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Stability and oscillations of multistage SIS models depend on the number of stages

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  • Röst, Gergely
  • Tekeli, Tamás

Abstract

In this paper we consider multistage SIS models of infectious diseases, where infected individuals are passing through infectious stages I1,I2,⋯In and then return to the susceptible compartment. First we calculate the basic reproduction number R0, and prove that the disease dies out for R0≤1, while a unique endemic equilibrium exists for R0>1. Our main result is that the stability of the endemic equilibrium depends on the number of stages: the endemic equilibrium is always stable when n ≤ 3, while for any n > 3 it can be either stable or unstable, depending on the particular choice of the parameters. We generalize previous stability results for SIRS models as well and point out a mistake in the literature for multistage SEIRS models. Our results have important implications on the discretization of infectious periods with varying infectivity.

Suggested Citation

  • Röst, Gergely & Tekeli, Tamás, 2020. "Stability and oscillations of multistage SIS models depend on the number of stages," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    • Handle: RePEc:eee:apmaco:v:380:y:2020:i:c:s0096300320302289
    DOI: 10.1016/j.amc.2020.125259
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