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 Citations (Scopus)

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

Fingerprint

disease models
Time Delay
Discrete Delay
Time delay
disease transmission
Basic Reproduction Number
Liapunov Function
Basic Reproduction number
Endemic Equilibrium
Global Dynamics
Distributed Delay
Pathogens
Global Stability
Population
pathogens
Model
Feedback
Necessary
Sufficient Conditions
Interaction

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

Cite this

Global properties of vector–host disease models with time delays. / Cai, Li Ming; Li, Xue Zhi; Fang, Bin; Ruan, Shigui.

In: Journal of Mathematical Biology, 22.09.2016, p. 1-27.

Research output: Contribution to journalArticle

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