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

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Abstract

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 R₀ was calculated, and the disease-free equilibrium (DFE), denoted as E⁰, was locally and globally asymptotically stable when R₀ < 1. Further, there existed a unique endemic equilibrium (EE), denoted as E^*, which was locally and globally asymptotically stable when R₀ > 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 R₀ to curb the spread of AIDS.

Keywords

AIDS model / reaction-diffusion / media coverage / population heterogeneity / awareness conversion

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