Control of HPV infection leading to cervical cancer

HPV is the most common sexually transmitted infection and can lead to cancer. Vaccination has been considered as a very effective measure against HPV and along with regular screenings is recommended for the prevention of cervical cancer. In this study we propose and analyze a model for the transmission dynamics of Human Papilloma Virus (HPV). We discuss the optimal vaccination strategy in the case when multiple vaccines are available. We have considered an ODE based compartmental model, incorporating sex structure, we also consider HPV leading to cervical cancer by including pre-cancerous and cancerous compartments in the model. Adding the pre-cancerous and cancerous compartments will help us better understand the role of vaccination in prevention of cancers due to HPV. Using standard techniques from dynamical systems theory, we determine the disease free (DFE) and endemic steady states (EE). We determine a threshold quantity, the basic reproductive number R₀ in terms of the model parameters, such that, the DFE is stable when R₀<1 and the EE is stable in the case R₀>1. The goal of control measures is to try an reduce R₀ to be below the threshold value of 1, the regime in which the disease will ultimately be driven to extinction. We also prove the existence of a backward bifurcation in the model, epidemiologically this means that the long time behavior of the model depends on the initial infected population and that the disease may be harder to control, and the condition R₀<1 may not suffice to eradicate the disease. Finally, using optimal control theory we consider the effective vaccination strategies using multiple vaccines, the goal is to study the best vaccination strategy using multiple vaccines. Our results show that a higher coverage with vaccines that provide protection against multiple strains, although more expensive, is best suited to control HPV transmission and subsequent development of cancer.