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Stationary distribution and extinction of SIR model with nonlinear incident rate under Markovian switching

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  • Guo, Xiaoxia
  • Luo, Jiaowan

Abstract

Taking into account of both white and colored noises, a stochastic epidemic model with nonlinear incident rate under regime switching is formulated. Based on this model, we investigate the dynamic behaviors such as ergodicity and extinction of the SIR model with Beddington–DeAngelis incidence rate and Markov switching. First, we study the existence of the unique positive solution of system (1.3). Secondly, by using Lyapunov functions, we prove that the system has a ergodic stationary distribution under certain sufficient conditions. Then, we obtain the conditions for extinction. Finally, numerical simulations are employed to illustrate our theoretical analysis.

Suggested Citation

  • Guo, Xiaoxia & Luo, Jiaowan, 2018. "Stationary distribution and extinction of SIR model with nonlinear incident rate under Markovian switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 471-481.
    • Handle: RePEc:eee:phsmap:v:505:y:2018:i:c:p:471-481
    DOI: 10.1016/j.physa.2018.02.024
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    References listed on IDEAS

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    Cited by:

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