Contribution to the mathematical modelling and analysis of spatial distribution of the anopheles mosquito

Abstract

Mosquitoes represent a major threat to public health. Constants efforts are being made to develop or improve control strategies in the framework of control vectors. Control vectors aims to maintain mosquitoes at a low levels that do not represent risk for health. Planning of efficient control strategies requires in-depth knowledge of the mosquito’s biology and ecology, as well as good understanding of the processes governing the dynamics of the population in time and space. In malaria endemic regions, dispersal of mosquitoes from one location to another for 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. In published literature, most models that addressed mosquito dynamics rely on temporal modelling in which spatial dynamics and movements of mosquito are not taken into account. My investigations in this thesis deals with spatial distribution of anopheles mosquito. I develop spatio-temporal models that consider mosquito dispersal, spatial dynamics, environmental heterogeneity and age structure of the mosquitoes, which are needed for designing, planning, and management of the control strategies. In the first, I develop a spatio-temporal model of mosquito dynamics using discrete patches as a representation of space. I analyze and simulate the spreading of mosquitoes on a complex metapopulation, that is, network of population connected by migratory flows. The theoretical study of this model is done using the theory of monotone dynamical systems. This study allow to identify threshold values that ensure an effective control of mosquitoes. Secondly, using an alternative approach to discrete-space model developed previously, I develop an advection-reaction-diffusion model in order to take into account the mosquito dispersal and spatial heterogeneity of their resources. The model incorporates female mosquitoes of oviposition’s cycle, which provides a framework to study the life style of the adult mosquito. I carry out a qualitative analysis that highlights some biological thresholds that summarize the dynamics of the systems. In addition, for these models, meaningful numerical schemes are developed through nonstandard finite difference methods. The aim is to illustrate the theoretical part and investigate the effect of heterogeneous distribution of resources used by mosquitoes. Results reveal that due to dispersal, the distribution of mosquitoes highly depends on the distribution of hosts and breeding sites.