Threshold dynamics of a nonlocal dispersal HIV/AIDS epidemic model with spatial heterogeneity and antiretroviral therapy

Antiretroviral therapy and long-range diffusion of HIV-infected individuals in heterogeneous environments can greatly impact the transmission and distribution of HIV/AIDS in a population. In this paper, we present a nonlocal dispersal HIV/AIDS epidemic model incorporating spatial heterogeneity as well as antiretroviral therapy to study the spatial and temporal dynamics of HIV/AIDS in China. To overcome the difficulty about a lack of compactness of the semiflow and the challenge about the existence and uniqueness of the principal eigenvalue of an eigenvalue problem without obvious compactness, we apply the operator semigroup and dissipative system theories. We establish the well-posedness and the existence of the global attractor for the system. Then we derive the basic reproduction number R0 which is defined as the spectral radius of the next generation operator by the renewal equation. Afterwards, we obtain the global dynamics of the system in terms of R0. Our numerical simulations suggest that: (1) the dynamics of HIV/AIDS transmission largely depends on the nonlocal dispersal kernel function; (2) it is necessary to monitor and design/refine rules for the mobility of HIV-infected population between remote and metropolitan areas to control the HIV/AIDS transmission; (3) antiretroviral therapy benefits not only each treated individual but also the entire community, and increasing the therapy coverage rate is one of the most effective ways to prolong the longevity of HIV-infected population. Moreover, spatial dispersal is also an important factor that cannot be ignored for designing antiretroviral therapy strategies.