Mathematical Analysis of HPV and Cervical Cancer Model in the Presence of Protection
Jacinta M. Mutwiwa *
Department of Mathematics, Kibabii University, Bungoma, Kenya.
Samuel B. Apima
Department of Mathematics and Statistics, Kaimosi Friends University, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Human papilloma Virus (HPV) is the primary infection that causes Cervical cancer. Due to the high cost of treatment for cervical cancer, protection against HPV and Cervical cancer infection may be preferable in a scarce resource settings. In this paper, a deterministic model that incorporates protection against the infection was developed and analysed. The endemic state is shown to exist provided that the reproduction number is greater than unity. Furthermore, by the use of Routh-Hurwitz criterion and suitable Lyapunov functions, Endemic Equilibrium (EE) is shown to exist provided that the reproduction number is greater than unity. By use of a suitable Lyapunov function, the endemic state was shown to be globally asymptotically stable. The effectiveness of protection is achieved if well done hence, an increase in protection leads to low disease prevalence in a population.
Keywords: Protection, human papilloma virus, cervical cancer, reproduction number, stability analysis