aids model, reaction-diffusion, media coverage, population heterogeneity, awareness conversion, Mathematics, QA1-939, Applied mathematics. Quantitative methods, T57-57.97

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^* $, 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.