Analysis of a model for hepatitis C virus transmission that includes the effects of vaccination with waning immunity

TL;DR

This paper develops and analyzes a mathematical model for hepatitis C transmission that incorporates vaccination with waning immunity, revealing conditions for disease eradication and stability of disease states through theoretical and numerical analysis.

Contribution

It introduces a comprehensive hepatitis C model including vaccination and waning immunity, and analyzes its equilibrium stability and bifurcation behavior.

Findings

Backward bifurcation occurs when $R_0$<1, complicating eradication efforts.

A perfect vaccine can eliminate backward bifurcation.

The endemic equilibrium can be globally stable under certain conditions.

Abstract

This paper considers a mathematical model based on the transmission dynamics of hepatitis C virus (HCV) infection. In addition to the usual compartments for susceptible, exposed, and infected individuals, this model includes compartments for individuals who are under treatment and those who have had vaccination against HCV infection. It is assumed that the immunity provided by the vaccine fades with time. The basic reproduction number, $R_0$, and the equilibrium solutions of the model are determined. The model exhibits the phenomenon of backward bifurcation where a stable disease-free equilibrium co-exists with a stable endemic equilibrium whenever $R_0$ is less than unity. It is shown that the use of only a perfect vaccine can eliminate backward bifurcation completely. Furthermore, a unique endemic equilibrium of the model is proved to be globally asymptotically stable under certain restrictions on the parameter values. Numerical simulation results are given to support the theoretical predictions. [epidemiological model; equilibrium solutions; backward bifurcation; global asymptotic stability; Lyapunov function.]