Abstract and Applied Analysis

The Global Behavior of a Periodic Epidemic Model with Travel between Patches

Luosheng Wen, Bin Long, Xin Liang, and Fengling Zeng

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Abstract

We establish an SIS (susceptible-infected-susceptible) epidemic model, in which the travel between patches and the periodic transmission rate are considered. As an example, the global behavior of the model with two patches is investigated. We present the expression of basic reproduction ratio R 0 and two theorems on the global behavior: if R 0 < 1 the disease-free periodic solution is globally asymptotically stable and if R 0 > 1, then it is unstable; if R 0 > 1, the disease is uniform persistence. Finally, two numerical examples are given to clarify the theoretical results.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 295060, 12 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1355495778

Digital Object Identifier
doi:10.1155/2012/295060

Mathematical Reviews number (MathSciNet)
MR2947749

Zentralblatt MATH identifier
1246.34040

Citation

Wen, Luosheng; Long, Bin; Liang, Xin; Zeng, Fengling. The Global Behavior of a Periodic Epidemic Model with Travel between Patches. Abstr. Appl. Anal. 2012 (2012), Article ID 295060, 12 pages. doi:10.1155/2012/295060. https://projecteuclid.org/euclid.aaa/1355495778


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