Abstract
ABSTRACTIn this paper, we consider a stochastic SIRS epidemic model with seasonal variation and saturated incidence. Firstly, we obtain the threshold of stochastic system which determines whether the epidemic occurs or not. Secondly, we prove that there is a non-trivial positive periodic solution if .
Highlights
Understanding the periodic behaviour of epidemic dynamical system is of paramount importance in applications
In order to predict sustained oscillatory, many authors take the effect of seasonal variation and stochasticity into account, see, for example [2,6]
The existence of non-trivial positive periodic solution could not be obtained by Wang et al [12]
Summary
Understanding the periodic behaviour of epidemic dynamical system is of paramount importance in applications. [2,6] the authors prove the the existence of positive periodic solution for a stochastic epidemic model only by numerical methods, but not by theoretical methods. [12] the authors considered a periodic stochastic SIR epidemic model with pulse vaccination. The existence of non-trivial positive periodic solution could not be obtained by Wang et al [12]. Lin et al [8] later filled this gap They provided the sufficient conditions for the existence of non-trivial periodic solution. Liu et al [9] considered positive periodic solution for a stochastic non-autonomous SIR epidemic model with logistic growth.
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