Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 12, Issue 1, Pages 119-127Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2010.06.001
Keywords
Global stability; Infinite distributed delay; Nonlinear incidence; Lyapunov functions
Categories
Funding
- NNSF of China [10601042]
- SRF of Harbin Institute of Technology [HITC200714]
- Harbin Institute of Technology
- NSERC of Canada
- MITACS
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A mathematical model for a disease with a general exposed distribution, the possibility of relapse and nonlinear incidence rate is proposed. By the method of Lyapunov functionals, it is shown that the disease dies out if H-0 <= 1 and that the disease becomes endemic if H-0 > 1. Applications are also made to the special case with a discrete delay and the result confirms that the endemic equilibrium is globally asymptotically stable as suggested in van den Driessche et al. (2007) [4]. (C) 2010 Elsevier Ltd. All rights reserved.
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