Semi-Analytical Solution of Cervical Cancer Model using the Adomian Decomposition Method

Abstract

This study presents a semi-analytical solution for a deterministic 8-compartment model of cervical cancer using the Adomian Decomposition Method (ADM). Unlike purely numerical schemes, ADM yields a continuous, exponentially convergent series solution that explicitly reveals the role of each model parameter in disease progression. Novel contributions include the derivation of recursive formulas and Adomian polynomials specific to the nonlinear HPV transmission term, a sensitivity analysis of screening and treatment rates directly from the ADM series, and an assessment of the convergence radius for realistic epidemiological parameters. The ADM solution with only 11 terms achieves a maximum absolute error below 10^−0.95 ≈ 0.112 for the recovered population, demonstrating rapid convergence. Validation against the fourth-order Runge-Kutta (RK4) method shows excellent agreement. The continuous nature of ADM allows for a precise estimation of the time to peak infection and the long-term equilibrium, providing actionable insights for public health interventions in high-burden regions such as Nigeria.