Journal of Mathematical Biology

, Volume 63, Issue 1, pp 125–139 | Cite as

Global analysis on delay epidemiological dynamic models with nonlinear incidence

  • Gang Huang
  • Yasuhiro TakeuchiEmail author


In this paper, we derive and study the classical SIR, SIS, SEIR and SEI models of epidemiological dynamics with time delays and a general incidence rate. By constructing Lyapunov functionals, the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium is shown. This analysis extends and develops further our previous results and can be applied to the other biological dynamics, including such as single species population delay models and chemostat models with delay response.


Epidemic model Nonlinear incidence rate Time delay Lyapunov functional Global stability 

Mathematics Subject Classification (2000)

92D30 34A34 34D20 34D23 


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Graduate School of Science and TechnologyShizuoka UniversityHamamatsuJapan

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