Authors: Abosede Mary Oke, Sheid Avidime Momohjimoh, Pauline Olayemi Obafaiye
Abstract: This study presents a unified mathematical framework integrating two critical biomedical domains: cervical cancer transmission dynamics and magnetohydrodynamic (MHD) blood-based nanofluid flow, both solved using the Gaussian Process-Homotopy Analysis Method (GP-HAM). Cervical cancer, driven by persistent high-risk HPV infection, progresses through multi-stage carcinogenesis over 10-20 years, creating a stiff epidemiological system with widely separated time scales. Concurrently, MHD-controlled blood-based nanofluid transport offers a promising modality for targeted drug delivery and thermal regulation in cardiovascular prosthetics. The GP-HAM framework synergistically combines the Homotopy Analysis Method for stable semi-analytical solutions with Gaussian Process regression for Bayesian uncertainty quantification of time-varying parameters. The 8-compartment cervical cancer model captures nonlinear HPV transmission, cancer progression, and treatment interventions, while the MHD model describes blood as an electrically conducting Newtonian base fluid containing therapeutic nanoparticles over a stretching surface. Detailed mathematical operator formulation of GP-HAM is provided, including A-stability and L-stability proofs. The framework is validated on both epidemiological and fluid dynamics problems. Numerical results demonstrate that GP-HAM achieves RMSE reductions of 63-75% compared to RK4 and 54-62% compared to BDF2, with 93-94% coverage of nominal 95% credible intervals. The integrated framework provides a powerful tool for public health decision-making and targeted therapeutic interventions.
