An age-structured model of human papillomavirus vaccination

Recently, a vaccine for human papillomavirus was introduced, but made available only for girls and adult women aged 13-26. Since rates of sexual activity vary by age and gender, vaccinating only an age-limited subset of one cohort may be insufficient to control the disease across all age groups and genders. We develop an age-dependent two-sex mathematical model to describe the HPV vaccination program for a vaccine targeting HPV types 16 and 18 in both childhood and adult stages. A stability analysis is performed to determine the stability of the disease-free and endemic equilibria for different vaccination programs. The basic reproduction number is derived for perfect childhood vaccination, perfect adult vaccination and childhood-adult vaccination. We show that the effects of age dependency are complex, but that vaccinating a single age cohort in one gender, as current programs do, can result in eventual control of the disease across all age groups. We also support our theoretical analysis with numerical simulations. This provides a framework for future research and public-health policy to determine the dependence of HPV vaccination programs on age and sexual behaviour, as well as how the vaccine can reduce the number of infections and deaths due to cervical cancer.