Volume 13, no. 2Pages 80 - 92

Modelling the Human Papilloma Virus Transmission in a Bisexually Active Host Community

O.M. Ogunmiloro
In this article, we construct a mathematical model describing the transmission dynamics of Human Papilloma Virus (HPV) in a bisexually active host community. Comprehensive mathematical techniques are used to qualitatively and quantitatively analyze the model. We analyze the local and global stabilities of the model's equilibria and show that if the basic reproduction number is less than unity, then the model is locally and globally asymptotically stable at the HPV-free static states. Also, if the basic reproduction number is less than unity, then the HPV-endemic static state is globally asymptotically stable. Numerical simulations are carried out and graphical illustrations are presented to validate the theoretical results.
Full text
HPV; basic reproduction number; local stability; global stability.
1. World Health Organization (WHO), WHO Fact Sheet. Available at: https://www.who.int (accessed 2019).
2. Center for Disease Control (CDC), STD Facts-Human Papilloma Virus (HPV). Available at: https://www.medicalnewstoday.com (accessed 2019).
3. Medical News Today, Human Papilloma Virus (HPV): Treatment, Symptoms and Causes. Available at: https://www.medicalnewstoday.com/articles/246670 (accessed 2019).
4. Ogunmiloro O.M., Fadugba S.E., Ogunlade T.O. Stability Analysis and Optimal Control of Vaccination and Treatment of a SIR Epidemiological Deterministic Model with Relapse. International Journal of Mathematical Modelling and Computations, 2018, vol. 8, no. 1, pp. 39-51.
5. La-Salle J., Lefschetz S. Stability by Lyapunov's Direct Method with Applications. N.Y., Academic Press, 1961.
6. Anderson R.M., May R.M. Population Biology of Infectious Diseases. Berlin, Springer, 1982.
7. Lee S.L., Tameru A.M. A Mathematical Model of Human Papilloma Virus (HPV) in the United States (US) and its Impact on Cervical Cancer. Journal of Cancer, 2012, vol. 3, pp. 262-268. DOI: 10.2150/jca.4161, 2012
8. Dasbach E.J., Elbasha E.H., Insinga R.P. Predicting the Epidemiologic Impact of Vaccination Against Human Papilloma Virus Infection and Disease. Epidemiologic Reviews, 2006, vol. 28, no. 1, pp. 88-100.
9. Omame A., Umana R.A., Okounghae D., Inyama S.C. Mathematical Analysis of a Two-Sex Human Papilloma Virus (HPV) Model. International Journal of Biomathematics, 2018, vol. 11, no. 7, article ID: 1850092. DOI: 10.1142/S1793626810000397
10. Sado A.E. Mathematical Modeling of Cervical Cancer with HPV Transmission and Vaccination. Science Journal of Applied Mathematics and Statistics, 2019, vol. 7, no. 2, pp. 21-25. DOI: 1011648/j.sjams.20190702
11. Najat Ziyadi. A Male-Female Mathematical Model of Human Papilloma Virus (HPV) in African American Population. American Institute of Mathematical Sciences, 2017, vol. 14, no. 1, pp. 339-358. DOI: 10.3934/mbe.2017022
12. Ryser M.D., Gravitt P.E., Myers E.R. Mechanistic Mathematical Models: An Underused Platform for HPV Research. Papilloma Research, 2017, vol. 3, pp 46-49.
13. Brower A.F. Models of HPV as an Infectious Disease and as an Etiological Agent. PhD Thesis, University of Michigan, 2015.
14. Sharomi O., Malik T. A Model to Assess the Effect of Vaccine Compliance on Human Papilloma Virus Infection and Cervical Cancer. Applied Mathematical Modelling, 2017, vol. 47, pp. 528-550.
15. Elbasha E.H. Global Stability of Equilibria in a Two-Sex HPV Vaccination Model. Bulletin of Mathematical Biology, 2008, vol. 70, pp. 894-909.
16. Dietz C.A., Nyberg C.R. Genital, Oral and Anal Human Papilloma Virus Infection in Men Who Have Sex with Men. The Journal of the American Osteopathic Association, 2011, vol. 111, pp. 19-25.
17. Independent News, Lesbians and Bisexual Women at Risk from Dangerous Myth "They Cannot Get Cervical Cancer" Warns Nhs. Available at: https://www.independent.co.uk (accessed 2019).