Age-structured two-sex HPV transmission dynamics with a carrier state and reactivation

Human papillomavirus (HPV) remains one of the most common sexually transmitted infections worldwide, and its persistence and possible reactivation complicate efforts to understand and control transmission. In particular, the presence of a carrier stage and variation in reactivation across age and sex may play important roles in maintaining HPV prevalence. In this paper, we develop a two-sex Susceptible-Infectious-Carrying-Recovered (SICR) model with n discrete age groups to investigate how age-specific and sex-specific reactivation rates affect HPV transmission dynamics and how control measures can be designed accordingly. We derive the basic reproduction number $R_0$ and show that it provides a threshold criterion for disease elimination. The existence and stability of both the disease-free equilibrium and the endemic equilibrium are established rigorously. Using epidemiological data from Hangzhou in 2011, we estimate $R_0$ to be 2.177. Analytical and numerical results show that viral reactivation plays an important role in sustaining HPV endemicity and highlight the need for age-specific and sex-specific public health strategies. We also find that an excessively low viral reactivation rate is not always beneficial for controlling HPV prevalence. In particular, regulating reactivation alone is insufficient to control HPV transmission effectively, and our results suggest that combined interventions targeting both transmission and reactivation are more effective.