Modelación y análisis de la dinámica del Virus del Papiloma Humano en células epiteliales.

Abstract

In this work, a mathematical model for cell and viral dynamics is developed based on three and seven non-linear ordinary differential equations, respectively. The cell dynamics model describes the differentiation of the cells of the stratified epithelium of the cervix, while the viral dynamics model describes human papillomavirus infection during the keratinocytes differentiation. The existence and stability of the infection-free equilibrium of the cell dynamics model is determined, in addition, the non-existence of periodic orbits for a subsystem of this model is proved. We calculated the basic reproductive number of the viral dynamics model. We proved that the infection-free equilibrium is locally asymptotically stable if the basic reproductive number is less than unity. We showed the existence of the infected equilibrium when the basic reproductive number is greater than unity, and the solutions are studied numerically using values of the parameters reported in the literature. The viral dynamics model reproduces transient, acute, latent and chronic infections that have been reported in studies of the natural history of the infection for human papillomavirus.