Global dynamics of a simple model for wild and sterile mosquitoes
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 u...
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AIMS Press
2024-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2024308 |
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| author | Yu Ichida Yukihiko Nakata |
| author_facet | Yu Ichida Yukihiko Nakata |
| author_sort | Yu Ichida |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e63377815392472ca703bd116d1120f9 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-e63377815392472ca703bd116d1120f92025-01-23T07:47:53ZengAIMS PressMathematical Biosciences and Engineering1551-00182024-09-012197016703910.3934/mbe.2024308Global dynamics of a simple model for wild and sterile mosquitoesYu Ichida0Yukihiko Nakata1Department of Mathematical Sciences, School of Science, Kwansei Gakuin University, Gakuen Uegahara 1, Sanda, Hyogo 669-1330, JapanDepartment of Mathematical Sciences, College of Science and Engineering, Aoyama Gakuin University, 5-10-1, Fuchinobe, Chuoku, Sagamihara, Kanagawa 252-5258, JapanThere 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.https://www.aimspress.com/article/doi/10.3934/mbe.2024308sterile insecticide techniquedesingularization of vector fields (blow-up)center manifold theoryglobal dynamicsratio-dependent model |
| spellingShingle | Yu Ichida Yukihiko Nakata Global dynamics of a simple model for wild and sterile mosquitoes Mathematical Biosciences and Engineering sterile insecticide technique desingularization of vector fields (blow-up) center manifold theory global dynamics ratio-dependent model |
| title | Global dynamics of a simple model for wild and sterile mosquitoes |
| title_full | Global dynamics of a simple model for wild and sterile mosquitoes |
| title_fullStr | Global dynamics of a simple model for wild and sterile mosquitoes |
| title_full_unstemmed | Global dynamics of a simple model for wild and sterile mosquitoes |
| title_short | Global dynamics of a simple model for wild and sterile mosquitoes |
| title_sort | global dynamics of a simple model for wild and sterile mosquitoes |
| topic | sterile insecticide technique desingularization of vector fields (blow-up) center manifold theory global dynamics ratio-dependent model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2024308 |
| work_keys_str_mv | AT yuichida globaldynamicsofasimplemodelforwildandsterilemosquitoes AT yukihikonakata globaldynamicsofasimplemodelforwildandsterilemosquitoes |