Journal of Applied Mathematics

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

Lin Li and Zhicheng Liu

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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.

Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 765498, 10 pages.

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425305528

Digital Object Identifier
doi:10.1155/2014/765498

Mathematical Reviews number (MathSciNet)
MR3170447

Zentralblatt MATH identifier
07010748

Citation

Li, Lin; Liu, Zhicheng. Existence of Periodic Solutions and Stability of Zero Solution of a Mathematical Model of Schistosomiasis. J. Appl. Math. 2014 (2014), Article ID 765498, 10 pages. doi:10.1155/2014/765498. https://projecteuclid.org/euclid.jam/1425305528


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