A dynamical model for the number of infertile couples

Area of Science:

• Mathematical modeling
• Reproductive health
• Dynamical systems theory

Background:

• Infertility affects numerous couples globally, necessitating effective prediction models for treatment outcomes.
• Current models may not fully capture the complex dynamics of infertility and treatment responses.
• Understanding patient trajectories is key to optimizing reproductive medicine strategies.

Purpose of the Study:

• To develop and analyze a dynamic model for predicting couples' infertility treatment results.
• To identify stable equilibrium points within the model representing treatment success or failure.
• To investigate the stability of different equilibrium points in the infertility treatment model.

Main Methods:

• Formulation of a dynamic model encompassing five groups of couples: susceptible, patient, medicine-only treatment, surgery treatment, and cured.
• In-depth analysis of the model's dynamical properties to locate equilibrium points.
• Numerical simulation using the Rung-Kutta method to solve the differential equations.
• Graphical representation of the model's solutions.

Main Results:

• The dynamic model successfully identifies an asymptotically stable free equilibrium point, indicating a predictable outcome.
• A second, non-sign-stable equilibrium point was discovered, suggesting potential complexities or alternative states.
• Numerical solutions visualized through graphs provide insights into the model's behavior over time.

Conclusions:

• The proposed dynamic model offers a valuable tool for predicting infertility treatment outcomes.
• The identification of stable and unstable equilibrium points enhances our understanding of fertility treatment dynamics.
• Further research can refine this model for clinical application in reproductive medicine.