The impact of an imperfect vaccine and pap cytology screening on the transmission of human papillomavirus and occurrence of associated cervical dysplasia and cancer

Tufail Malik, Jody Reimer, Abba Gumel, Elamin Elbasha, Salaheddin Mahmud

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

A mathematical model for the natural history of human papillomavirus (HPV) is designed and used to assess the impact of a hypothetical anti-HPV vaccine and Pap cytology screening on the transmission dynamics of HPV in a population. Rigorous qualitative analysis of the model reveals that it undergoes the phenomenon of backward bifurcation. It is shown that the backward bifurcation is caused by the imperfect nature of the HPV vaccine or the HPV-induced and cancer-induced mortality in females. For the case when the disease-induced and cancer-induced mortality is negligible, it is shown that the disease-free equilibrium (i.e., equilibrium in the absence of HPV and associated dysplasia) is globally-asymptotically stable if the associated reproduction number is less than unity. The model has a unique endemic equilibrium when the reproduction threshold exceeds unity. The unique endemic equilibrium is globally- asymptotically stable for a special case, where the associated HPVinduced and cancer-induced mortality is negligible. Numerical simulations of the model, using a reasonable set of parameter values, support the recent recommendations by some medical agencies and organizations in the USA to offer Pap screening on a 3-year basis (rather than annually).

Original languageEnglish (US)
Pages (from-to)1173-1205
Number of pages33
JournalMathematical Biosciences and Engineering
Volume10
Issue number4
DOIs
StatePublished - Aug 2013
Externally publishedYes

Fingerprint

Cytology
Uterine Cervical Dysplasia
Vaccines
Papillomaviridae
Vaccine
Imperfect
Uterine Cervical Neoplasms
cell biology
Screening
Cell Biology
Cancer
vaccines
screening
Papillomavirus Vaccines
neoplasms
Mortality
Backward Bifurcation
Reproduction
Endemic Equilibrium
Globally Asymptotically Stable

Keywords

  • Backward bifurcation
  • Cervical cancer
  • Endemic equilibrium
  • Human papillomavirus
  • Pap cytology screening
  • Vaccine

ASJC Scopus subject areas

  • Applied Mathematics
  • Modeling and Simulation
  • Computational Mathematics
  • Agricultural and Biological Sciences(all)
  • Medicine(all)

Cite this

The impact of an imperfect vaccine and pap cytology screening on the transmission of human papillomavirus and occurrence of associated cervical dysplasia and cancer. / Malik, Tufail; Reimer, Jody; Gumel, Abba; Elbasha, Elamin; Mahmud, Salaheddin.

In: Mathematical Biosciences and Engineering, Vol. 10, No. 4, 08.2013, p. 1173-1205.

Research output: Contribution to journalArticle

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