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Journal of Applied Mathematics
Volume 2014, Article ID 765498, 10 pages
http://dx.doi.org/10.1155/2014/765498
Research Article

Existence of Periodic Solutions and Stability of Zero Solution of a Mathematical Model of Schistosomiasis

Lin Li1,2 and Zhicheng Liu1,2

1School of Biomedical Engineering, Capital Medical University, Beijing 100069, China
2Beijing Key Laboratory of Fundamental Research on Biomechanics in Clinical Application, Capital Medical University, Beijing 100069, China

Received 29 July 2013; Revised 23 November 2013; Accepted 28 November 2013; Published 13 February 2014

Academic Editor: Yongkun Li

Copyright © 2014 Lin Li and Zhicheng Liu. 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 mathematical model on schistosomiasis governed by periodic differential equations with a time delay was studied. By discussing boundedness of the solutions of this model and construction of a monotonic sequence, the existence of positive periodic solution was shown. The conditions under which the model admits a periodic solution and the conditions under which the zero solution is globally stable are given, respectively. Some numerical analyses show the conditional coexistence of locally stable zero solution and periodic solutions and that it is an effective treatment by simply reducing the population of snails and enlarging the death ratio of snails for the control of schistosomiasis.