Evolutionary Safe Padé Approximation Scheme for Dynamical Study of Nonlinear Cervical Human Papilloma Virus Infection Model

Abstract

This study proposes a structure-preserving evolutionary framework to find a semi-analytical approximate solution for a nonlinear cervical cancer epidemic (CCE) model. The underlying CCE model lacks a closed-form exact solution. Numerical solutions obtained through traditional finite difference schemes do not ensure the preservation of the model's necessary properties, such as positivity, boundedness, and feasibility. Therefore, the development of structure-preserving semi-analytical approaches is always necessary. This research introduces an intelligently supervised computational paradigm to solve the underlying CCE model's physical properties by formulating an equivalent unconstrained optimization problem. Singularity-free safe Padé rational functions approximate the mathematical shape of state variables, while the model's physical requirements are treated as problem constraints. The primary model of the governing differential equations is imposed to minimize the error between approximate solutions. An evolutionary algorithm, the Genetic Algorithm with Multi-Parent Crossover (GA-MPC), executes the optimization task. The resulting method is the Evolutionary Safe Padé Approximation (ESPA) scheme. The proof of unconditional convergence of the ESPA scheme on the CCE model is supported by numerical simulations. The performance of the ESPA scheme on the CCE model is thoroughly investigated by considering various orders of non-singular Padé approximants.