A study of stochastically perturbed epidemic model of HPV infection and cervical cancer in Indian female population

This study introduces a novel stochastic SICR (susceptible, infected, cervical cancer and recovered) model to illustrate HPV (Human papillomavirus) infection dynamics and its impact on cervical cancer in the female population of India. We prove the existence of a unique positive global solution that ensures stochastic boundedness and permanence. Moreover, sufficient conditions for HPV extinction are established through the stochastic extinction parameter $R_0^e$, indicating that the infection will die out if $R_0^e<1$. Conversely, the persistence of HPV is established by the existence and uniqueness of an ergodic stationary distribution of the solution when the stochastic threshold $R_0^s>1$, using the suitable selection of Lyapunov functions. Furthermore, data on cervical cancer cases in India from 2016 to 2020 is fitted to the model, providing parameter values suitable for the region. The theoretical findings are validated using the Positive-Preserving Truncated Euler–Maruyama method. Additionally, effective control strategies for India are suggested based on model predictions and sensitivity of key parameters.