Spatial and temporal dynamics of SARS‐CoV‐2: Modeling, analysis and simulation

•Propose a novel reaction-diffusion viral infection model to characterize the infection process.•Viral production, infection and death rates are given by more general functions.•Well-posedness, global stability and uniform persistence for the model are discussed.•Simulations are performed to reveal: diffusion, spatial heterogeneity should not be neglected. A reaction-diffusion viral infection model is formulated to characterize the infection process of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in a heterogeneous environment. In the model, the viral production, infection and death rates of compartments are given by the general functions. We consider the well-posedness of the solution, derive the basic reproduction number R0, discuss the global stability of uninfected steady state and explore the uniform persistence for the model. We further propose a spatial diffusion SARS-CoV-2 infection model with humoral immunity and spatial independent coefficients, and analyze the global attractivity of uninfected, humoral inactivated and humoral activated equilibria which are determined by two dynamical thresholds. Numerical simulations are performed to illustrate our theoretical results which reveal that diffusion, spatial heterogeneity and incidence types have evident impact on the SARS-CoV-2 infection process which should not be neglected for experiments and clinical treatments.