Mathematical modeling of population dynamics, applications to vector control of Aedes spp. (Diptera:Culicidae)

Deterministic systems are used to model time dynamics of mosquito populations undergoing human intervention. The models can have a spatial, compartmental or phentoypical structure. This study focuses on two kinds of intervention relying on releases of mosquitoes from the same species as the wild population: incompatible males for population elimination or males-and-females together for population replacement (there the released individuals have a phenotype different from that of the wild population). These methods aim at reducing the nuisance in highly infested areas and more importantly at limiting (or even stopping) vector-borne disease circulation. Mathematical result are concerned with: asymptotic behavior of solutions to parabolic systems modeling the frequency of the introduced phenotype in the population, motivated by population replacement; a qualitative property of solutions to some ordinary differential systems (convergence to a periodic limit cycle) stemming from a compartmental structure; optimal control by males-and-females releases of an ordinary differential system modeling population replacement in a homogeneous environment, and the control to 0 of a model of population elimination by incompatible males releases; lastly time dynamics of the phenotypical structure in a sexual population. As often as possible these results are specified using experimental data parametrization and illustrated through numerical simulations. Practical conclusions are drawn and the relevance with respect to the application is systematically highlighted.