested under true field conditions before an actual intervention attempt. Mathematical models are a crucial first step to assess control strategies for safety and efficacy prior to implementation. Models are also useful for improving the implementation of traditional control measures. From a basic standpoint, models are useful for investigating the environmental factors that govern mosquito population dynamics.

The most detailed models of mosquito population dynamics have been previously developed for Aedes aegypti. Similar models for Anopheles mosquitoes are needed, especially in light of recent interest in novel strategies for control of malaria. ANOSPEX is a flexible model that can be customized to fit any area of interest, by modifying the underlying property setup and weather files. As currently coded, ANOSPEX simulations will be exceeding useful for examining the control strategies based on population suppression, such as insecticide usage [77][81], RIDL (Release of Insects carrying a Dominant Lethal) [82][87] habitat modification [88][89], or lethal densovirus [90][92]. ANOSPEX will also be useful to examine the impact of environmental change on mosquito population dynamics. ANOSPEX currently lacks a mosquito genetics component, but this could easily be added to investigate population replacement strategies based on genetic modification or Wolbachia symbionts [93][95].

Model Limitations

It has been said, “all models are wrong, but some are useful” [96]. ANOSPEX is no exception. ANOSPEX results are based on the complex interaction of many parameters, all with varying degrees of uncertainty. It is likely that we have overemphasized the impact of some parameters, while possibly missing others that are important. Sensitivity analysis of model parameters will help to refine model results. Nevertheless, our preliminary validation results indicate that ANOSPEX can provide a reasonable description of the dynamics of Anopheles populations. As ANOSPEX is further developed and refined, it will be a useful tool to understand Anopheles population dynamics and develop malaria control strategies.

Supporting Information

Figure S1.

Daily egg hatching flowchart for hatch probabilities within containers.

https://doi.org/10.1371/journal.pone.0068040.s001

(PDF)

Figure S2.

Anopheles larvae development flowchart.

https://doi.org/10.1371/journal.pone.0068040.s002

(PDF)

Figure S3.

Flowchart for emergence probabilities of Anopheles pupae within a container.

https://doi.org/10.1371/journal.pone.0068040.s003

(PDF)

Figure S4.

Flowchart for Anopheles male adult development.

https://doi.org/10.1371/journal.pone.0068040.s004

(PDF)

Figure S5.

Flowchart for Anopheles female adult development.

https://doi.org/10.1371/journal.pone.0068040.s005

(PDF)

Table S1.

References for parameter values used in simulations.

https://doi.org/10.1371/journal.pone.0068040.s006

(XLS)

Acknowledgments

We thank Dr. Mathieu Legros for kindly providing SkeeterBuster codes.

Author Contributions

Conceived and designed the experiments: OOO JLR EFA. Performed the experiments: OOO. Analyzed the data: OOO JLR. Contributed reagents/materials/analysis tools: CMF DEN. Wrote the paper: OOO JLR.

