Mathematical analysis of a disease transmission model with quarantine, isolation and an imperfect vaccine

Mohammad A. Safi, Abba Gumel

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

A new mathematical model for the transmission dynamics of a disease subject to the quarantine (of latent cases) and isolation (of symptomatic cases) and an imperfect vaccine is designed and analyzed. The model undergoes a backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction threshold is less than unity. It is shown that the backward bifurcation phenomenon can be removed if the vaccine is perfect or if mass action incidence, instead of standard incidence, is used in the model formulation. Further, the model has a unique endemic equilibrium when the threshold quantity exceeds unity. A nonlinear Lyapunov function, of the GohVolterra type, is used to show that the endemic equilibrium is globally-asymptotically stable for a special case. Numerical simulations of the model show that the singular use of a quarantine/isolation strategy may lead to the effective disease control (or elimination) if its effectiveness level is at least moderately high enough. The combined use of the quarantine/isolation strategy with a vaccination strategy will eliminate the disease, even for the low efficacy level of the universal strategy considered in this study. It is further shown that the imperfect vaccine could induce a positive or negative population-level impact depending on the size (or sign) of a certain associated epidemiological threshold.

Original languageEnglish (US)
Pages (from-to)3044-3070
Number of pages27
JournalComputers and Mathematics with Applications
Volume61
Issue number10
DOIs
StatePublished - May 2011
Externally publishedYes

Fingerprint

Quarantine
Vaccines
Vaccine
Mathematical Analysis
Imperfect
Isolation
Endemic Equilibrium
Backward Bifurcation
Incidence
Disease control
Vaccination
Globally Asymptotically Stable
Lyapunov functions
Nonlinear Function
Model
Lyapunov Function
Elimination
Efficacy
Exceed
Eliminate

Keywords

  • Backward bifurcation
  • Equilibria
  • Isolation
  • Quarantine
  • Stability
  • Vaccine

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Modeling and Simulation
  • Computational Mathematics

Cite this

Mathematical analysis of a disease transmission model with quarantine, isolation and an imperfect vaccine. / Safi, Mohammad A.; Gumel, Abba.

In: Computers and Mathematics with Applications, Vol. 61, No. 10, 05.2011, p. 3044-3070.

Research output: Contribution to journalArticle

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