The threshold dynamics of a discrete-time echinococcosis transmission model

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 \begin{document}$ R_{0} $\end{document}. It is shown that when \begin{document}$ R_{0}\leq1 $\end{document} then the disease-free equilibrium is globally asymptotically stable and when \begin{document}$ R_{0}>1 $\end{document} 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.