Mathematical Analysis and Numerical Simulation of a Vector-Borne Zika Model with Sexual Transmission and Spatial Displacement

In this paper, we investigate a reaction–diffusion system governing the vector-borne and sexual transmission dynamics of the Zika virus between host (human) and vector (mosquito) populations. Adopting the compartmental methodology, the human population is divided into susceptible, exposed, infected, and recovered classes, while the mosquito population is partitioned into susceptible, exposed, and infected compartments. We consider several assumptions for disease transmission; in particular, we consider the transmission from infected to susceptible humans to occur through sexual interaction. The first contribution of this work lies in incorporating spatial displacement for both populations, modeled via Fick’s law with a spatially varying diffusion coefficient to capture environmental heterogeneity. To reflect an epidemiologically closed domain, homogeneous Neumann (zero-flux) boundary conditions are imposed, ensuring total population mass conservation principles. As a second advancement, we establish rigorous mathematical results regarding the well-posedness, boundedness, and positivity of solutions to the resulting reaction–diffusion system. The third innovation of the paper is the fact that an unconditional convergent and biologically consistent finite difference numerical scheme is developed to resolve the coupled non-linear governing equations. Finally, we provide a comprehensive set of numerical simulations focused on the parameter sensitivity.