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A stochastic SIRS epidemic model with infectious force under intervention strategies. (English) Zbl 1330.35464
In this work, the classical SIRS (Susceptible$$\to$$Infected$$\to$$Recovered$$\to$$Susceptible) with an additional mortality and the constant influx of susceptible individuals is sullied with the small stochastic term (a Gaussian white noise) included into the reaction rate. As a result, the basic reproductive number is obtained as function of noise characteristic. The corresponding changes in the epidemic onset are discussed. In addition, the noise-induced dynamics around the steady state is analysed. It is shown that noise does not change principally the standard stable behaviour except fluctuations around this state.

##### MSC:
 35Q92 PDEs in connection with biology, chemistry and other natural sciences 92D30 Epidemiology 60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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