Analysis and numerical approximation of a mathematical model for Aedes aegypti populations

Abstract

We consider the rigorous analysis and the numerical approximation of a mathematical model for geographical spreading of Aedes aegypti. The complete model is composed of a system of parabolic partial differential equations coupled with one ordinary differential equation and has control terms related to the effects of insecticide application and sterile male release. The existence and uniqueness of solutions for the model are proven, and an efficient numerical methodology for approximating the unique solution of the mathematical model is proposed. The proposed numerical approach is based on a time-splitting scheme combined with locally conservative finite element methods. This combination of a well-posed mathematical model with a robust and efficient numerical formulation provides a suitable tool for the simulation of different scenarios of the spreading of Aedes aegypti. Numerical experiments, including a convergence study and a series of simulations that illustrate how the numerical model can be used in the decision-making process of controlling Aedes aegypti populations through the release of sterile male mosquitoes, assessing the responses to different inputs such as the total of sterile males released, the period for the release and locations for the intervention.