Abstract:

The spatial heterogeneity and infection age profoundly affect the infection process of HIV in the within-host. In order to investigate the effects of spatial heterogeneity and infection age on the infection dynamics of HIV, in this paper, we propose an age structured and nonlocal diffusion HIV latent infection model to describe the diffusion of HIV in different organs of the within-host. Firstly, we investigate the global existence of the model solution. Secondly, by establishing the general update equation of the model, the next generation regeneration operator $\mathcal{R}$ is derived, and the basic regeneration number $R_0$ of the model is obtained as the spectral radius of the operator $\mathcal{R}$. As the dynamics threshold of the infectious disease model, $R_0$ determines the extinction and outbreak of HIV infection in the host. Finally, the existence of non trivial solutions for the system was proved by using Krasnoselskii fixed point theorem. In addition, the asymptotic profiles of the positive steady state of the system were proved in special case.

Key words: HIV, nonlocal dispersal, age structure, spatial heterogeneity, basic reproduction number, threshold dynamics