A Mathematical Model for The Spread of Varroa-Mites in Honeybee Colony with Fractional Order

Abstract

Honeybees live in colonies with one queen running the whole hive. Worker honeybees are all females and are the only bees most people ever see flying around outside of the hive. They forage for food, build the honeycombs, and protect the hive. This study developed and analyzed the honeybee’s transmission dynamics under fractional order derivative via Laplace Adomian Decomposition Method, spread of varroa-mite by analyzing the disease-free equilibrium and global stability of endemic of our formulated model were investigated. Based on the trajectories, it was concluded that the memory index or fractional order could use to control the honeybees infested by varroa-mite carrying virus transmission dynamics.