Dynamics of a diffusive virus model with general incidence function, cell-to-cell transmission and time delay

Abstract

In this paper, we revisit a diffusive virus dynamics model with general incidence function and time delay. One novelty of our model is that we introduce cell-to-cell transmission via formation of virological synapses to reflect the fact that it may play a more important role in virus spreading in addition to virus-to-cell infection. We justify the well-posedness of the model and identify the basic reproduction number ℜ0 for the model to be a sharp threshold value. The global stability of equilibria is determined by constructing suitable Lyapunov functionals in the sense that: the infection-free equilibrium is globally asymptotically stable if ℜ0≤1, and when ℜ0>1, the global asymptotic stability of infection equilibrium implies that the infection will persist. A significant impact of the cell-to-cell transmission is that they increase the basic reproduction number. If one neglects either the cell-to-cell transmission or virus-to-cell infection, the basic reproduction number of the model that is under-evaluated. Last, we perform numerical simulation to support our theoretic results. We set the domain of the viruses to be a two-dimensional square domain with the homogeneous Neumann boundary conditions to reflect the spatial spreading.