A mathematical model for the interplay of Nosema infection and forager losses in honey bee colonies.

Abstract

We present a mathematical model (a) for the infection of a honey bee colony with Nosema ceranae. This is a system of five ordinary differential equations for the dependent variables healthy and infected worker bees in the hive, healthy and infected forager bees, and disease potential deposited in the hive. The model is then (b) extended to account for increased forager losses, e.g. caused by exposure to external stressors. The model is non-autonomous with periodic coefficient functions. Algebraic complexity prevents a rigorous mathematical analysis. Therefore, we resort to computer simulations in addition to some analytical results in the constant coefficient case. We investigate each of the two stressors (a) and (b) individually and jointly. Our results indicate that the combined effect of two stressors, both of which can be tolerated by the colony individually, might lead to colony failure, suggesting multi-factorial causes behind losses of honey bee colonies.