Global dynamics of a simple model for wild and sterile mosquitoes.

IF 2.6 4区 工程技术 Q1 Mathematics Mathematical Biosciences and Engineering Pub Date : 2024-09-05 DOI:10.3934/mbe.2024308
Yu Ichida, Yukihiko Nakata
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Abstract

There are known methods to manage the population dynamics of wild and sterile mosquitoes by releasing genetically engineered sterile mosquitoes. Even if a two-dimensional system of ordinary differential equations is considered as a simple mathematical model for developing release strategies, fully understanding the global behavior of the solutions is challenging, due to the fact that the probability of mating is ratio-dependent. In this paper, we combine a geometric approach called the time-scale transformation and blow-up technique with the center manifold theorem to provide a complete understanding of dynamical systems near the origin. Then, the global behavior of the solution of the two-dimensional ordinary differential equation system is classified in a two-parameter plane represented by the natural death rate of mosquitoes and the sterile mosquito release rate. We also offer a discussion of the sterile mosquito release strategy. In addition, we obtain a better exposition of the previous results on the existence and local stability of positive equilibria. This paper provides a framework for the mathematical analysis of models with ratio-dependent terms, and we expect that it will theoretically withstand the complexity of improved models.

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野生蚊子和不育蚊子简单模型的全球动态。
目前已知的方法是通过释放基因工程不育蚊子来管理野生蚊子和不育蚊子的种群动态。即使将二维常微分方程系统视为制定释放策略的简单数学模型,但由于交配概率与比率有关,要完全理解解的全局行为仍具有挑战性。在本文中,我们将一种称为时间尺度变换和吹胀技术的几何方法与中心流形定理相结合,以提供对原点附近动力系统的完整理解。然后,在以蚊子自然死亡率和不育蚊子释放率为代表的双参数平面内,对二维常微分方程系统解的全局行为进行了分类。我们还对无菌蚊子释放策略进行了讨论。此外,我们还更好地阐述了之前关于正均衡存在性和局部稳定性的结果。本文为带有比率依赖项的模型的数学分析提供了一个框架,我们期望它能在理论上承受改进模型的复杂性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Mathematical Biosciences and Engineering
Mathematical Biosciences and Engineering 工程技术-数学跨学科应用
CiteScore
3.90
自引率
7.70%
发文量
586
审稿时长
>12 weeks
期刊介绍: Mathematical Biosciences and Engineering (MBE) is an interdisciplinary Open Access journal promoting cutting-edge research, technology transfer and knowledge translation about complex data and information processing. MBE publishes Research articles (long and original research); Communications (short and novel research); Expository papers; Technology Transfer and Knowledge Translation reports (description of new technologies and products); Announcements and Industrial Progress and News (announcements and even advertisement, including major conferences).
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