Analysis of human papillomavirus model with vaccination and individual heterogeneity

The dynamic system of HPV transmission with age subgroups, sexual and nonsexual transmission is established based on HPV vaccination. Firstly, the transmission threshold R₀ of the system is given. Local asymptotically stabilization of disease-free equilibrium when R₀ < 1 is proved. It is proved that there is a positive equilibrium and disease persistence in the system when R₀ > 1. Secondly, parameters estimation of the system is carried out based on the data from Chinese STD surveillance sites using the least square method. Finally, optimal control theory is applied to the system, the existence of optimal control is proved, and Pontryagin maximum principle is utilized to find optimal control strategy, and the spread of human papillomavirus in different age groups is predicted. The results show that for different age groups, vaccination of 16–45 years old is more beneficial to HPV control than vaccination of 9–15 years old, and that for different control costs, low-cost control is more advantageous.