A numerical method for a diffusive virus model with general incidence function, cell-to-cell transmission and time delay

In this paper, we propose a numerical method for a diffusive virus dynamics model with general incidence function, cell-to-cell transmission and time delay. We justify the wellposedness of the numerical model, and prove that the proposed method preserves the global stability of equilibria by constructing suitable discrete Lyapunov functionals with no constraints on the time and space step sizes. we perform numerical simulation to verify our theoretic results. Epidemiologically, we deduce that the spatial heterogeneity of transmission rate can enlarge the risk of disease outbreaks, and the larger time delay is conductive to cure diseases.