Analysis of a reaction–diffusion HCV model with general cell-to-cell incidence function incorporating B cell activation and cure rate

Abstract

A spatio-temporal model for HCV dynamics incorporating the spatial mobility of viruses and immune B cells, with general nonlinear incidence functions for both modes of infection transmission, namely, virus-to-cell as well as cell-to-cell transmission, is proposed and analyzed with the homogeneous Neumann boundary conditions. In addition, the model includes the role of B cell or antibody response and considers the non-cytolytic cure of productively infected hepatocytes. The existential conditions and global stability for the system equilibrium points are examined. The analytical results shows that the three types of equilibria for the model with general incidence functions are globally asymptotically stable under certain conditions along with criteria on the basic reproductive ratio. The numerical illustration of the analytical findings are presented for the case of bilinear as well as Holling type-II incidence function in a one-dimensional spatial domain. For both the incidence functions, the model populations converge to the corresponding levels of the infected or infection-free equilibrium, contingent upon the case of the basic reproductive ratio being greater than unity or not, respectively. Furthermore, it is observed that the diffusive coefficients do not influence the asymptotic behavior of the system. The infection will be eliminated when basic reproductive ratio is less than unity.