Population dynamics of Varroa mite and honeybee: Effects of parasitism with age structure and seasonality

Honeybees play an important role in the production of many agricultural crops and in sustaining plant diversity in undisturbed ecosystems. The rapid decline of honeybee populations have sparked great concern worldwide. Field and theoretical studies have shown that the parasitic Varroa mite (Varroa destructor Anderson and Trueman) could be the main reason for colony losses. In order to understand how mites affect population dynamics of honeybees and the health of a colony, we propose a brood-adult bee-mite interaction model in which the time lag from brood to adult bee is taken into account. Noting that the temporal dynamics of a honeybee colony varies with respect to season, we validate the model and perform parameter estimations under both constant and fluctuating seasonality scenarios. Our analytical and numerical studies reveal the following: (a) In the presence of parasite mites, the large time lag from brood to adult bee could destabilize population dynamics and drive the colony to collapse; however the small natural mortality of the adult bee population can promote a mite-free colony when time lag is small or at an intermediate level; (b) Small brood’ infestation rates could stabilize all populations at the unique interior equilibrium under constant seasonality while may drive the mite population to die out when seasonality is taken into account; (c) High brood’ infestation rates can destabilize the colony dynamics leading to population collapse depending on initial population size under constant and seasonal conditions; (d) Results from our sensitivity analysis indicate that the queen's egg-laying may have the greatest effect on colony population size.The death rate of the brood and the colony size at which brood survivability is the half maximal were also shown to be highly sensitive with an inverse correlation to the colony population size. Our results provide insights on the effects of seasonality on the dynamics. For example, mites may die out leaving a healthy colony with brood and adult bees in the presence of seasonality while the colony collapses without seasonality.