Traveling waves of a delayed HIV/AIDS epidemic model with treatment and spatial diffusion

In this paper,a delayed HIV/AIDS epidemic model with treatment and spatial diffusion is introduced.By analyzing the corresponding characteristic equations,the local stability of a disease-free steady state and an endemic steady state is discussed.By using the cross-iteration method and Schauder’s fixed point theorem,we reduce the existence of traveling waves to the existence of a pair of upper-lower solutions.By constructing a pair of upper-lower solutions,we derive the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state.It is shown that the existence of traveling waves of the proposed HIV/AIDS epidemic model is fully determined by the basic reproduction number and the minimal wave speed.Finally,numerical simulations are performed to show the feasibility and effectiveness of the theoretical results.