Modeling and analysis of a periodic delays spatial diffusion HIV model with three-stage infection process

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Considering the antiviral drugs can act on the fusion, reverse transcription, and budding stages of HIV infected cells, in this paper, we formulate a two-periodic delay heterogeneous space diffusion HIV model with three-stage infection process to study the effects of periodic antiviral treatment and spatial heterogeneity on HIV infection process. We first study the well-posedness of the full system and then derive the basic reproduction number [Formula: see text], which is defined as the spectral radius of the next generation operator. We further prove that [Formula: see text] is a threshold for the elimination and persistence of HIV infection by comparison principle and persistence theory for non-autonomous system. In the spatial homogeneous case, the explicit expression of [Formula: see text] is derived and the global attractivity of the positive steady state is proved by using the fluctuation method. Some numerical simulations are conducted to illustrate the theoretical results and our works suggest that both spatial heterogeneity and periodic delays caused by periodic antiviral therapy have a remarkable impact on the progression of HIV infection and should not be overlooked in clinical treatment process.