A Stochastic Age-Structured Model for Human Papillomavirus and Cervical Cancer Dynamics Under Vaccination and Treatment Interventions

Human Papillomavirus (HPV) remains the most prevalent sexually transmitted infection globally and is the leading etiological agent of cervical cancer, especially in low- and middle-income countries. Deterministic models have provided valuable insights into HPV dynamics and control strategies, yet they often neglect the intrinsic randomness associated with infection transmission, vaccination uptake, and treatment adherence. This study develops a stochastic age- structured model for HPV and cervical cancer incorporating vaccination and treatment interventions. The model extends existing deterministic frameworks by introducing stochastic processes through continuous-time Markov chains and stochastic differential equations. Analytical results establish probabilistic thresholds for extinction and persistence using a stochastic reproduction number R0s. Monte Carlo simulations are employed to evaluate the variability of HPV prevalence, cancer incidence, and extinction probabilities across age groups. Results indicate that early adolescent vaccination (ages 8– 12) remains the most effective and robust intervention, yielding extinction probabilities exceeding 95% within 25 years, even under stochastic fluctuations. However, stochastic noise in infection and treatment processes broadens uncertainty intervals, delaying elimination timelines in young adult cohorts. The combined implementation of vaccination and treatment reduces both mean prevalence and variance, enhancing the probability of long-term eradication. These findings highlight the importance of accounting for randomness in epidemiological modeling to inform resilient and realistic public health policies for HPV elimination.