Dynamics of solutions of adiffusive time-delayed HIV/AIDS epidemic model: Traveling wave solutions and spreading speeds

We study a diffusive time-delayed HIV/AIDS epidemic model with information and education campaigns and investigate the dynamics of classical solutions of the model. In particular, we address the questions of disease's persistence-extinction, existence of epidemic waves, and spreading speeds. When the basic reproduction number is less than or equal to one, we show that the disease-free equilibrium solution is globally stable, hence there is no epidemic wave in this case. However, if it is bigger than one, we show that the disease will eventually persist. Furthermore, there is a minimum wave speed c(u)(*), which decreases as a function of time-delay u, such that the system has an epidemic traveling wave solution with speed cfor every cgreater than c(u)(*) and that there is no such traveling wave solution of speed less than c(u)(*). Moreover the minimum wave speed c(u)(*) converges to 0 as the time-delay approaches infinity. We also study the disease spreading speeds interval and show that in the absence of time-delay, there is a single disease spreading speed and this coincides with the minimal wave speed. We conclude with numerical simulations to illustrate our findings. (c) 2022 Elsevier Inc. All rights reserved.

Automated summary

In this study, we investigate a diffusive time-delayed HIV/AIDS epidemic model with information and education campaigns and analyze the dynamics of its classical solutions. We examine the disease's persistence-extinction, existence of epidemic waves, and spreading speeds. The results show that when the basic reproduction number is less than or equal to one, the disease-free equilibrium solution is globally stable, indicating the absence of epidemic waves. However, if the basic reproduction number is greater than one, the disease is shown to persist. Moreover, there is a minimum wave speed that decreases as the time-delay increases, and the system exhibits an epidemic traveling wave solution for speeds greater than this minimum speed. Additionally, we explore the disease spreading speeds interval and find that in the absence of time-delay, there is a single spreading speed which coincides with the minimal wave speed. This study provides important insights into the dynamics of HIV/AIDS epidemics and can inform strategies for prevention and control.