Parsamanesh Mahmood, Izadi Mohammad
Department of Mathematics, Technical and Vocational University, Tehran, Iran.
Department of Applied Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran.
Sci Rep. 2024 Sep 2;14(1):20328. doi: 10.1038/s41598-024-71182-z.
The use of plastic is very widespread in the world and the spread of plastic waste has also reached the oceans. Observing marine debris is a serious threat to the management system of this pollution. Because it takes years to recycle the current wastes, while their amount increases every day. The importance of mathematical models for plastic waste management is that it provides a framework for understanding the dynamics of this waste in the ocean and helps to identify effective strategies for its management. A mathematical model consisting of three compartments plastic waste, marine debris, and recycle is studied in the form of a system of ordinary differential equations. After describing the formulation of the model, some properties of the model are given. Then the equilibria of the model and the basic reproduction number are obtained by the next generation matrix method. In addition, the global stability of the model are proved at the equilibria. The bifurcations of the model and sensitivity analysis are also used for better understanding of the dynamics of the model. Finally, the numerical simulations of discussed models are given and the model is examined in several aspects. It is proven that the solutions of the system are positive if initial values are positive. It is shown that there are two equilibria and and if , it is proven that is globally stable, while when , the equilibrium exists and it is globally stable. Also, at the model exhibits a forward bifurcation. The sensitivity analysis of concludes that the rates of waste to marine, new waste, and the recycle rate have most effect on the amount of marine debris.
塑料在世界范围内的使用非常广泛，塑料垃圾的传播也已蔓延到海洋。观测海洋垃圾对这种污染的管理系统构成严重威胁。因为回收目前的垃圾需要数年时间，而其数量却每天都在增加。数学模型对塑料垃圾管理的重要性在于，它为理解这种垃圾在海洋中的动态提供了一个框架，并有助于确定有效的管理策略。一个由塑料垃圾、海洋垃圾和回收三个隔室组成的数学模型以常微分方程组的形式进行研究。在描述了模型的公式后，给出了模型的一些性质。然后通过下一代矩阵法得到模型的平衡点和基本再生数。此外，还证明了模型在平衡点处的全局稳定性。模型的分岔和敏感性分析也用于更好地理解模型的动态。最后，给出了所讨论模型的数值模拟，并从几个方面对模型进行了检验。证明了如果初始值为正，则系统的解为正。结果表明，存在两个平衡点 和 ，并且如果 ，则证明 是全局稳定的，而当 时，平衡点 存在且是全局稳定的。此外，在 时模型表现出前向分岔。对 的敏感性分析得出结论，垃圾到海洋的速率、新垃圾的速率和回收率对海洋垃圾的数量影响最大。
