Cervical cancer is primarily caused by human papillomavirus (HPV) that typically progresses through detectable precancerous lesions. To better understand the spread of HPV and its inevitable role in cervical cancer, this study presents an SIPCR epidemic model incorporating the standard incidence rate in both deterministic and stochastic settings. The unavoidable randomness in the population is modeled using the logarithmic mean-reverting Ornstein–Uhlenbeck process in the transmission rate. Firstly, the deterministic system is analyzed to bring out the nonnegativity and boundedness of solutions, the disease-free equilibrium and the basic reproduction number \(\mathcal {R}_0\) . The local and global asymptotic stability of the disease-free equilibrium is proved under the condition \(\mathcal {R}_0 < 1\) . Later, the stochastic model is examined for the existence and uniqueness of a global positive solution. To determine the persistence and extinction of infection, two threshold quantities \(\mathcal {R}_0^s\) and \(\mathcal {R}_0^e\) are derived using appropriate Lyapunov functionals. Specifically, the infection persists with a stationary solution when \(\mathcal {R}_0^s > 1\) and goes extinct when \(\mathcal {R}_0^e < 1\) . Importantly, the model is fitted to cervical cancer incidence data from India, with an estimated value of \(\mathcal {R}_0^e=0.890270\) , indicating a likely long-term decline in HPV infection. Also, a global sensitivity analysis using Latin Hypercube Sampling combined with Partial Rank Correlation Coefficients identifies the most influential parameters on model outcomes. Based on these findings, real-world intervention scenarios are simulated until 2060 to evaluate strategies for accelerating infection extinction and reducing the prevalence of HPV and cervical cancer. These insights offer valuable guidance for public health efforts aimed at achieving HPV elimination in India.
