Stability and Hopf Bifurcation in a delayed viral infection model with mitosis transmission

TL;DR

This paper analyzes a delayed viral infection model incorporating mitosis, establishing stability conditions, bifurcation points, and the impact of delay on infection persistence, supported by numerical simulations.

Contribution

It introduces a comprehensive analysis of a HCV model with delay and mitosis, including stability, bifurcation, and sensitivity analysis, which advances understanding of viral dynamics.

Findings

Global stability of infection-free equilibrium

Existence of Hopf bifurcation under certain delays

Conditions for permanence and stability of infected equilibrium

Abstract

In this paper we study a model of HCV with mitotic proliferation, a saturation infection rate and a discrete intracellular delay: the delay corresponds to the time between infection of a infected target hepatocytes and production of new HCV particles. We establish the global stability of the infection-free equilibrium and existence, uniqueness, local and global stabilities of the infected equilibrium, also we establish the occurrence of a Hopf bifurcation. We will determine conditions for the permanence of model, and the length of delay to preserve stability. The unique infected equilibrium is globally-asymptotically stable for a special case, where the hepatotropic virus is non-cytopathic We present a sensitivity analysis for the basic reproductive number. Numerical simulations are carried out to illustrate the analytical results.