Mathematical analysis of an SIS model with imperfect vaccination and backward bifurcation

Muntaser Safan, Fathalla A. Rihan

Research output: Contribution to journalArticlepeer-review

44 Citations (Scopus)


In this paper, we analyze an SIS epidemic model with partially protective vaccination of efficacy e ε [0, 1]. The model exhibits backward bifurcation for certain parameter values. The primary aim of this paper is to investigate the possibility of eliminating the infections in static as well as exponentially growing populations with a public health strategy based solely on vaccination. The critical vaccination rate ψ* above which the endemic infection dies out and the conditions on model parameters that ensure its existence are obtained. It has been found that eliminating the infection requires an application of control measures other than vaccination to reduce the basic reproduction number to below the reinfection threshold and then vaccinate susceptible individuals with a rate slightly greater than ψ *. The implication is that, generally, even if all newborns get vaccinated immediately after birth, an effective control is not necessarily assured except if the basic reproduction number is reduced to below the reinfection threshold. We further include the fatality of the infection and investigate its impact on the dynamics. Some numerical simulations are given to illustrate the theoretical analysis.

Original languageEnglish
Pages (from-to)195-206
Number of pages12
JournalMathematics and Computers in Simulation
Publication statusPublished - 2014


  • Backward bifurcation
  • Controllability
  • Epidemic model
  • Exponentially growing population
  • Vaccination

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science
  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics


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