Mathematical modelling of mosquito dispersal for malaria vector control

In malaria endemic regions, dispersal of mosquitoes from one location to another searching for resources for their survival and reproduction is a fundamental biological process that operates at multiple temporal and spatial scales. This dispersal behaviour is an important factor that causes uneven distribution of malaria vectors causing heterogeneous transmission. Although mosquito dependence in a heterogeneous environment has several implications for malaria vector control and in public health in general, its inclusion in mathematical models of malaria transmission and control has received limited attention.
Most models of malaria transmission and control explain relationships between the number of mosquitoes and malaria transmission in humans while assuming enclosed systems of mosquitoes in which spatial dynamics and movements are not taken into account. These models have limited ability to assess and quantify the distribution of risks and interventions at local scales. Therefore, in order to overcome this limitation, mathematical models that consider the interaction between dispersal behaviour, population dynamics, environmental heterogeneity, and age structures of the mosquito are needed for designing, planning, and management of the control strategies at local scales. Advances in malaria modelling have recently begun to incorporate spatial heterogeneity and highlight the need for more spatial explicit models that include all the vital components of ecological interactions.
In response to this need, this thesis develops a spatial mathematical model that captures mosquito dispersal and includes all of the above characteristics to achieve a broader and deeper understanding of mosquito foraging behaviour, population dynamics, and its interactions with environmental heterogeneity, distribution of malaria risk, and vector control interventions. The model is applied to assess the impact of dispersal and heterogeneous distribution of mosquito resources on the spatial distribution, dynamics, and persistence of mosquito populations, to estimate the distance travelled by mosquitoes, and to evaluate and assess the impact of spatial distribution of vector control interventions on effectiveness of interventions under mosquitoes' natural dispersal behaviour.
Chapter 2 develops a spatial mathematical model of mosquito dispersal in heterogeneous environments with a framework that is simple to allow investigation of aspects that affects malaria transmission. The model incorporates age distribution in form of the aquatic and adult stages of the mosquito life cycle and further divides the adult mosquito population into three stages of the mosquitoes searching for hosts, those resting, and those searching for oviposition sites. These three adult stages provide an opportunity to study the life style of the adult mosquito, and also offer a direct opportunity to assess the impact of interventions targeting different adult states such as insecticide treated bednets (ITNs), indoor residual spraying (IRS), and spatial repellents that reduce contacts between host seeking mosquitoes and human hosts. The spatial characteristics of the model are based on discretization of space into discrete patches. Host and oviposition site searching mosquitoes disperse to the nearest neighbours across the spatial platform where hosts and breeding sites are distributed.
In the same Chapter, the model is applied to investigate the effect of heterogeneous distribution of resources used by mosquitoes, estimate the dispersal distance, and to assess the impact of spatial repellents on the dispersal distance. Results revealed that due to dispersal, the distribution of mosquitoes highly depend on the distribution of hosts and breeding sites and the random distribution of spatial repellents reduces the distance travelled by mosquitoes; offering a promising vector control strategy for malaria. In addition, analysis indicated that when only a single patch is considered, and movement ignored, the recruitment parameter and parameters related to the larval and host seeking stages of the mosquito strongly determine mosquito population persistence and extinction.
Chapter 3 extends the model developed in Chapter 2 to include vector control interventions. As vector control intervention deployment plans need to consider the spatial distribution of intervention packages, the model extension developed in this chapter is used to examine the effect of spatial arrangement of vector control interventions on their effectiveness. Application of the model to IRS, larvicide, and ITNs showed that randomly distributing these interventions will in general be more effective than clustering them on side of an area.
Mosquito dispersal and the different patterns of heterogeneity have different effects on population distribution and dynamics of mosquitoes, and thus, that of malaria. Models that incorporate dispersal when integrated with environmental heterogeneity allow predictions to capture ecological behaviour of mosquitoes, the main source of variations in malaria risk at local spatial scales, providing information needed for determining risk areas for malaria vector control purposes.