Global Stability of Equilibria in a Two-Sex HPV Vaccination Model |
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Authors: | Elamin H Elbasha |
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Institution: | (1) Merck Research Laboratories, UG1C-60, P.O. Box 1000, North Wales, PA 19454-1099, USA |
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Abstract: | Human papillomavirus (HPV) is the primary cause of cervical carcinoma and its precursor lesions, and is associated with a
variety of other cancers and diseases. A prophylactic quadrivalent vaccine against oncogenic HPV 16/18 and warts-causing genital
HPV 6/11 types is currently available in several countries. Licensure of a bivalent vaccine against oncogenic HPV 16/18 is
expected in the near future. This paper presents a two-sex, deterministic model for assessing the potential impact of a prophylactic
HPV vaccine with several properties. The model is based on the susceptible-infective-removed (SIR) compartmental structure.
Important epidemiological thresholds such as the basic and effective reproduction numbers and a measure of vaccine impact
are derived. We find that if the effective reproduction number is greater than unity, there is a locally unstable infection-free
equilibrium and a unique, globally asymptotically stable endemic equilibrium. If the effective reproduction number is less
than unity, the infection-free equilibrium is globally asymptotically stable, and HPV will be eliminated. |
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Keywords: | HPV HPV disease Cancer Vaccine Mathematical model Global stability Endemic equilibrium Reproduction number |
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