References

  1. 1. Greenwood B, Mutabingwa T (2002) Malaria in 2002. Nature 415: 670–672.
  2. 2. Mugittu K, Genton B, Mshinda H, Beck HP (2006) Molecular monitoring of Plasmodium falciparum resistance to artemisinin in Tanzania. Malaria Journal 5: 126.
  3. 3. Roper C, Pearce R, Nair S, Sharp B, Nosten F, et al. (2004) Intercontinental spread of pyrimethamine-resistant malaria. Lancet 305: 1123–1124.
  4. 4. Sachs J, Malaney P (2002) The economic and social burden of malaria. Nature 415: 680–685.
  5. 5. Axtell R, Axelrod R, Epstein J, Cohen M (1996) Aligning simulation models: A case study and results. Computational and Mathematical Organization Theory 1: 123–141.
  6. 6. Wilensky U, Rand W (2007) Making models match: Replicating an agent-based model. Journal of Artificial Societies and Social Simulation 10: 1–22.
  7. 7. Purchase S, Olaru D, Denize S (2008) Exploring innovation networks: two simulations, two perspectives and the mechanisms that drive innovation performance. IMP conference Proceedings, Uppsala.
  8. 8. McKenzie FE (2000) Why model malaria? Parasitology Today. 16: 511–517.
  9. 9. Ross R (1911) The Prevention of Malaria, 2nd edition. London, John Murray.
  10. 10. Ross R (1928) Studies on Malaria. London, John Murray.
  11. 11. Macdonald G (1952) The analysis of equilibrium in malaria. Tropical Disease Bulletin. 49: 813–829.
  12. 12. Macdonald G (1957) The epidemiology and control of malaria. Oxford Univ. Press; London.
  13. 13. Garrett-Jones C, Grab B (1964) The assessment of insecticidal impact on the malaria mosquito’s vectorial capacity, from data on the proportion of parous females. Bulletin of the World Health Organization. 31: 71–86.
  14. 14. Cuellar CB (1969) A theoretical model of the dynamics of an Anopheles gambiae population under challenge with eggs giving Rrse to sterile males. Bulletin of the World Health Organization. 40: 205–212.
  15. 15. Dietz K, Molinaux L, Thomas A (1974) A malaria model tested in the African savannah, Bullettin of the World Health Organization. 50: 347–357.
  16. 16. Seawright JA, Haile DG, Rabbani MG, Weidhaas DE (1979) Computer simulation of the effectiveness of male-linked translocations for the control of Anopheles albimanus Wiedemann. The American Journal of Tropical Medicine and Hygiene 28: 155–160.
  17. 17. Molineaux L, Gramiccia G (1980) The Garki project. Geneva: World Health Organization.
  18. 18. Focks DA, Haile DG (1993a) Dynamic life table model of a container-inhabiting mosquito, Aedes aegypti(L.) (Diptera:Culicidae). Part 1. Analysis of the literature and model development. Journal of Medical Entomology 30: 1003–1017.
  19. 19. Focks DA, Haile DG (1993b) Dynamic life table model of a container-inhabiting mosquito, Aedes aegypti (L.) (Diptera: Culicidae). Part 2. Simulation results and validation. Journal of Medical Entomology 30: 1018–1028.
  20. 20. Williams CR, Johnson PH, Long SA, Rapley LP, Ritchie SA (2008) Rapid estimation of Aedes aegypti population size using simulation modeling, with a novel approach to calibration and field validation. Journal of Medical Entomology 45: 1173–1179.
  21. 21. Magori K, Legros M, Puente ME, Focks DA, Scott TW, et al. (2009) SkeeterBuster: A stochastic, spatially explicit modeling tool for studying Aedes aegypti population replacement and population suppression strategies. PLoS Neglected Tropical Diseases 3: e508.
  22. 22. Hoshen MB, Morse AP (2004) A weather-driven model of malaria transmission, Malaria Journal. 3: 32.
