Mathematical Analysis of Eco-System Stability of Honeybee Colony Infected by Virus

International Journal of Research and Innovation in Applied Science (IJRIAS) | Volume VII, Issue I, January 2022 | ISSN 2454–6194

Mathematical Analysis of Eco-System Stability of Honeybee Colony Infected by Virus

S.A. Adebayo, S. O. Adewale
Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, PMB 4000, Ogbomoso, Nigeria

Abstract: An eco-epidemiological model interaction between hive and forager honeybee with consideration of varroa mite diseases spread in the ecosystem is represented. The model is governed by a new five-dimensional nonlinear system of ordinary differential equations to investigate the dynamics of the honeybee colony. The well-posedness of the model is established concerning the positivity and boundedness of solutions. The basic reproduction number (R0) was also computed, and a sensitivity analysis was carried out on R0. The stability of the equilibrium points was determined using the Jacobian matrix with the Routh-Hurwitz criterion. Additionally, numerical simulations were performed to validate the result of the recovery class and analyzed the effect of social inhibition and disinfestation on an infected hive honeybee population in an eco-epidemiological model.

Keywords: Epidemiology, Stability, Recovered class, Disinfestation, Effect of social inhibition, Sensitivity

I. INTRODUCTION

The interaction between organisms of different species such as the honeybee and varroa mite is an intrinsic feature of the ecosystem. Honeybee and varroa mite interaction is the study of living organisms that are subject to infestation or attack by their natural enemies acting either directly as predators, or indirectly, by disturbing the life of the colony in various ways in which the honeybees of the genus Apis are no exception (MAAREC). The honeybee is a member of the genus Apis which produces and stores honey and constructs perennial and colonial nests from wax. The best-known species of the genus is the Western honeybee (Apis mellifera, also called European or common honeybee) which was domesticated for honey production and crop pollination or at least exploited for honey and beeswax at least since the time of the building of the Egyptian pyramids (Smith et al 2000).
Colony collapse disorder (CCD) is the phenomenon in which the majority of worker bees in a colony disappear and leave behind a queen, plenty of food, and some nurse bees to care for the remaining immature bees.

Read More