Modelling and Simulation of Competition for Students’ Population with Holling Type II Response
The increase in the country’s population attracted the establishment of more schools, both public and private schools, to cater for the increasing number of students. However, there have been dynamics of students’ population both in public and private schools through transfer from one category of sc...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/4102242 |
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| author | Brian Odhiambo Cyrus Ngari Patrick Kimani Peter Njori |
| author_facet | Brian Odhiambo Cyrus Ngari Patrick Kimani Peter Njori |
| author_sort | Brian Odhiambo |
| collection | DOAJ |
| description | The increase in the country’s population attracted the establishment of more schools, both public and private schools, to cater for the increasing number of students. However, there have been dynamics of students’ population both in public and private schools through transfer from one category of school to the other, through completion of the learning period, and through dropout due to unknown reasons which have subjected both the public and private schools to compete in order to maintain a good number of students. In this work, a modified Lotka–Volterra model of schools and nonenrolled entities population in the education system is studied. Private schools and nonenrolled entities play the role of a predator in public schools. Again, public schools and nonenrolled entities play the role of predators in private schools. Holling type II functional responses have been integrated in the analysis of the Lotka–Volterra model. The equilibrium points are established and their stability are determined using the Routh–Hurwitz criterion and eigenvalue method. Global stability has been done for the positive equilibrium point. Bifurcation is also done around the positive equilibrium point. Finally, a graphical illustration of various parameter is derived to show their effect on schools when they are varied. It is revealed that the increase in parameters θ2, θ3, and η3 greatly affects the schools population as they are the ones leading to predation in school. Therefore, proper strategies should be developed to focus on reducing the mentioned parameters to avoid leading schools’ population to extinct. |
| format | Article |
| id | doaj-art-4ddd72411183420a8ee8794e514c0e2e |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-4ddd72411183420a8ee8794e514c0e2e2025-08-20T02:17:57ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/4102242Modelling and Simulation of Competition for Students’ Population with Holling Type II ResponseBrian Odhiambo0Cyrus Ngari1Patrick Kimani2Peter Njori3Department of Mathematics and StatisticsDepartment of Pure and Applied SciencesDepartment of Mathematics and StatisticsDepartment of Pure and Applied SciencesThe increase in the country’s population attracted the establishment of more schools, both public and private schools, to cater for the increasing number of students. However, there have been dynamics of students’ population both in public and private schools through transfer from one category of school to the other, through completion of the learning period, and through dropout due to unknown reasons which have subjected both the public and private schools to compete in order to maintain a good number of students. In this work, a modified Lotka–Volterra model of schools and nonenrolled entities population in the education system is studied. Private schools and nonenrolled entities play the role of a predator in public schools. Again, public schools and nonenrolled entities play the role of predators in private schools. Holling type II functional responses have been integrated in the analysis of the Lotka–Volterra model. The equilibrium points are established and their stability are determined using the Routh–Hurwitz criterion and eigenvalue method. Global stability has been done for the positive equilibrium point. Bifurcation is also done around the positive equilibrium point. Finally, a graphical illustration of various parameter is derived to show their effect on schools when they are varied. It is revealed that the increase in parameters θ2, θ3, and η3 greatly affects the schools population as they are the ones leading to predation in school. Therefore, proper strategies should be developed to focus on reducing the mentioned parameters to avoid leading schools’ population to extinct.http://dx.doi.org/10.1155/2023/4102242 |
| spellingShingle | Brian Odhiambo Cyrus Ngari Patrick Kimani Peter Njori Modelling and Simulation of Competition for Students’ Population with Holling Type II Response Journal of Mathematics |
| title | Modelling and Simulation of Competition for Students’ Population with Holling Type II Response |
| title_full | Modelling and Simulation of Competition for Students’ Population with Holling Type II Response |
| title_fullStr | Modelling and Simulation of Competition for Students’ Population with Holling Type II Response |
| title_full_unstemmed | Modelling and Simulation of Competition for Students’ Population with Holling Type II Response |
| title_short | Modelling and Simulation of Competition for Students’ Population with Holling Type II Response |
| title_sort | modelling and simulation of competition for students population with holling type ii response |
| url | http://dx.doi.org/10.1155/2023/4102242 |
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