Viral infection dynamics in a spatial heterogeneous environment with cell-free and cell-to-cell transmissions

In this paper, we investigate a diffusive viral infection model in a spatial heterogeneous environment with two types of infection mechanisms and distinct dispersal rates for the susceptible and infected target cells. After establishing well-posedness of the model system, we identify the basic reproduction number R₀ and explore the properties of R₀ when the dispersal rate for infected target cells varies from zero to infinity. Moreover, we demonstrate that the basic reproduction number is a threshold parameter: the infection and virus will be cleared out if R₀ ≤ 1, while if R₀ > 1, the infection will persist and the model system admits at least one positive (chronic infection) steady state. For the special case when all model parameters are spatial homogeneous, this chronic infection steady state is unique and globally asymptotically stable.