  23. 23. Knols BGJ, Njiru BN, Mathenge EM, Mukabana WR, Beier JC, et al. (2002) MalariaSphere: A greenhouse-enclosed simulation of a natural Anopheles gambiae (Diptera: Culicidae) ecosystem in western Kenya. Malaria Journal 1: 19.
  24. 24. Depinay JMO, Mbogo CM, Killeen G, Knols B, Beier J, et al. (2004) A simulation model of African Anopheles ecology and population dynamics for the analysis of malaria transmission. Malaria Journal 3: 29.
  25. 25. Ermert V, Fink AH, Jones AE, Morse AP (2011a) 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. Malaria Journal 10: 35.
  26. 26. Ermert V, Fink AH, Jones AE, Morse AP (2011b) Development of a new version of the Liverpool Malaria Model. II. Calibration and validation for West Africa. Malaria Journal 10: 62.
  27. 27. Eckhoff PA (2011) A malaria transmission-directed model of mosquito life cycle and ecology. Malaria Journal 10: 303.
  28. 28. White MT, Griffin JT, Churcher TS, Ferguson NM, Basáñez M, et al. (2011) Modeling the impact of vector control interventions on Anopheles gambiae population dynamics. Parasites & Vectors 4: 153.
  29. 29. Arifin SMN, Davis GJ, Zhou Y (2011) A spatial agent-based model of malaria: Model verification and effects of spatial heterogeneity. International Journal of Agent Technologies and Systems 3: 1–18.
  30. 30. Munga S, Minakawa N, Zhou G, Barrack OJ, Githeko AK, et al. (2005) Oviposition site preference and egg hatchability of Anopheles gambiae: Effects of land cover types. Journal of Medical Entomology 42: 993–997.
  31. 31. Impoinvil DE, Cardenas GA, Gihture JI, Mbogo CM, Beier JC (2007) Constant temperature and time period effects on Anopheles gambiae egg hatching. Journal of the American Mosquito Control Association 23: 124–30.
  32. 32. Yaro AS, Dao A, Adamou A, Crawford JE, Ribeiro JMC, et al. (2006) The distribution of hatching time in Anopheles gambiae. Malaria Journal 5: 19.
  33. 33. Jepson WF, Moutia A, Courtois C (1947) The malaria problem in Mauritius: The bionomics of Mauritian anophelines. Bulletin of Entomological Research 38: 177–208.
  34. 34. Sharpe PJH, DeMichelle DW (1977) Reaction kinetics of poikilotherm development. Journal of Theoretical Biology 64: 649–670.
  35. 35. Olayemi IK, Ande AT (2009) Life table analysis of Anopheles gambiae (Diptera: Culicidae) in relation to malaria transmission. Journal of Vector Borne Diseases 46: 295–298.
  36. 36. Schoolfield RM, Sharpe PJH, Magnuson CE (1981) Non-linear regression of biological temperature-dependent rate models based on absolute reaction-rate theory. Journal of Theoretical Biology 88: 719–731.
  37. 37. Ward JV, Stanford JA (1982) Thermal responses in the evolutionary ecology of aquatic insects. Annual Review of Entomology 27: 97–117.
  38. 38. Omlin FX, Carlson JC, Ogbunugafor CB, Hassanali A (2007) Anopheles gambiae exploits the treehole ecosystem in western Kenya: A new urban malaria risk? American Journal of Tropical Medicine and Hygiene 77: 264–269.
  39. 39. Dhiman RC, Pahwa S, Dash AP (2008) Climate change and malaria in India: Interplay between temperatures and mosquitoes. Regional Health Forum 12: 27–31.
  40. 40. Macan TT (1961) Factors that limit the range of freshwater animals. Biological Reviews 36: 151–195.
  41. 41. Becker N (2008) Influence of climate change on mosquito development and mosquito-borne diseases in Europe. Parasitology Research 103(Suppl (1)) 19–28.
  42. 42. Kavanau JL (1950) Enzyme kinetics and the rate of biological processes. The Journal of General Physiology 34: 193–209.
  43. 43. Yurista PM (1999) A model for temperature correction of size-specific respiration in Bythotrephes cederstroemi and Daphnia middendorffiana. Journal of Plankton Research 21: 721–734.
