Analysis of the Influence of Brood Deaths on Honeybee Population

Many mathematical models using ordinary differential equations (ODEs) have been used to investigate what type of stressors cause honeybee colonies collapse. We propose a simple model of a delayed differential equation system (DDE) to describe the effect of insecticides over brood death rate and its influence over honeybee population dynamics. First, we remember some basic facts for the model with no delay. To analyze our model, we study the equilibria and perform stability and sensitivity analysis of the DDE system. Next, by using the delay time τ as a bifurcation parameter, we find that no Hopf bifurcation could arise as the time lag τ varies within biologically plausible ranges. Numerical simulations with real data are studied for the biological significance of the model.