MATHEMATICAL MODELLING OF HUMAN PAPILLOMAVIRUS DYNAMICS WITH VACCINATION INCORPORATING OPTIMAL CONTROL ANALYSIS

Abstract

Cervical Cancer (CC) is primarily caused by Human Papillomavirus (HPV). If untreated in the early stages the abnormal development of cervical cells can be fatal. CC is clearly a threat with about half a million documented cases worldwide and over 200 000 reported deaths per year. Particularly in Sub-Saharan Africa, cervical cancer prevalence still remains high. Early stages of the disease can be treated and prevented but later stages have very low survival rates. Women, particularly in low-income nations are more likely to die from cervical cancer as it enters its advanced stages. Numerous mathematical models have been formulated in order to better understand the dynamics of how HPV causes cervical cancer. However, optimal control strategies with the lowest potential cost of preventing HPV and CC have been given little attention. The objective of this study was to formulate a deterministic mathematical model of HPV dynamics with vaccination that incorporates optimal control analysis. The methodology used in developing the model involved the use of qualitative theory of ODEs, the basic reproduction number using next generation matrix, optimal control analysis and numerical simulations. The analysis of the model shows that the model is positively invariant and bounded. Both disease free equilibrium point and endemic equilibrium point exists and shown to be asymptotically stable when some conditions are met. The optimal control problem is also shown to exist using the Pontryagin Maximum Principle. The analysis also shows that when the basic reproduction number is less than one, HPV dies out in the population but when the basic reproduction number is greater than one, HPV spreads and becomes endemic. The result shows that, combining the three interventions (effective awareness, screening and treatment of HPV and CC, and vaccination) at the rates (ϕ1 = 0.2, ϕ2 = 0.3, ϕ3 = 0.03 ) the infection begins to reduce significantly and dies out in the community when the interventions are intensified. The findings of this study will help epidemiologists and healthcare professionals in concentrating on necessary parameters when formulating an infectious disease control policy. Additionally, it will provide as a basic framework for future study on HPV and CC dynamics. In the interest of HPV and CC prevention, the relevant authorities should encourage effective awareness, treatment of HPV and CC, and vaccination in order to prevent the disease from spreading.