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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 576365, 13 pages
http://dx.doi.org/10.1155/2014/576365
Research Article

Analysis of a Patch Model for the Dynamical Transmission of Echinococcosis

1Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China
2Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, China
3College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China

Received 18 January 2014; Accepted 4 February 2014; Published 18 March 2014

Academic Editor: Weiming Wang

Copyright © 2014 Kai Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 . The mathematical results show that the dynamics of the model can be completely determined by . If , the disease-free equilibrium is globally asymptotically stable. When , 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.