Abstract

A new deterministic model for the transmission dynamics of two strains of polio, the vaccine-derived polio virus (VDPV) and the wild polio virus (WPV), in a population is designed and rigorously analysed. It is shown that Oral Polio Vaccine (OPV) reversion (leading to increased incidences of WPV and VDPV strains), together with the combined effect of vaccinating a fraction of the unvaccinated susceptible and missed susceptible children, could induce the phenomenon of backward bifurcation when the associated reproduction number of the model is less than unity. Furthermore, the model undergoes competitive exclusion, where the strain with the higher reproduction number (greater than unity) drives the other (with reproduction number less than unity) to extinction. In the absence of OPV reversions (leading to the co-existence of both strains in the population), it is shown that the disease-free equilibrium of the model is globally-asymptotically stable whenever the associated reproduction number is less than unity. Numerical simulations of the model suggest that the model undergoes the phenomenon of competitive exclusion, where the strain with the higher reproduction number (greater than unity) drives the other to extinction. Furthermore, co-existence of the two strains is feasible if their respective reproduction number are equal or approximately equal (and greater than unity).

Original languageEnglish (US)
Pages (from-to)167-189
Number of pages23
JournalNonlinear Analysis: Real World Applications
Volume25
DOIs
StatePublished - Oct 1 2015

Fingerprint

Reproduction number
Vaccination
Poliomyelitis
Vaccines
Reproduction
Vaccine
Viruses
Virus
Competitive Exclusion
Coexistence
Extinction
Model
Backward Bifurcation
Approximately equal
Globally Asymptotically Stable
Deterministic Model
Incidence
Population
Numerical Simulation
Computer simulation

Keywords

  • Equilibria
  • Polio
  • Reproduction number
  • Stability

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Computational Mathematics
  • Engineering(all)
  • Medicine(all)
  • Economics, Econometrics and Finance(all)

Cite this

Dynamics of a two-strain vaccination model for polio. / Okuonghae, D.; Gumel, Abba; Safi, M. A.

In: Nonlinear Analysis: Real World Applications, Vol. 25, 01.10.2015, p. 167-189.

Research output: Contribution to journalArticle

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