  44. 44. Gahan JB, Smith CN (1964) Problems connected with raising mosquitos in the laboratory. Bulletin of the World Health Organization 31: 445–448.
  45. 45. Behrisch HW (1969) Temperature and the regulation of enzyme activity in Poikilotherms. Biochemical Journal 115: 687–696.
  46. 46. Irlich UM, Terblanche JS, Blackburn TM, Chown SL (2009) Insect rate-temperature relationships: Environmental variation and the metabolic theory of ecology. The American Naturalist 174: 819–835.
  47. 47. Richards AG (1964) The generality of temperature effects on developmental rate and on oxygen consumption in insect eggs. Physiological Zoology 37: 199–211.
  48. 48. Kirby MJ, Lindsay SW (2009) Effect of temperature and inter-specific competition on the development and survival of Anopheles gambiae sensu stricto and Anopheles arabiensis larvae. Acta Tropica 109: 118–123.
  49. 49. Tuno N, Okeka W, Minakawa N, Takagi M, Yan G (2005) Survivorship of Anopheles gambiae sensu stricto (Diptera: Culicidae) Larvae in Western Kenya Highland Forest. Journal of Medical Entomology 42: 270–277.
  50. 50. Gimnig JE, Ombok M, Kamau L, Hawley WA (2001) Characteristics of larval Anopheline (Diptera: Culicidae) habitats in western Kenya. Journal of Medical Entomology 38: 282–288.
  51. 51. Mwangangi JM, Shililu J, Muturi EJ, Muriu S, Jacob B, et al. (2010) Anopheles larval abundance and diversity in three rice agro-village complexes Mwea irrigation scheme, central Kenya. Malaria Journal 9: 228.
  52. 52. Sattler MA, Mtasiwa D, Kiama M, Premji Z, Tanner M, et al. (2005) Habitat characterization and spatial distribution of Anopheles sp. mosquito larvae in Dar es Salaam (Tanzania) during an extended dry period. Malaria Journal 4: 4.
  53. 53. Service MW (1973) Mortalities of the larvae of the Anopheles gambiae Giles complex and detection of predators by the precipitin test. Bulletin of Entomological Research 62: 359–369.
  54. 54. Louca V, Lucas MC, Green C, Majambere S, Fillinger U, et al. (2009) Role of fish as predators of mosquito larvae on the floodplain of the Gambia river. Journal of Medical Entomology 46: 546–556.
  55. 55. Munga S, Minakawa N, Zhou G, Barrack OO, Githeko AK, et al. (2006) Effects of larval competitors and predators on pviposition site selection of Anopheles gambiae sensu stricto, Journal of Medical Entomology. 43: 221–224.
  56. 56. Mogi M (2007) Insects and other invertebrate predators, Journal of the American Mosquito Control Association. 23: 93–109.
  57. 57. Diabaté A, Dabiré RK, Heidenberger K, Crawford J, Lamp WO, et al. (2008) Evidence for divergent selection between the molecular forms of Anopheles gambiae: role of predation. BMC Evolutionary Biology 8: 5.
  58. 58. Kaufman MG, Wanja E, Maknojia S, Bayoh MN, Vulule JM, et al. (2006) Importance of algal biomass to growth and development of Anopheles gambiae Larvae. Journal of Medical Entomology 43: 669–676.
  59. 59. Paaijmans KP, Huijben S, Githeko AK, Takken W (2009) Competitive interactions between larvae of the malaria mosquitoes Anopheles arabiensis and Anopheles gambiae under semi-field conditions in western Kenya. Acta Tropica 109: 124–130.
  60. 60. Schneider P, Takken W, Mccall PJ (2000) Interspecific competition between sibling species larvae of Anopheles arabiensis and Anopheles gambiae. Medical and Veterinary Entomology 14: 165–170.
  61. 61. Kessler S, Guerin PM (2008) Responses of Anopheles gambiae, Anopheles stephensi, Aedes aegypti, and Culex pipiens mosquitoes (Diptera: Culicidae) to cool and humid refugium conditions. Journal of Vector Ecology 33: 145–149.
