The impact of an imperfect vaccine and pap cytologyscreening on the transmission of human papillomavirus and occurrenceof associated cervical dysplasia and cancer

Tufail Malik; Jody Reimer; Abba Gumel; Elamin H. Elbasha; Salaheddin Mahmud

doi:10.3934/mbe.2013.10.1173

Article Contents

2013, Volume 10, Issue 4: 1173-1205. Doi: 10.3934/mbe.2013.10.1173

This issue Previous Article Modelling seasonal HFMD with the recessive infection in Shandong, China Next Article Graph-theoretic conditions for zero-eigenvalue Turing instability in general chemical reaction networks

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

1.
Department of Applied Mathematics and Sciences, Khalifa University of Science, Technology and Research, PO Box 127788, Abu Dhabi
2.
Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford OX1 3LB
3.
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2
4.
Merck Research Laboratories, UG1C-60, PO Box 1000, North Wales, PA 19454-1099
5.
Community Health Sciences, University of Manitoba, Winnipeg, Manitoba

Received: March 31, 2012

Revised: January 31, 2013

Published: May 2013

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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 HPV-induced 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).

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Mathematics Subject Classification: Primary: 92D30; Secondary: 37N25.

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