Mathematical Analysis for Honeybee Dynamics Under the Influence of Seasonality
In this paper, we studied a mathematical model for honeybee population diseases under the influence of seasonal environments on the long-term dynamics of the disease. The model describes the dynamics of two different beehives sharing a common space. We computed the basic reproduction number of the s...
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2024-11-01
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| Series: | Mathematics |
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| author | Miled El Hajji Fahad Ahmed S. Alzahrani Mohammed H. Alharbi |
| author_facet | Miled El Hajji Fahad Ahmed S. Alzahrani Mohammed H. Alharbi |
| author_sort | Miled El Hajji |
| collection | DOAJ |
| description | In this paper, we studied a mathematical model for honeybee population diseases under the influence of seasonal environments on the long-term dynamics of the disease. The model describes the dynamics of two different beehives sharing a common space. We computed the basic reproduction number of the system as the spectral radius of either the next generation matrix for the autonomous system or as the spectral radius of a linear integral operator for the non-autonomous system, and we deduced that if the reproduction number is less than unity, then the disease dies out in the honeybee population. However, if the basic reproduction number is greater than unity, then the disease persists. Finally, we provide several numerical tests that confirm the theoretical findings. |
| format | Article |
| id | doaj-art-79dccc6c616c40b99ceb4f59373684c4 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-79dccc6c616c40b99ceb4f59373684c42024-11-26T18:11:36ZengMDPI AGMathematics2227-73902024-11-011222349610.3390/math12223496Mathematical Analysis for Honeybee Dynamics Under the Influence of SeasonalityMiled El Hajji0Fahad Ahmed S. Alzahrani1Mohammed H. Alharbi2Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi ArabiaDepartment of Mathematics and Statistics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi ArabiaDepartment of Mathematics and Statistics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi ArabiaIn this paper, we studied a mathematical model for honeybee population diseases under the influence of seasonal environments on the long-term dynamics of the disease. The model describes the dynamics of two different beehives sharing a common space. We computed the basic reproduction number of the system as the spectral radius of either the next generation matrix for the autonomous system or as the spectral radius of a linear integral operator for the non-autonomous system, and we deduced that if the reproduction number is less than unity, then the disease dies out in the honeybee population. However, if the basic reproduction number is greater than unity, then the disease persists. Finally, we provide several numerical tests that confirm the theoretical findings.https://www.mdpi.com/2227-7390/12/22/3496honeybees dynamicsseasonalityperiodic solutionLyapunov stabilitypersistence |
| spellingShingle | Miled El Hajji Fahad Ahmed S. Alzahrani Mohammed H. Alharbi Mathematical Analysis for Honeybee Dynamics Under the Influence of Seasonality Mathematics honeybees dynamics seasonality periodic solution Lyapunov stability persistence |
| title | Mathematical Analysis for Honeybee Dynamics Under the Influence of Seasonality |
| title_full | Mathematical Analysis for Honeybee Dynamics Under the Influence of Seasonality |
| title_fullStr | Mathematical Analysis for Honeybee Dynamics Under the Influence of Seasonality |
| title_full_unstemmed | Mathematical Analysis for Honeybee Dynamics Under the Influence of Seasonality |
| title_short | Mathematical Analysis for Honeybee Dynamics Under the Influence of Seasonality |
| title_sort | mathematical analysis for honeybee dynamics under the influence of seasonality |
| topic | honeybees dynamics seasonality periodic solution Lyapunov stability persistence |
| url | https://www.mdpi.com/2227-7390/12/22/3496 |
| work_keys_str_mv | AT miledelhajji mathematicalanalysisforhoneybeedynamicsundertheinfluenceofseasonality AT fahadahmedsalzahrani mathematicalanalysisforhoneybeedynamicsundertheinfluenceofseasonality AT mohammedhalharbi mathematicalanalysisforhoneybeedynamicsundertheinfluenceofseasonality |