Abstract
The emergence of drug resistance poses a significant challenge to the clinical treatment of HIV/AIDS, making the spread of drug-resistant strains among the infected population a key focus in the monitoring and control of HIV/AIDS. In this paper, we construct a reaction-diffusion model with two HIV strains (drug-sensitive and drug-resistant) to study the spatio-temporal dynamics of HIV/AIDS transmission. With spatial heterogeneity, we derive the basic reproduction number R
and show that it is a threshold for the outbreak of the disease; that is, when R
<1 the disease will eventually die out, while when R
>1 the disease is uniformly persistent. In particular, when the model parameters are independent of the space variable, global stability of the infection equilibrium is proven by constructing an appropriate Lyapunov functional. In the numerical simulation part, we discuss the traveling wave phenomenon of HIV/AIDS infection in the population under different diffusion forms and different initial value distributions. We combine the population statistical data, geographical data, and data of different strain infection cases in Zhejiang Province, China, and simulate the spatial spread of HIV/AIDS in Zhejiang Province through the finite element method with the aid of COMSOL Multiphysics software. This provides a new perspective to analyze the impact of dispersal on the spatio-temporal transmission of HIV/AIDS. Numerical simulations show that: (i) High adherence to treatment can effectively reduce the proportion of acquired drug-resistant cases among the total number of cases; (ii) The form of population diffusion has a huge impact on the spatio-temporal transmission of HIV/AIDS, which means that population movement will be one of the important contents of HIV/AIDS prevention and monitoring; (iii) Ignoring the differences in population movement will misjudge the overall trend of HIV/AIDS in the region, so the differences in spatial diffusion in HIV/AIDS prevention and control cannot be ignored.