A Qualitative Study of a Diffusive HIV/AIDS Model With Screening Effects

Abstract

ABSTRACT In this article, we investigated a diffusive HIV/AIDS model with the effect of screening of infectives among adults and female sex workers. In the deterministic compartmental model without spatial movement, we determined the basic reproduction number and proved the existence of disease‐free and endemic equilibria. We also analyzed the long‐term behavior of the system through the global stability of the model. To understand how infection fronts propagate spatially, we extended the HIV system to the reaction–diffusion model. We analyzed the properties of critical spreading speed , as well as the existence of a traveling wave linking disease‐free equilibrium and endemic equilibrium for with , and their non‐existence for with , and for with . Numerical simulations were conducted to validate the theoretical findings, and we have shown that although screening individual groups helps minimize HIV progression, targeting all groups is more efficient because it disrupts the transmission chain more effectively.