The threshold dynamics of a discrete-time echinococcosis transmission model

Abstract

<p style='text-indent:20px;'>In this paper, based on the transmission mechanism of echinococcosis in China, we propose a discrete-time dynamical model for the transmission of echinococcosis. The research results indicate that transmission dynamics of this discrete-time model are determined by basic reproduction number <inline-formula><tex-math id="M1">\begin{document}$ R_{0} $\end{document}</tex-math></inline-formula>. It is shown that when <inline-formula><tex-math id="M2">\begin{document}$ R_{0}\leq1 $\end{document}</tex-math></inline-formula> then the disease-free equilibrium is globally asymptotically stable and when <inline-formula><tex-math id="M3">\begin{document}$ R_{0}&gt;1 $\end{document}</tex-math></inline-formula> then the model is permanent while the disease-free equilibrium is unstable. Finally, on the basis of the theoretical results established in this paper, we come up with some specific measures to control the transmission of echinococcosis.