弱连接亚居群的异质性和全局动态效应

IF 2.6 4区数学 Q2 MATHEMATICAL & COMPUTATIONAL BIOLOGY

Mathematical Modelling of Natural Phenomena Pub Date : 2021-06-14 DOI:10.1051/MMNP/2021034

Derdei Bichara, A. Iggidr, Souâd Yacheur

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引用次数: 2

摘要

我们开发了一种方法，该方法完全表征了具有弱互连的多个子种群的模型的全局动力学。该方法应用于两类具有多个子种群的模型：一类是涉及多个宿主物种和多个媒介物种的流行病模型，另一类是斑片状媒介传播模型。该方法包括两个主要步骤：使用大型系统的工具对系统进行简化，以及研究与原始系统相关的辅助系统的动力学。所开发的方法确定了基本动力学和每个子种群相对于整个种群动力学的“权重”，以及连通矩阵的拓扑结构如何改变整个种群的动力学。该方法为所有类型的平衡提供了全局稳定性结果，即平凡平衡、边界平衡或内部平衡。

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Effects of Heterogeneity and Global Dynamics of Weakly Connected Subpopulations

We develop a method that completely characterizes the global dynamics of models with multiple subpopulations that are weakly interconnected. The method is applied on two classes of models with multiple subpopulations: an epidemic model that involves multiple host species and multiple vector species and a patchy vector-borne model. The method consists of two main steps: reducing the system using tools of large scale systems and studying the dynamics of an auxiliary system related the original system. The developed method determines the underlying dynamics and the ``weight" of each subpopulations with respect to the dynamics of the whole population, and how the topology of the connectivity matrix alters the dynamics of the overall population. The method provides global stability results for all types of equilibria, namely trivial, boundary or interior equilibria.

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来源期刊

Mathematical Modelling of Natural Phenomena MATHEMATICAL & COMPUTATIONAL BIOLOGY-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

5.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Mathematical Modelling of Natural Phenomena (MMNP) is an international research journal, which publishes top-level original and review papers, short communications and proceedings on mathematical modelling in biology, medicine, chemistry, physics, and other areas. The scope of the journal is devoted to mathematical modelling with sufficiently advanced model, and the works studying mainly the existence and stability of stationary points of ODE systems are not considered. The scope of the journal also includes applied mathematics and mathematical analysis in the context of its applications to the real world problems. The journal is essentially functioning on the basis of topical issues representing active areas of research. Each topical issue has its own editorial board. The authors are invited to submit papers to the announced issues or to suggest new issues. Journal publishes research articles and reviews within the whole field of mathematical modelling, and it will continue to provide information on the latest trends and developments in this ever-expanding subject.