Date of Award

Spring 2019

Document Type

Honors Thesis



First Advisor

Dr. Dan Van Peursem

Second Advisor

Dr. Jos´e Flores

Third Advisor

Dr. Catalin Georgescu


Honey bees, differential equations, population modeling


Over a decade ago, Colony Collapse Disorder (CCD) began to plague honey bee colonies in the United States. An identified contributor has been the Varroa destructor parasitic mite that infests honeybee cells in the early stages of development. Bees with this mite as a parasite are weakened and their lifespan decreases. A system of differential equations with a control on the mites was created to model the populations of the hive bee, forager bee, and mites. The different equilibrium points that result from the varying levels of the mites’ death rate is investigated. A bifurcation point at approximately 0.0165 was found. With a mite death rate less 0.0165, the hive and foragers bees, and mites coexist in a hive over the course of a year with an initial low mite population. These values are based on other set parameters: the daily laying rate of eggs by the queen, brood mortality, the transition rate from hive bee to forager bee, social inhibition, the death rate of foragers, the death rate of hive and forager bees due to mites, growth rate of the mite population, and the carrying capacity of the hive, all parameters which are found in literature.



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