期刊
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
卷 24, 期 -, 页码 18-35出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2015.01.001
关键词
SEIR epidemic model; Age-dependent latency; Age-dependent relapse; Global stability; Lyapunov functional
资金
- National Natural Science Foundation of China [11271303, 11401182]
- Shenzhen Demonstration Project of Science & Technology Applications [20120618102906924]
- Technology Innovation Team in Higher Education Institutions of Heilongjiang Province [2014TD005]
In this paper, an SEIR epidemic model for a disease with age-dependent latency and relapse is proposed. Such a model is very appropriate for tuberculosis and herpes. The basic reproduction number R-0 is defined and proved as a classic threshold parameter. Asymptotic smoothness of solutions and uniform persistence of the system are shown via reformulating the system as a system of Volterra integral equations. The local stability and global stability of equilibria are obtained by analyzing the corresponding characteristic equations and constructing the proper Volterra-type Lyapunov functionals, respectively. Finally, some special cases of the model as key functions reducing to constant are discussed in the last section. (C) 2015 Elsevier Ltd. All rights reserved.
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