Dynamical analysis of a nonlocal delayed and diffusive HIV latent infection model with spatial heterogeneity

highlights•We formulate a nonlocal delayed HIV latent infection model with spatial heterogeneity.•The dynamics of the steady states for heterogeneous and homogeneous cases are studied.•The effects of spatial heterogeneity and delays on viral dynamics are investigated.•Simulations stress the spatial heterogeneity cannot be ignored when HIV clinical treatment. To study the impact of two time delays (latency period caused by HIV latency infected cell and viral production period caused by HIV infected cell) on the HIV infection processes in heterogenous environment, an HIV latent infection model with spatial diffusion and non-local infections is derived and investigated in this paper. Applying the definition of the next reproduction operator, we obtain the basic reproduction number R0, which is a threshold value for determining whether the breakout of HIV infection or not. More precisely, the infection-free equilibrium is globally attractive if R01. In particular, an explicit formula of R˜0 is obtained in the homogeneous case and the global dynamics of the homogeneous case are also analyzed. The influences of time delays, HAART treatment and infection heterogeneity on HIV infections are discussed via numerical simulations. This work reveals that the use of the spatially averaged parameters may underestimate HIV infection. Therefore, the spatial heterogeneity is a key factor that cannot be ignored when clinical medical staff design the treatment strategies for HIV infection.