A New Approach to Solve Dynamical Fractional Model of Infertile Couples by the Finite Element Method

Abstract

In this paper, we propose a dynamic model designed to predict the treatment outcomes of infertility in couples. To this end, five main groups of couples are considered: susceptible couples, patient couples, those undergoing treatment only, those receiving treatment with surgery, and cured couples. Our primary contribution lies in the formulation of a fractional-order model that captures the dynamics of infertile couples and identifies asymptotically stable disease-free equilibrium points. The main objective is to develop a novel numerical approach based on the finite element method to solve a nonlinear system of fractional differential equations. This
method transforms the fractional system into a system of algebraic equations. Moreover, the proposed technique proves to be robust,
efficient, and particularly well-suited to modeling infertility. To validate our model, we apply the proposed method and conclude with a comprehensive numerical analysis.

Keywords: Infertility modeling; fractional differential equations; Caputo derivative; finite element method; stability analysis; basic reproduction number; numerical simulation.

2010 Mathematics Subject Classification. 26A25; 26A35