期刊
APPLIED MATHEMATICAL MODELLING
卷 36, 期 11, 页码 5293-5300出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2011.12.037
关键词
Latent period; Vaccination; Time delay; Global stability
资金
- National Natural Science Foundation of China [11071254]
- Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry
In this paper, a mathematical model describing the transmission dynamics of an infectious disease with an exposed (latent) period and waning vaccine-induced immunity is investigated. The basic reproduction number is found by applying the method of the next generation matrix. It is shown that the global dynamics of the model is completely determined by the basic reproduction number. By means of appropriate Lyapunov functionals and LaSalle's invariance principle, it is proven that if the basic reproduction number is less than or equal to unity, the disease-free equilibrium is globally asymptotically stable and the disease fades out; and if the basic reproduction number is greater than unity, the endemic equilibrium is globally asymptotically stable and therefore the disease becomes endemic. (C) 2011 Elsevier Inc. All rights reserved.
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