Phenomenology of an in-host model of hepatitis C

TL;DR

This paper analyzes an in-host hepatitis C model, revealing new stable states, bifurcations, and conditions for infection persistence, providing insights into disease dynamics and stability.

Contribution

It introduces a previously unknown stable steady state and characterizes the conditions for multiple steady states and bifurcations in the hepatitis C model.

Findings

Discovery of a new stable steady state on the boundary

Proof of Hopf bifurcations leading to periodic solutions

Condition that positive steady states exist when reproductive ratio > 1

Abstract

This paper carries out an analysis of the global properties of solutions of an in-host model of hepatitis C for general values of its parameters. A previously unknown stable steady state on the boundary of the positive orthant is exhibited. It is proved that the model exhibits Hopf bifurcations and hence periodic solutions. A general parametrization of positive steady states is given and it is determined when the number of steady states is odd or even, according to the value of a certain basic reproductive ratio. This implies, in particular, that when this reproductive ratio is greater than one there always exists at least one positive steady state. A positive steady state which bifurcates from an infection-free state when the reproductive ratio passes through one is always stable, i.e. no backward bifurcation occurs in this model.