Modeling and Transmission Dynamics of a Stochastic Fractional Delay Cervical Cancer Model with Efficient Numerical Analysis

According to the World Health Organization (WHO), globally, cervical cancer ranks as the fourth most common cancer in women, with around 660,000 new cases in 2022. In the same year, about 94 percent of the 350,000 deaths caused by cervical cancer occurred in low- and middle-income countries. This paper focuses on the dynamics of HPV by modeling the interactions between four compartments, as follows: S(t), the number of susceptible females; I(t), females infected with HPV; X(t), females infected with HPV but not yet affected by cervical cancer (CCE); and V(t), females infected with HPV and affected by CCE. A compartmental model is formulated to analyze the progression of HPV, ensuring all key mathematical properties, such as existence, uniqueness, positivity, and boundedness of the solution. The equilibria of the model, such as the HPV-free equilibrium and HPV-present equilibrium, are analyzed, and the basic reproduction number, R0, is computed using the next-generation matrix method. Local and global stability of these equilibria are rigorously established to understand the conditions for disease eradication or persistence. Sensitivity analysis around the reproduction number is carried out using partial derivatives to identify critical parameters influencing R0, which gives insights into effective intervention strategies. With appropriate positivity, boundedness, and numerical stability, a new stochastic non-standard finite difference (NSFD) scheme is developed for the proposed model. A comparison analysis of solutions shows that the NSFD scheme is the most consistent and reliable method for a stochastic fractional delay model. Graphical simulations are presented to provide visual insights into the development of the disease and lend the results to a more mature discourse. This research is crucial in highlighting the mathematical rigor and practical applicability of the proposed model, contributing to the understanding and control of HPV progression.