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

Luosheng Wen | Zendy; Bin Long | Zendy; Xinan Liang | Zendy; Fengling Zeng | Zendy

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

Author(s) -

Luosheng Wen,

Bin Long,

Xinan Liang,

Fengling Zeng

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/295060

Subject(s) - algorithm , computer science , artificial intelligence

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 R0 and two theorems on the global behavior: if R0 < 1 the disease-free periodic solution is globally asymptotically stable and if R0 > 1, then it is unstable; if R0 > 1, the disease is uniform persistence. Finally, two numerical examples are given to clarify the theoretical results

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