A Mathematical Study of a Model for HPV with Two High-Risk Strains

Abstract

A new two-sex deterministic model for two strains (HPV type 16/18 and type 31/45) of human papillomavirus (HPV) infection is designed and rigorously analyzed to gain insights into its transmission dynamics. The model features the use of the bivalent Cervarix vaccine targeted at one group of high-risk HPV: type 16/18 but with cross-immunity property against other high-risk HPV; and type 31/45. The model is shown to exhibit the phenomenon of backward bifurcation, where a stable disease-free equilibrium (DFE) coexists with one or more stable endemic equilibria when the associated reproduction number is less than unity. It is further shown that the backward bifurcation phenomenon is caused by the imperfect vaccine as well as the reinfection of individuals who recover naturally from previous infection with the same strain of the disease. Numerical simulations of the model reveal that increasing the fraction of vaccinated females against strain 1 (HPV type 16/18) infection could significantly bring down the burden of strain 2 (HPV type 31/45) infection.