Analysis of a reaction-diffusion AIDS model with media coverage and population heterogeneity

Considering the influence of population heterogeneity, media coverage and spatial diffusion on disease transmission, this paper investigated an acquired immunodeficiency syndrome (AIDS) reaction-diffusion model with nonlinear incidence rates and media coverage. First, we discussed the positivity and boundedness of system solutions. Then, the basic reproduction number ${\mathcal{R}}_0$ was calculated, and the disease-free equilibrium (DFE), denoted as $E^0$, was locally and globally asymptotically stable when ${\mathcal{R}}_0<1$. Further, there existed a unique endemic equilibrium (EE), denoted as $E^{\ast }$, which was locally and globally asymptotically stable when ${\mathcal{R}}_0>1$ and certain additional conditions were satisfied. In addition, we showed that the disease was uniformly persistent. Finally, the visualization results of the numerical simulations illustrated that: The media coverage was shown to mitigate the AIDS transmission burden in the population by lowering the infection peak and the time required to reach it; a higher awareness conversion rate can effectively reduce the basic reproduction number ${\mathcal{R}}_0$ to curb the spread of AIDS.