A Markovian switching diffusion for an SIS model incorporating Lévy processes

Abstract

<p style='text-indent:20px;'>The purpose of this work is to investigate the asymptotic properties of a stochastic version of the classical SIS epidemic model with three noises. The stochastic model studied here includes white noise, telegraph noise and Lévy noise. We established conditions for extinction in probability and in <inline-formula><tex-math id="M1">\begin{document}$ pth $\end{document}</tex-math></inline-formula> moment. We also showed the persistence of disease under different conditions. The presented results are demonstrated by numerical simulations.</p>