| In this thesis, two dynamic disease models for the honeybee colony are presented. The first model is the bee-mite model consisting of two autonomous non-linear ordinary differential equations. The second model is bee-mite-APV model consisting of four autonomous non-linear ordinary differential equations. In the absence of disease in a honeybee colony, a critical number of healthy worker bees are required for the colony to establish. If the worker bee population falls below this critical value, the colony will die out. If the mites move into the colony, the colony cannot fight off the mites. In such situations, the model parameters play an important role. Depending on these parameters, either the mite infestation is strong enough to kill the colony or the colony attains a stable mite infested equilibrium(bees and mites attain a certain population). If the viruses are introduced into the colony, based on the model parameters, it is possible that the viruses are fought off and we have a mite infested established colony. It is also possible that the viruses cannot be fought off.;The theoretical properties of both the models are studied. The qualitative behavior of the two dimensional model is obtained by using local stability analysis. The qualitative behavior of the four dimensional model is studied algebraically and by using the results from the bee-mite model. Equilibrium points are studied for the bee-mite model and the bee-mite-APV model. The results are interpreted ecologically. |