  62. 62. Benedict MQ, Sandve SR, Wilkins EE, Roberts JM (2010) Relationship of larval desiccation to Anopheles gambiae Giles and Anopheles arabiensis Patton survival. Journal of Vector Ecology 35: 116–123.
  63. 63. Lee Y, Meneses CR, Fofana A, Lanzaro GC (2009) Desiccation resistance among subpopulations of Anopheles gambiae s.s. From Selinkenyi, Mali. Journal of Medical Entomology 46: 316–320.
  64. 64. Goltsev Y, Rezende GL, Vranizan K, Lanzaro G, Valle D, et al. (2009) Developmental and evolutionary basis for drought tolerance of the Anopheles gambiae embryo. Developmental Biology 30: 462–470.
  65. 65. Aboagye-Antwi F, Tripet F (2010) Effects of larval growth condition and water availability on desiccation resistance and its physiological basis in adult Anopheles gambiae sensu strictu. Malaria Journal 9: 225.
  66. 66. Dominic AD, Sivagnaname N, Das PK (2005) Effect of food on immature development, consumption rate, and relative growth rate of Toxorhynchites splendens (Diptera: Culicidae), a predator of container breeding mosquitoes. Memórias do Instituto Oswaldo Cruz 100: 893–902.
  67. 67. Aly C, Mulla MS (1986) Orientation and ingestion rates of larval Anopheles albimanus in response to floating particles. Entomologia Experimentalis et Applicata 42: 83–90.
  68. 68. Gilpin MEC, McClelland GAH (1979) Systems-analysis of the yellow fever mosquito Aedes aegypti. Forts Zool 25: 355–388.
  69. 69. Cloern JE, Grenz C, Vidergar-Lucas L (1995) An empirical model of the phytoplankton chlorophyll: Carbon ratio - the conversion factor between productivity and growth rate. Limnology and Oceanography 40: 1313–1321.
  70. 70. von Neumann J (1950) Functional Operators Vol. II, Princeton University Press.
  71. 71. Franchetti C, Light W (1986) On the von Neumann algorithm in Hilbert Space. Journal of Mathematical Analysis and Applications 114: 305–314.
  72. 72. Bauschke HH, Borwein JM (1993) On the convergence of von Neumann’s alternating projection algorithm for two sets. Set-Valued Analysis 1: 185–212.
  73. 73. Gillies MT (1961) Studies on the dispersion and survival of Anopheles gambiae Giles in East Africa, by means of marking and release experiments. Bulletin of Entomological Research 52: 99–127.
  74. 74. Baber I, Keita M, Sogoba N, Konate M, Diallo M, et al. (2010) Population size and migration of Anopheles gambiae in the Bancoumana region of Mali and their significance for efficient vector control. PLoS ONE 5(4): e10270.
  75. 75. Silver JB (2008) Mosquito ecology: field sampling methods, 3rd Edition, Chapter 15, Measuring Adult Dispersal.
  76. 76. Fornadel CM, Norris LC, Norris DE (2010) Centers for Disease Control light traps for monitoring Anopheles arabiensis human biting rates in an area with low vector density and high insecticide-treated bed net use. American Journal of Tropical Medicine and Hygiene 83: 838–842.
  77. 77. Curtis CF (1985) Theoretical models of the use of insecticide mixtures for the management of resistance. Bulletin of Entomological Research 75: 259–266.
  78. 78. Asidi AN, N’Guessan R, Koffi AA, Curtis CF, Hougard JM, et al. (2005) Experimental hut evaluation of bednets treated with an organophosphate (chlorpyrifos-methyl) or a pyrethroid (lambdacyhalothrin) alone and in combination against insecticide-resistant Anopheles gambiae and Culex quinquefasciatus mosquitoes. Malaria Journal 4: 25.
  79. 79. Greenwood BM, Pickering H (1993) A malaria control trial using insecticide-treated bed nets and targeted chemoprophylaxis in a rural area of The Gambia, West Africa: 1. A review of the epidemiology and control of malaria in The Gambia, West Africa. Transactions of the Royal Society of Tropical Medicine and Hygiene (suppl. 2): 3–11.
