Mathematical Biosciences and Engineering, 2013, 10(4): 1173-1205. doi: 10.3934/mbe.2013.10.1173

Primary: 92D30; Secondary: 37N25.

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The impact of an imperfect vaccine and pap cytologyscreening on the transmission of human papillomavirus and occurrenceof 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

A mathematical model for the natural history of human papillomavirus(HPV) is designed and used to assess the impact of a hypotheticalanti-HPV vaccine and Pap cytology screening on the transmissiondynamics of HPV in a population. Rigorous qualitative analysis ofthe model reveals that it undergoes the phenomenon of backwardbifurcation. It is shown that the backward bifurcation is caused bythe imperfect nature of the HPV vaccine or the HPV-induced andcancer-induced mortality in females. For the case when thedisease-induced and cancer-induced mortality is negligible, it isshown that the disease-free equilibrium (i.e., equilibrium in theabsence of HPV and associated dysplasia) is globally-asymptoticallystable if the associated reproduction number is less than unity. Themodel has a unique endemic equilibrium when the reproductionthreshold exceeds unity. The unique endemic equilibrium isglobally-asymptotically stable for a special case, where theassociated HPV-induced and cancer-induced mortality is negligible.Numerical simulations of the model, using a reasonable set ofparameter values, support the recent recommendations by some medicalagencies and organizations in the USA to offer Pap screening on a3-year basis (rather than annually).
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