Abstract:

In this paper, a non-autonomous reaction-diffusion HIV cell model is established to study the effects of periodic antiviral therapy, non local infection and spatial heterogeneity on HIV infection spatio-temporal dynamics. Specifically, we derive the functional expression of the basic regeneration number of the model$\mathcal{R}_0$, which is defined by the spectral radius of the next generation regeneration operator$\mathcal{R}$. Then the dynamical behaviors of the model is analyzed, including the global stability of the HIV infection-free steady state, the uniform persistence of HIV infection and the existence of periodic positive steady state. Finally, we conduct some numerical simulations to verify the theoretical results, and study the influence of relevant important factors on the process of HIV infection. Our works can provide some valuable reference suggestions for the clinical treatment of HIV infection.

Key words: HIV, Reaction-diffusion model, Spatial heterogeneity, Nonlocal infection, Periodic antiviral therapy, Threshold dynamics