Analytical and numerical modeling of the evolution of human papillomavirus infected cells

In this paper analytical properties of solutions of a novel human papillomavirus (HPV) infected cells model is investigated. We show existence, uniqueness and stability of solutions by using standard techniques based on the energy method and the method of upper and lower solutions. For the numerical counterpart, we develop and implement one efficient numerical algorithm scheme which satisfies nonnegative conditions and dynamical consistency. Efficiency of this method is shown by its longtime approximations, which are of paramount importance for a slow process like the evolution of HPV infected cells.