Qualitative analysis of an age-and sex-structured vaccination model for human papillomavirus

Tufail Malik, Abba Gumel, Elamin Elbasha

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

A new model for the transmission dynamics of human pappilomavirus (HPV) is designed and analysed. The model, which stratifies the total population in terms of age and gender, incorporates an imperfect anti-HPV vaccine with some therapeutic benefits. Rigorous qualitative analysis of the resulting age-structured model, which takes the form of a deterministic system of non-linear partial differential equations with separable transmission coefficients, shows that the disease-free equilibrium of the model is locallyasymptotically stable whenever the effective reproduction number (denoted by Rv) is less than unity. It is shown to be globally-asymptotically stable if certain additional conditions hold. Furthermore, it is shown that the model has at least one endemic equilibrium when Rv exceeds unity. Hence, the effective control of HPV spread in a community, using a vaccine, is governed by the threshold quantity Rv (the use of the vaccine will lead to effective disease control or elimination only if it reduces the threshold quantity to a value less than unity; and the use of such vaccine will not lead to effective disease control if it fails to make the threshold quantity to be less than unity).

Original languageEnglish (US)
Pages (from-to)2151-2174
Number of pages24
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume18
Issue number8
DOIs
StatePublished - Oct 2013
Externally publishedYes

Fingerprint

Vaccination
Vaccine
Qualitative Analysis
Vaccines
Disease control
Age-structured Model
Reproduction number
Transmission Coefficient
Endemic Equilibrium
Globally Asymptotically Stable
Nonlinear Partial Differential Equations
Imperfect
Model
Elimination
Exceed
Partial differential equations
Human

Keywords

  • Age-structure
  • Effective reproduction number
  • Endemic equilibrium
  • Human papillomavirus
  • Vaccination

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Qualitative analysis of an age-and sex-structured vaccination model for human papillomavirus. / Malik, Tufail; Gumel, Abba; Elbasha, Elamin.

In: Discrete and Continuous Dynamical Systems - Series B, Vol. 18, No. 8, 10.2013, p. 2151-2174.

Research output: Contribution to journalArticle

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