Modeling the impact of screening, vaccination and treatment on the transmission dynamics of HPV and Cervical cancer

Cervical cancer remains a significant cause of mortality and economic burden, particularly in developing countries with low rates of human papillomavirus (HPV) vaccination and screening. To address this, we present a mathematical model for controlling cervical cancer by integrating strategic HPV vaccination, screening and treatment. The population is divided into seven compartment: susceptible, vaccinated, infected with HPV, screened, cervical cancer, under treatment, and recovered. The models well-posedness is first established by proving the boundedness and non-negativity of solutions, ensuring biological relevance. The basic reproduction number R0 is computed using the next-generation matrix. The local and global stability of the disease-free equilibrium is analysed using the Jacobian matrix and Lyapunov function respectively. Furthermore, bifurcation analysis is performed using the Castillo-Chavez and Song theorem and sensitivity analysis is conducted on key parameters to identify their influence on disease dynamics. Numerical simulations of the model supports the analytical results. The findings of the study indicate that if the reproduction number is less than one, the solution converges to the disease-free state, signifying the asymptotic stability of the HPV-Cervical cancer free steady state. Crucially, the model demonstrates that increasing vaccination, screening and treatment rates significantly reduces HPV and cervical cancer incidence. This study underscores the value of mathematical modeling in informing the public health policy and provides a framework for optimizing control measures against HPV and Cervical cancer.