Analysis of a Patch Model for the Dynamical Transmission of Echinococcosis

Abstract

A patch model for echinococcosis due to dogs migration is proposed to explore the effect of dogs migration among patches on the spread of echinococcosis. We firstly define the basic reproduction number $R_0$. The mathematical results show that the dynamics of the model can be completely determined by $R_0$. If , the disease-free equilibrium is globally asymptotically stable. When $R_0>1$, the model is permanence and endemic equilibrium is globally asymptotically stable. According to the simulations, it is shown that the larger diffusion of dogs from the lower epidemic areas to the higher prevalence areas can intensify the spread of echinococcosis. However, the larger diffusion of dogs from the higher prevalence areas to the lower epidemic areas can reduce the spread and is beneficial for disease control.