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

Abstract

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.

Keywords

• spatial heterogeneity
• viral infection
• basic reproduction number
• global stability