Mathematical Analysis for Honeybee Dynamics Under the Influence of Seasonality

Miled El Hajji (), Fahad Ahmed S. Alzahrani and Mohammed H. Alharbi
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Miled El Hajji: Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia
Fahad Ahmed S. Alzahrani: Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia
Mohammed H. Alharbi: Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia

Mathematics, 2024, vol. 12, issue 22, 1-21

Abstract: 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.

Keywords: honeybees dynamics; seasonality; periodic solution; Lyapunov stability; persistence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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