Global properties of vector–host disease models with time delays

Li Ming Cai, Xue Zhi Li, Bin Fang, Shigui Ruan

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

Since there exist extrinsic and intrinsic incubation periods of pathogens in the feedback interactions between the vectors and hosts, it is necessary to consider the incubation delays in vector–host disease transmission dynamics. In this paper, we propose vector–host disease models with two time delays, one describing the incubation period in the vector population and another representing the incubation period in the host population. Both distributed and discrete delays are used. By constructing suitable Liapunov functions, we obtain sufficient conditions for the global stability of the endemic equilibria of these models. The analytic results reveal that the global dynamics of such vector–host disease models with time delays are completely determined by the basic reproduction number. Some specific cases with discrete delay are studied and the corresponding results are improved.

Original languageEnglish (US)
Pages (from-to)1-27
Number of pages27
JournalJournal of Mathematical Biology
DOIs
StateAccepted/In press - Sep 22 2016

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Keywords

  • Basic reproduction number
  • Global stability
  • Liapunov functional
  • Time delay
  • Vector–host disease model

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

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