Phenomenology of an in-host model of hepatitis C

Alexis Nangue; Alan D. Rendall

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arXiv · 2206.05176

Phenomenology of an in-host model of hepatitis C

Alexis Nangue·Alan D. Rendall

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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.

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Alexis Nangue, Alan D. Rendall. 2022-06-10. Phenomenology of an in-host model of hepatitis C. https://arxiv.org/abs/2206.05176

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