Global asymptotic properties of an SEIRS model with multiple infectious stages

Dessalegn Y. Melesse, Abba B. Gumel

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


The paper presents a rigorous mathematical analysis of a deterministic model, which uses a standard incidence function, for the transmission dynamics of a communicable disease with an arbitrary number of distinct infectious stages. It is shown, using a linear Lyapunov function, that the model has a globally-asymptotically stable disease-free equilibrium whenever the associated reproduction threshold is less than unity. Further, the model has a unique endemic equilibrium when the threshold exceeds unity. The equilibrium is shown to be locally-asymptotically stable, for a special case, using a Krasnoselskii sub-linearity trick. Finally, a non-linear Lyapunov function is used to show the global asymptotic stability of the endemic equilibrium (for the special case). Numerical simulation results, using parameter values relevant to the transmission dynamics of influenza, are presented to illustrate some of the main theoretical results.

Original languageEnglish (US)
Pages (from-to)202-217
Number of pages16
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - Jun 1 2010
Externally publishedYes


  • Equilibria
  • Infectious disease
  • Lyapunov function
  • Reproduction number
  • Stability

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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