Persistence of global stability: the case of adaptive dynamics in mosquito populations

In this talk, we present a nonlocal reaction-diffusion equation of Fisher-KPP type that models the the spread of malaria. It incorporates key factors such as human populations, mosquito behavior, and the mosquitoes’ plasticity and adaptation to control measures like widespread insecticide-treated mosquito nets and indoor residual spraying. Through analysis of the model, we identify and describe the convergence and persistence properties of the solutions, using a small parameter that represents the typical size of the nonlocal interactions between mosquitoes in relation to their activity patterns. In our analysis, we extend some ideas from the theory of uniform persistence to the case of semiflow without dissipativity. We then extend the problem to account for time heterogeneities of almost periodic type and we prove the existence and the stability of a positive and almost periodic entire solution for a perturbed problem.