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<p>This study presents a mathematical model based on partial differential equations (PDEs) to analyze the dynamics of in vitro fertilization (IVF). The model captures key biological processes, including follicle growth, sperm-egg interaction, and embryo development. We prove the existence, uniqueness, and stability of solutions and develop efficient numerical methods for simulation. Sensitivity and optimization analyses reveal critical factors, including hormone regulation, sperm quality, and embryo incubation duration, that significantly impact IVF success rates. Numerical simulations using finite difference methods reveal that hormone regulation, sperm motility, and embryo incubation duration are dominant factors influencing IVF success rates, with optimal hormonal control significantly improving follicle density and implantation outcomes. Sensitivity analysis further identifies embryo quality and sperm morphology as key determinants of treatment efficacy. Our findings provide a foundational framework for optimizing IVF protocols and improving clinical outcomes.</p>

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A Comprehensive Analysis and Numerical Study of a Partial Differential Equation Model for In Vitro Fertilization

  • 期刊论文

  • 发表日期：

    2025年8月11日

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  • David Amilo,
  • Khadijeh Sadri,
  • Bilgen Kaymakamzade,
  • Evren Hincal

摘要

This study presents a mathematical model based on partial differential equations (PDEs) to analyze the dynamics of in vitro fertilization (IVF). The model captures key biological processes, including follicle growth, sperm-egg interaction, and embryo development. We prove the existence, uniqueness, and stability of solutions and develop efficient numerical methods for simulation. Sensitivity and optimization analyses reveal critical factors, including hormone regulation, sperm quality, and embryo incubation duration, that significantly impact IVF success rates. Numerical simulations using finite difference methods reveal that hormone regulation, sperm motility, and embryo incubation duration are dominant factors influencing IVF success rates, with optimal hormonal control significantly improving follicle density and implantation outcomes. Sensitivity analysis further identifies embryo quality and sperm morphology as key determinants of treatment efficacy. Our findings provide a foundational framework for optimizing IVF protocols and improving clinical outcomes.