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Dynamical Behavior of the SEIS Infectious Disease Model with White Noise Disturbance

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  • Yuheng Song
  • Qixing Han
  • Antonio Di Crescenzo

Abstract

Mathematical model plays an important role in understanding the disease dynamics and designing strategies to control the spread of infectious diseases. In this paper, we consider a deterministic SEIS model with a saturation incidence rate and its stochastic version. To begin with, we propose the deterministic SEIS epidemic model with a saturation incidence rate and obtain a basic reproduction number R0. Our investigation shows that the deterministic model has two kinds of equilibria points, that is, disease-free equilibrium E0 and endemic equilibrium E∗. The conditions of asymptotic behaviors are determined by the two threshold parameters R0 and R0c. When R0 1. E∗ is locally asymptotically stable when R0c>R0>1. In addition, we show that the stochastic system exists a unique positive global solution. Conditions d>σˇ2/2 and R0s 1 by constructing appropriate Lyapunov function. Our theoretical finding is supported by numerical simulations. The aim of our analysis is to assist the policy-maker in prevention and control of disease for maximum effectiveness.

Suggested Citation

  • Yuheng Song & Qixing Han & Antonio Di Crescenzo, 2022. "Dynamical Behavior of the SEIS Infectious Disease Model with White Noise Disturbance," Journal of Mathematics, Hindawi, vol. 2022, pages 1-15, August.
    • Handle: RePEc:hin:jjmath:2747320
    DOI: 10.1155/2022/2747320
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