具有标准发生率和疫苗接种的随机 SIRS 传染病模型的动力学。

Dynamics of a stochastic SIRS epidemic model with standard incidence and vaccination.

机构信息

School of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi, Xinjiang, China.

School of Safety Science, Xinjiang Institute of Engineering, Urumqi, Xinjiang, China.

出版信息

Math Biosci Eng. 2022 Jul 26;19(10):10618-10636. doi: 10.3934/mbe.2022496.

DOI:10.3934/mbe.2022496

PMID:36032009

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.

摘要

本文讨论了具有接种的随机 SIRS 传染病模型。确定了新的随机阈值 $ R_0^s $。当噪声非常低（$ R_0^s < 1 $）时，疾病会灭绝，如果$ R_0^s > 1 $，疾病则会持续存在。此外，我们表明随机模型的解围绕地方病平衡点振荡，并且波动的强度与白噪声的强度成正比。计算机模拟用于支持我们的发现。