Vaccination-driven suppression, stochastic variability, and contact saturation in HPV-cervical cancer transmission in...

This study develops two stochastic models (one representing the pre-vaccination era and the other representing the vaccination era) describing human papillomavirus infection and its progression to cervical cancer in India. Both models incorporate Holling type-II incidence, with transmission dynamics perturbed by the Black-Karasinski stochastic process. A rigorous theoretical analysis is conducted for these models. The existence and uniqueness of global positive solutions are established, followed by the derivation of threshold quantities governing persistence and extinction. When R_i^s>1(i=1,2), each model admits at least one stationary distribution, indicating long-term persistence of infection. In contrast, when R_i^e<1(i=1,2), the infection undergoes exponential extinction. The non-vaccination model is fitted to annual cervical cancer incidence data from India for the period 2003 to 2017. Substituting the fitted parameter values within the specified time horizon implies that the system remains persistent under the current conditions. Subsequently, for the vaccination model, the remaining parameters are estimated from reliable scientific data, and simulations are carried out from 2025 onward. For the vaccination period, the estimated parameter values indicate eventual eradication of infection. Extensive numerical simulations support the theoretical findings. A global sensitivity analysis using Latin hypercube sampling and partial rank correlation coefficients identifies the most influential parameters. Finally, extinction time distributions and survival probabilities are examined to provide policy-relevant insights toward achieving an HPV-free India within the next 50 years.