Dynamics of a model of nonlocal dispersion viral infection that includes humoral immunity, intracellular delay, and virus-to-cell and cell-to-cell transmissions

This paper investigates a delayed spatiotemporal viral infection model with two types of transmissions, namely, virus-to-cell transmission, and virus-to-cell transmission, and a special focus on the cell-mediated immunity. First, we establish that the model system has a global attractor and that the model admits a unique positive solution which is globally defined. The basic reproduction numbers of immunity ℜ1 and infection ℜ0 are then determined. The existence of the immunity related reproduction number ℜ1 exists in the case when ℜ0 > 1 which serves as a threshold parameter. Indeed, it is obtained that the immunity-free infection is globally asymptotically stable when ℜ1 ≤ 1 < ℜ0, infection-free infection is globally asymptotically stable when ℜ1 > 1, and infection-immune is globally asymptotically stable when ℜ1 ≤ 1 < ℜ0. Finally, numerical simulation is performed in order to validate of our theoretical results.