Xue T, Fan X, Chang Z. Dynamics of a stochastic SIRS epidemic model with standard incidence and vaccination.
MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022;
19:10618-10636. [PMID:
36032009 DOI:
10.3934/mbe.2022496]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
A stochastic SIRS epidemic model with vaccination is discussed. A new stochastic threshold $ R_0^s $ is determined. When the noise is very low ($ R_0^s < 1 $), the disease becomes extinct, and if $ R_0^s > 1 $, the disease persists. Furthermore, we show that the solution of the stochastic model oscillates around the endemic equilibrium point and the intensity of the fluctuation is proportional to the intensity of the white noise. Computer simulations are used to support our findings.
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