Dynamical behaviors of an Echinococcosis epidemic model with distributed delays

Abstract

In this paper, a novel spreading dynamical model for Echinococcosis with distributed time delays is proposed. For the model, we firstly give the basic reproduction number R0 and the existence of a unique endemic equilibrium when R0 > 1. Furthermore, we analyze the dynamical behaviors of the model. The results show that the dynamical properties of the model is completely determined by R0. That is, if R0 < 1, the disease-free equilibrium is globally asymptotically stable, and if R0 > 1, the model is permanent and the endemic equilibrium is globally asymptotically stable. According to human Echinococcosis cases from January 2004 to December 2011 in Xinjiang, China, we estimate the parameters of the model and study the transmission trend of the disease in Xinjiang, China. The model provides an approximate estimate of the basic reproduction number R0 = 1:23 in Xinjiang, China. From theoretic results, we further find that Echinococcosis is endemic in Xinjiang, China. Finally, we perform some sensitivity analysis of several model parameters and give some useful measures on controlling the transmission of Echinococcosis.