Epidemiological Modelling of the Population Dynamics of Bee Colonies
Keywords:bee colonies, basic reproduction number, asymptotic stability, center manifold theory, bifurcation, sensitivity analysis
A mathematical model that combines the normal demographic dynamics of a bee colony, including the population of the broods, with the dynamics of Nosema infection affecting foragers during foraging duties was designed. The model included the brood population and determined how it affects the population dynamics of the colony. An epidemiological threshold called the basic reproduction number of the model was derived and a qualitative analysis of the model was carried out to investigate the asymptotic stability of both the disease-free and endemic equilibria. A locally asymptotically stable disease-free equilibrium at the basic reproduction number less than unity was proven via the analysis of characteristic equation. Furthermore, the existence of a locally asymptotically stable endemic equilibrium was established at the basic reproduction number greater than unity based on the use of the center manifold theory of bifurcation. In addition, a sensitivity analysis was performed to examine the contributory effects of the model parameters on the transmission and spread of the Nosema infection with respect to the basic reproduction number. Lastly, numerical simulations using Python were conducted to analyze the dynamics of the colony in the presence of infection.