REAL

Global dynamics of a mathematical model for a honeybee colony infested by virus-carrying Varroa mites

Dénes, Attila and Ibrahim, Mahmoud A. (2019) Global dynamics of a mathematical model for a honeybee colony infested by virus-carrying Varroa mites. Journal of Applied Mathematics and Computing. ISSN 1598-5865 (In Press)

[img]
Preview
Text
Dénes-Ibrahim2019_Article_GlobalDynamicsOfAMathematicalM.pdf - Published Version
Available under License Creative Commons Attribution.

Download (1MB) | Preview

Abstract

We establish a new four-dimensional system of differential equations for a honeybee colony to simultaneously model the spread of Varroa mites among the bees and the spread of a virus transmitted by the mites. The bee population is divided to forager and hive bees, while the latter are further divided into three compartments: susceptibles, those infested by non-infectious vectors and those infested by infectious vectors. The system has four potential equilibria. We identify three reproduction numbers that determine the global asymptotic stability of the four possible equilibria. By using Dulac’s criterion, Poincaré–Bendixson and persistence theory, we show that the solutions always converge to one of the equilibria, depending on those three reproduction numbers. Hence we completely describe the global dynamics of the system.

Item Type: Article
Subjects: Q Science / természettudomány > QA Mathematics / matematika > QA74 Analysis / analízis
Depositing User: Dr. Attila Dénes
Date Deposited: 19 Sep 2019 11:20
Last Modified: 06 Apr 2023 07:23
URI: http://real.mtak.hu/id/eprint/99936

Actions (login required)

Edit Item Edit Item