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

Abstract

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, $$R_0$$ , and the humoral immune response reproduction number, $$R_1$$ . 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 $$R_0 \le 1$$ and persists in the body for $$R_0 > 1$$ . 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.