Reconstruction analysis of honeybee colony collapse disorder modeling

The honeybee has a significant impact on industry and nature. In recent years, a mysterious disease make honeybees die, often losses reach 80-100% of the apiaries. The causal syndrome of such massive die-off is called Colony Collapse Disorder. The model adopted in the paper is constituted by a system of three ordinary differential equations that account for the change in time of the population size of the hive bees, forage workers and infected foragers. It models the condition as a contagion, transmitted by both bee-to-bee and bee-to-plant interaction. What is more, it supports both healthy and unhealthy population dynamics. We solve a parameter identification inverse problem to reconstruct the values, which are directly unobservable but vital in honeybee management. We apply an adjoint equation optimization approach to solve this inverse problem. Numerical analysis confirms the results obtained theoretically.