This study presents a mathematical model to describe the spread of Varroa mites within a honeybee colony using fractional order derivatives. The model incorporates key parameters such as mite infestation rate, honeybee population dynamics, and the interaction between mites and bees. Fractional order derivatives provide a more accurate representation of real-world processes that exhibit memory and hereditary properties, unlike traditional integer-order models. Through analysis, the model shows the impact of varying mite infestation rates on the colony and provides insights into the possible long-term effects of mite infestations on honeybee populations. The model also presents potential strategies for controlling mite spread using various management practices.

Varroa mites, honeybee colonies, fractional-order modeling, mathematical modeling, parasite dynamics

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