Global dynamics of a delayed SIRS epidemic model with a wide class of nonlinear incidence rates
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- 作者：Yoichi Enatsu (1) yo1.gc-rw.docomo@akane.waseda.jp
Eleonora Messina (2) eleonora.messina@unina.it
Yukihiko Nakata (3) nakata@bcamath.org
Yoshiaki Muroya (4) ymuroya@waseda.jp
Elvira Russo (2) elvrusso@unina.it
Antonia Vecchio (5) a.vecchio@iac.cnr.it - 关键词：SIRS epidemic model – ; Nonlinear incidence rate – ; Global asymptotic stability – ; Lyapunov functional
- 刊名：Journal of Applied Mathematics and Computing
- 出版年：2012
- 出版时间：June 2012
- 年：2012
- 卷：39
- 期：1-2
- 页码：15-34
- 全文大小：691.3 KB
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- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Computational Mathematics and Numerical Analysis
Applied Mathematics and Computational Methods of Engineering
Theory of Computation
Mathematics of Computing - 出版者：Springer Berlin Heidelberg
- ISSN：1865-2085
文摘
In this paper, by constructing Lyapunov functionals, we consider the global dynamics of an SIRS epidemic model with a wide class of nonlinear incidence rates and distributed delays 貌h0 p(t)f(S(t),I(t-t)) dt\int^{h}_{0} p(\tau)f(S(t),I(t-\tau)) \mathrm{d}\tau under the condition that the total population converges to 1. By using a technical lemma which is derived from strong condition of strict monotonicity of functions f(S,I) and f(S,I)/I with respect to S≥0 and I>0, we extend the global stability result for an SIR epidemic model if R 0>1, where R 0 is the basic reproduction number. By using a limit system of the model, we also show that the disease-free equilibrium is globally asymptotically stable if R 0=1.