Mathematical analysis of an age-structured HIV/AIDS epidemic model with HAART and spatial diffusion

Compared with the existing HIV/AIDS host model that considers only age-since-infection or only spacial diffusion, we propose a new age-space structured model that incorporating both two infection ages, spacial diffusion, and HAART (highly active antiretroviral therapy) to analyze the global dynamics of HIV/AIDS epidemic and study the incident of its transmission among MSM (men who have sex with men) group. We first obtain the well-posedness and positivity of the solution for the model. The generation operator R is obtained by the process of renewal, followed by the basic reproduction number R-0. Then we prove that the disease-free equilibrium is globally asymptotically stable (g.a.s) when R-0 < 1, the space-independent steady state is g.a.s, and the disease will be present when R-0 > 1. Numerical simulations are conducted to reinforce these analytical results. Finally, numerical results show that key model parameters influence the value of R0 effectively, and indicate that the spatial factor plays a crucial role as a control measure and cannot be ignored during the intervention for HIV transmission among MSM group. Moreover, our work suggests that treatment adherence should be improved during the HAART for HIV infected individuals among MSM. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This study proposed a new age-space structured model for analyzing the dynamics of HIV/AIDS epidemic among MSM, incorporating infection ages, spatial diffusion, and HAART. Numerical simulations reinforced analytical results that spatial factor plays a crucial role in controlling HIV transmission, suggesting the improvement of treatment adherence during HAART for HIV infected individuals among MSM.