  80. 80. Howard SC, Omumbo J, Nevill C, Some ES, Donnelly CA, et al. (2000) Evidence for a mass community effect of insecticide-treated bednets on the incidence of malaria on the Kenyan coast. Transactions of the Royal Society of Tropical Medicine and Hygiene 94: 357–360.
  81. 81. Bayoh MN, Mathias DK, Odiere MR, Mutuku FM, Kamau L, et al. (2010) Anopheles gambiae: historical population decline associated with regional distribution of insecticide-treated bed nets in western Nyanza Province, Kenya. Malaria Journal 9: 62.
  82. 82. Phuc HK, Andreasen MH, Burton RS, Vass C, Epton MJ, et al. (2007) Late-acting dominant lethal genetic systems and mosquito control. BMC Biology 5: 11.
  83. 83. Curtis CF (2007) Review of previous applications of genetics to vector control, In: Bridging laboratory and field research for genetic control of disease vectors (Louis C & Knols BGJ eds): 33–43. Frontis, Springer Netherlands.
  84. 84. Alphey L, Benedict M, Bellini R, Clark GG, Dame DA, et al. (2010) Sterile-insect methods for control of mosquito-borne diseases: An analysis. Vector-Borne and Zoonotic Diseases 10: 295–311.
  85. 85. Scolari F, Siciliano P, Gabrieli P, Gomulski LM, Bonomi A, et al. (2010) Safe and fit genetically modified insects for pest control: from lab to field applications. Genetica 139: 41–52.
  86. 86. Wilke ABB, Nimmo DD, St John O, Kojin BB, Capurro ML, et al. (2009) Mini-review: Genetic enhancements to the sterile insect technique to control mosquito populations. Asian Pacific Journal of Molecular Biology and Biotechnology 17: 65–74.
  87. 87. Alphey L, Nimmo D, O’Connell S, Aksoy S (2008) Insect population suppression using engineered insects. Advances in Experimental Medicine and Biology 627: 93–103.
  88. 88. Bond JG, Rojas JC, Arredondo–Jiménez JI, Quiroz-Martínez H, Valle J, et al. (2004) Population control of the malaria vector Anopheles pseudopunctipennis by habitat manipulation. Proceedings of the Royal Society of London B 271: 2161–2169.
  89. 89. Gu W, Utzinger J, Novak RJ (2008) Habitat-based larval interventions: A new perspective for malaria control. The American Journal of Tropical Medicine and Hygiene 78: 2–6.
  90. 90. Ren X, Rasgon JL (2010) Potential for the Anopheles gambiae densonucleosis virus To Act as an “evolution-proof” biopesticide. Journal of Virology 84: 7726–7729.
  91. 91. Gu J, Liu M, Deng Y, Peng H, Chen X (2011) Development of an efficient recombinant mosquito densovirus-mediated RNA interference system and Its preliminary application in mosquito control. PLoS ONE 6: e21329.
  92. 92. Coutinho-Abreua IV, Zhub KY, Ramalho-Ortigao M (2010) Transgenesis and paratransgenesis to control insect-borne diseases: Current status and future challenges. Parasitology International 59: 1–8.
  93. 93. Windbichler N, Menichelli M, Papathanos PA, Thyme SB, Li H, et al. (2011) A synthetic homing endonuclease-based gene drive system in the human malaria mosquito. Nature 473: 212–215.
  94. 94. Hughes GL, Koga R, Xue P, Fukatsu T, Rasgon JL (2011) Wolbachia infections are virulent and inhibit the human malaria parasite Plasmodium falciparum in Anopheles gambiae. PLoS Pathogens 7: e1002043.
  95. 95. Bian G, Joshi D, Dong Y, Lu P, Zhou G, et al. (2013) Wolbachia invades Anopheles stephensi populations and induces refractoriness to Plasmodium infection. Science 340: 748–751.
  96. 96. Box GEP, Draper NR (1987) Empirical model-building and response surfaces. Wiley series in probability and mathematical statistics. Oxford, England: John Wiley & Sons.