Global stability analysis for a generalized delayed SIR model with vaccination and treatment

A. Elazzouzi, A. Lamrani Alaoui, M. Tilioua, A. Tridane

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


In this work, we investigate the stability of an SIR epidemic model with a generalized nonlinear incidence rate and distributed delay. The model also includes vaccination term and general treatment function, which are the two principal control measurements to reduce the disease burden. Using the Lyapunov functions, we show that the disease-free equilibrium state is globally asymptotically stable if R≤ 1 , where R is the basic reproduction number. On the other hand, the disease-endemic equilibrium is globally asymptotically stable when R> 1. For a specific type of treatment and incidence functions, our analysis shows the success of the vaccination strategy, as well as the treatment depends on the initial size of the susceptible population. Moreover, we discuss, numerically, the behavior of the basic reproduction number with respect to vaccination and treatment parameters.

Original languageEnglish
Article number532
JournalAdvances in Difference Equations
Issue number1
Publication statusPublished - Dec 1 2019


  • Distributed delay
  • Generalized nonlinear incidence
  • Lyapunov function
  • SIR epidemic model
  • Treatment
  • Vaccination

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics


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