Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (4): 1218-1234.

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Qualitative Analysis of a Stochastic SIVS Epidemic Model with Nonlinear Perturbations Under Regime Switching

Zhonghua Zhang*(),Qian Zhang()   

  1. School of Sciences, Xi'an University of Science and Technology, Xi'an 710054
  • Received:2020-09-11 Online:2021-08-26 Published:2021-08-09
  • Contact: Zhonghua Zhang;
  • Supported by:
    the NSFC(11201277)


In this paper, we present a stochastic SIVS epidemic model with nonlinear perturbations under regime switching. For the non-autonomous stochastic SIVS epidemic system with white noise, we provide results regarding the stochastic boundedness, stochastic permanence in mean, and we prove that the system has at least one nontrivial positive T-periodic solution by using Lyapunov function and Hasminskii's theory. For the system with Markov conversion, we establish sufficient conditions for existence of ergodic stationary distribution, and the thresholds for persistence in mean and the extinction of infected persons was obtained, respectively. Finally, some numerical simulations are carried out to support the theoretical results.

Key words: Stochastic SIVS epidemic model, Nonlinear perturbation, Markov chain, Nonlinear incidence

CLC Number: 

  • O211.63