Dynamics of solutions of a diffusive time-delayed HIV/AIDS epidemic model: traveling wave solutions and spreading speeds
In this paper, the authors study a diffusive time-delayed HIV/AIDS epidemic model with information and education campaigns. The dynamics of classical solutions of the model is investigated, such as (i) disease's persistence and extinction, (ii) existence of epidemic waves, and (iii) spreading speeds. For (i), when the basic reproduction number is less than or equal to one, they show that the disease-free equilibrium solution is globally stable, and hence there is no epidemic wave in this case. However, if it is bigger than one, the disease will eventually persist. For (ii), they prove that there is a minimum wave speed such that the model has an endemic traveling wave solution connecting the disease-free equilibrium at the right end when the wave speed is greater than the minimum wave speed, and that there is no such traveling wave solution when the wave speed is less than the minimum wave speed. Moreover, they obtain that the minimum wave speed converges to \(0\) as the time-delay approaches infinity. For (iii), they 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. The numerical simulations are presented to illustrate their theoretical results.
scientific article; zbMATH DE number 7624001
scientific article