Modeling the Epidemiology of Human Papilloma Virus Infection and Vaccination and Its Impact on Cervical Cancer in Ghana

Abstract

This paper is purported to assess the impact of the modeling of bivalent Human Papillomavirus (HPV) vaccine and Pap test on prevalence of carcinogenic HPV 16/18 types in Ghanaian females. For this purpose, a non-linear dynamic SIR model of homogeneous transmission for HPV 16/18 type’s infection is developed, which accounts for immunity due to vaccination in particular. The recovery class R was partitioned into two compartments, temporary recovery RT and permanent recovery RP. We propose ODE equations to study HPV infection in the general female population. The vaccinated reproduction number R0 for general female population was derived using the approach described by Diekmann (2010) called the Next Generation Operator approach. The proposed models were analyzed using quantitative method, with regard to steady-state stability and sensitivity analysis. Precisely, the stability of the models is investigated depending on the value for R0 for the disease free steady-state and Routh-Hurwitz criterion employed to study the stability of the endemic steady-state. Prevalence data are used to fit a numerical HPV model, so as to assess infection rates. We also support our theoretical analysis with numerical simulations. This provides a framework for future research and public-health policy to determine the dependence of HPV vaccination programs on age, as well as how the vaccine and Pap test can reduce the number of infections and deaths due to cervical cancer. We estimated the basic reproductive number for the general female population based on current vaccination statistics using the systems of ODE’s to be R0>1, which indicates that the pathogen is able to invade the general female population and cervical cancer cases will increase in the future. The derivation and analysis of the modified SIR mathematical model SIRTRT enabled a better understanding of the dynamics of the spread of Human Papilloma Virus infection and reduction of cervical cancer cases in Ghana.