Modeling the effect of non-cytolytic immune response on viral infection dynamics in the presence of humoral immunity

In this paper, a mathematical model describing the viral infection dynamics with non-cytolytic effect of humoral immune response is presented and analyzed. The effect of non-cytolytic immune response on the process of viral infectivity has been basically described by the non-cytolytic cure of infected cells and inhibition of viral replication, i.e., the non-lytic immune response. The sufficient criteria for the local and global stability of the equilibria, namely disease-free equilibrium, immune-free equilibrium and chronic equilibrium with humoral response, have been determined in terms of two threshold parameters, viz., the basic reproduction number, R0. The condition governing the occurrence of Hopf bifurcation around the chronic equilibrium with humoral response has been obtained using the rate of infection as a bifurcation parameter. The obtained results indicate that the infection gets eradicated for R0 <= 1. Numerical simulations are presented to support our analytical findings. The comparison of various viral dynamic models suggests that the incorporation of the non-cytolytic immune response increases the concentration of uninfected cells, but causes a depletion of humoral immune response. Further, the effect of non-cytolytic immune response on the dynamical behavior of the system has been demonstrated.