Threshold of a stochastic SIQS epidemic model with isolation

Author:

Dieu Nguyen Thanh,Sam Vu Hai,Du Nguyen Huu

Abstract

<p style='text-indent:20px;'>The aim of this paper is to give sufficient conditions, very close to the necessary one, to classify the stochastic permanence of SIQS epidemic model with isolation via a threshold value <inline-formula><tex-math id="M1">\begin{document}$ \widehat R $\end{document}</tex-math></inline-formula>. Precisely, we show that if <inline-formula><tex-math id="M2">\begin{document}$ \widehat R&lt;1 $\end{document}</tex-math></inline-formula> then the stochastic SIQS system goes to the disease free case in sense the density of infected <inline-formula><tex-math id="M3">\begin{document}$ I_z(t) $\end{document}</tex-math></inline-formula> and quarantined <inline-formula><tex-math id="M4">\begin{document}$ Q_z(t) $\end{document}</tex-math></inline-formula> classes extincts to <inline-formula><tex-math id="M5">\begin{document}$ 0 $\end{document}</tex-math></inline-formula> at exponential rate and the density of susceptible class <inline-formula><tex-math id="M6">\begin{document}$ S_z(t) $\end{document}</tex-math></inline-formula> converges almost surely at exponential rate to the solution of boundary equation. In the case <inline-formula><tex-math id="M7">\begin{document}$ \widehat R&gt;1 $\end{document}</tex-math></inline-formula>, the model is permanent. We show the existence of a unique invariant probability measure and prove the convergence in total variation norm of transition probability to this invariant measure. Some numerical examples are also provided to illustrate our findings.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics

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