A model to assess the effect of vaccine compliance on Human Papillomavirus infection and cervical cancer

Three doses of a Human Papillomavirus (HPV) vaccine are recommended for both males and females, and compliance is a major challenge. In this paper a deterministic model for HPV infection and cervical cancer is constructed and rigorously analyzed for the effects of vaccine compliance. The model is based on ordinary differential equations and incorporates cohort vaccination of males and females before entering the sexually-active class as well as a fraction that starts taking the vaccine after entering the sexually-active class. The female population is further stratified into two age groups. The first group is at a higher risk for new HPV infection, is not likely to develop cervical cancer, and is subject to three doses of an HPV vaccine. The second age group has reduced chances of acquiring new infections but is at a higher risk for developing cervical cancer resulting from a persistent HPV infection. No fresh HPV vaccine is administered in this age group. The model has a locally asymptotically-stable disease-free equilibrium but may also admit endemic equilibria when the epidemic threshold, namely the effective reproduction number, Rv, is below unity. Using the center manifold theory it is shown that the model exhibits a backward bifurcation at Rv=1, which is caused due to the imperfect HPV vaccine. For the case of a perfect vaccine, the disease-free equilibrium is proved to be globally asymptotically-stable, under certain additional conditions, when Rv≤1. Multiple endemic equilibria may exist when Rv>1. It is shown through numerical simulations that vaccine compliance (with all three doses) is necessary for the reduction of HPV infections and cervical cancer. Lack of compliance may lead to a higher number of infections and cancer cases in the long run.