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<p>Regional disparities constitute substantial inequalities in economic, social, and infrastructural development across various areas within a nation. These disparities are frequently the result of imbalanced public policies, disparities in access to natural resources, and differential availability of essential services. Such disparities have profound implications for social, economic, and political cohesion. They facilitate rural migration, intensify social inequalities, and have the potential to provoke political tensions and adverse environmental consequences. This paper explores the overall behavior of a stochastic model to evaluate the extent of interdependence between two regions with respect to population dynamics. Initially, the well-posedness of the model is verified, demonstrating the existence and uniqueness of a positive solution, which ensures the model’s robustness from a mathematical and practical standpoint. The study identifies the conditions necessary to ensure the sustainability of the dynamic balance of population distribution between the two regions. Special attention is given to scenarios characterized by significant regional disparities, reflecting imbalanced population distributions. Numerical simulations are carried out to validate the results. The paper ends with a discussion of the implications of the results and their potential applications.</p>

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Mathematical analysis of competitive dynamics between two regional areas

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月12日

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  • Lahcen Boulaasair,
  • Hassane Bouzahir,
  • Namana Seshagiri Rao,
  • Dania Santina,
  • Nabil Mlaiki

摘要

Regional disparities constitute substantial inequalities in economic, social, and infrastructural development across various areas within a nation. These disparities are frequently the result of imbalanced public policies, disparities in access to natural resources, and differential availability of essential services. Such disparities have profound implications for social, economic, and political cohesion. They facilitate rural migration, intensify social inequalities, and have the potential to provoke political tensions and adverse environmental consequences. This paper explores the overall behavior of a stochastic model to evaluate the extent of interdependence between two regions with respect to population dynamics. Initially, the well-posedness of the model is verified, demonstrating the existence and uniqueness of a positive solution, which ensures the model’s robustness from a mathematical and practical standpoint. The study identifies the conditions necessary to ensure the sustainability of the dynamic balance of population distribution between the two regions. Special attention is given to scenarios characterized by significant regional disparities, reflecting imbalanced population distributions. Numerical simulations are carried out to validate the results. The paper ends with a discussion of the implications of the results and their potential applications.