Global dynamics of a simple model for wild and sterile mosquitoes

被引：0

作者：

Ichida, Yu ^{[1
]}

Nakata, Yukihiko ^{[2
]}

机构：

[1] Department of Mathematical Sciences, School of Science, Kwansei Gakuin University, Gakuen Uegahara 1, Hyogo, Sanda

[2] Department of Mathematical Sciences, College of Science and Engineering, Aoyama Gakuin University, 5-10-1, Fuchinobe, Chuoku, Kanagawa, Sagamihara

来源：

Mathematical Biosciences and Engineering | 2024年 / 21卷 / 09期

基金：

日本学术振兴会;

关键词：

center manifold theory; desingularization of vector fields (blow-up); global dynamics; ratio-dependent model; sterile insecticide technique;

D O I：

10.3934/mbe.2024308

中图分类号：

学科分类号：

摘要：

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. © 2024 the Author(s)

引用

页码：7016 / 7039

页数：23

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