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Pré-Publication, Document De Travail Année : 2023

An SIS model in the Chemostat

Résumé

We study a mathematical model of bacterial growth on a single limiting nutrient in a chemostat where a virus is present. The assumption is that the virus can infect the population, resulting in the emergence of two distinct populations: the susceptible and the infected, which are in competition. The model has the structure of an SIS epidemic model. We assume that the growth functions are general and not just linear or of the Monod type as in previous works in the literature. We analyze the local stability of both disease-free and endemic equilibria. The model can exhibit a multiplicity of endemic equilibria, as well as the appearance of periodic orbits by supercritical or subcritical Hopf bifurcations. Bistability between several equilibrium states or limit cycles is also possible. We present an explicit expression for the basic reproduction number of the epidemic in terms of biologically significant parameters. To better understand the richness of the model's behavior, a few bifurcation diagrams with respect to input nutrient concentration are examined.
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Dates et versions

hal-04293111 , version 1 (18-11-2023)

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  • HAL Id : hal-04293111 , version 1

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Hayat Berhoune, Bachir Bar, Mustapha Lakrib, Tewfik Sari. An SIS model in the Chemostat. 2023. ⟨hal-04293111⟩
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