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<p>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: susceptible and 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 as in previous studies in the literature. We analyze the 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, some bifurcation diagrams are examined with respect to input nutrient concentration.</p>

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The SIS model in the chemostat, with general increasing growth functions

  • 期刊论文

  • 发表日期：

    2026年6月16日

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  • Hayat Berhoune,
  • Mustapha Lakrib,
  • Tewfik Sari

摘要

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: susceptible and 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 as in previous studies in the literature. We analyze the 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, some bifurcation diagrams are examined with respect to input nutrient concentration.