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Honeybees play an important role in the production of many agricultural cropsand in sustaining plant diversity in undisturbed ecosystems. The rapid declineof honeybee populations have sparked great concern worldwide. Previous studieshave shown that the parasitic Varroa mite could be the main reason for colonylosses. In order to understand how mites affect population dynamics ofhoneybees and a colony health, we propose a brood-adult bee-mite model in whichthe time lag from brood to adult is taken into account. Noting that thedynamics of a honeybee colony varies with respect to season, we validate themodel and perform parameter estimations under both constant and fluctuatingseasonality scenarios. Our analytical and numerical studies reveal thefollowing: (a) In the presence of parasite mites, the large time lag from broodto adult could destabilize population dynamics and drive the colony tocollapse; but the small natural mortality of the adult population can promote amite-free colony when time lag is small or at an intermediate level; (b) Smallbrood' infestation rates could stabilize all populations at the unique interiorequilibrium under constant seasonality while may drive the mite population todie out when seasonality is taken into account; (c) High brood' infestationrates can destabilize the colony dynamics leading to population collapsedepending on initial population size under constant and seasonal conditions;(d) Results from sensitivity analysis indicate the queen's egg-laying may havethe greatest effect on colony population size. The brood death rate and thecolony size at which brood survivability is the half maximal were also shown tobe highly sensitive with an inverse correlation to the colony population size.Our results provide insights on the effects of seasonality on the dynamics.

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