Analysis and numerical simulation of a spatio-temporal Ricker-type model for the control of Aedes aegypti mosquitoes with Sterile Insect Techniques

TL;DR

This paper develops a comprehensive spatio-temporal model for Aedes aegypti mosquito control using Sterile Insect Technique, analyzing its dynamics, numerical methods, and optimal deployment strategies to enhance disease prevention efforts.

Contribution

It introduces a novel reaction-diffusion model incorporating spatial heterogeneity and multiple mosquito subpopulations, along with a numerical scheme for simulation and analysis.

Findings

Existence and uniqueness of solutions established

Critical release-size threshold identified for eradication

Spatial distribution impacts control effectiveness

Abstract

Sterile Insect Technique (SIT) is widely regarded as a promising, environmentally friendly and chemical-free strategy for the prevention and control of dengue and other vector-borne diseases. In this paper, we develop and analyze a spatio-temporal reaction-diffusion model describing the dynamics of three mosquito subpopulations involved in SIT-based biological control of Aedes aegypti mosquitoes. Our sex-structured model explicitly incorporates fertile females together with fertile and sterile males that compete for mating. Its key features include spatial mosquito dispersal and the incorporation of spatially heterogeneous external releases of sterile individuals. We establish the existence and uniqueness of global, non negative, and bounded solutions, guaranteeing the mathematical well-posedness and biological consistency of the system. A fully discrete numerical scheme based on the finite element method and an implicit-explicit time-stepping scheme is proposed and analyzed. Numerical simulations confirm the presence of a critical release-size threshold governing eradication versus persistence at a stable equilibrium with reduced total population size, in agreement with the underlying ODE dynamics. Moreover, the spatial structure of the model allows us to analyze the impact of spatial distributions, heterogeneous releases, and periodic impulsive control strategies, providing insight into the optimal spatial and temporal deployment of SIT-based interventions.