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

13 Scopus citations


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
Issue number4
StatePublished - Aug 1 2013
Externally publishedYes



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

ASJC Scopus subject areas

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

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