A stochastic differential equation SIS epidemic model with regime switching

Abstract

<p style='text-indent:20px;'>In this paper, we combined the previous model in [<xref ref-type="bibr" rid="b2">2</xref>] with Gray <i>et al.</i>'s work in 2012 [<xref ref-type="bibr" rid="b8">8</xref>] to add telegraph noise by using Markovian switching to generate a stochastic SIS epidemic model with regime switching. Similarly, threshold value for extinction and persistence are then given and proved, followed by explanation on the stationary distribution, where the <inline-formula><tex-math id="M1">\begin{document}$ M $\end{document}</tex-math></inline-formula>-matrix theory elaborated in [<xref ref-type="bibr" rid="b20">20</xref>] is fully applied. Computer simulations are clearly illustrated with different sets of parameters, which support our theoretical results. Compared to our previous work in 2019 [<xref ref-type="bibr" rid="b2">2</xref>, <xref ref-type="bibr" rid="b3">3</xref>], our threshold value are given based on the overall behaviour of the solution but not separately specified in every state of the Markov chain.