Phenomenology of an in-host model of hepatitis C
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2022
- DOI:
- 10.48550/arXiv.2206.05176
- arXiv:
- arXiv:2206.05176
- Bibcode:
- 2022arXiv220605176N
- Keywords:
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- Quantitative Biology - Populations and Evolution;
- Mathematics - Dynamical Systems;
- 92BXX;
- 34AXX;
- 34DXX;
- 34C23;
- 37DXX