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. Previous studies have shown that the parasitic Varroa mite could be the main reason for colony losses. In order to understand how mites affect population dynamics of honeybees and a colony health, we propose a brood-adult bee-mite model in which the time lag from brood to adult is taken into account. Noting that the 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 could destabilize population dynamics and drive the colony to collapse; but the small natural mortality of the adult 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 sensitivity analysis indicate the queen's egg-laying may have the greatest effect on colony population size. The brood death rate 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.

中文翻译：

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瓦螨和蜜蜂的种群动态：寄生对年龄结构和季节性的影响

蜜蜂在许多农作物的生产和未受干扰的生态系统中维持植物多样性方面发挥着重要作用。蜜蜂种群的迅速减少引起了全世界的高度关注。先前的研究表明，寄生的瓦螨可能是菌落损失的主要原因。为了了解螨虫如何影响蜜蜂的种群动态和蜂群健康，我们提出了一种蜂螨幼虫模型，其中考虑了从幼虫到成虫的时间滞后。注意到蜂群的动态随季节而变化，我们验证了模型并在恒定和波动的季节性情景下执行参数估计。我们的分析和数值研究揭示了以下内容：(a) 在存在寄生虫螨的情况下，从育雏到成虫的大时间滞后可能会破坏种群动态并导致种群崩溃；但当时间滞后较小或处于中等水平时，成年人群的低自然死亡率可以促进无螨群体；(b) 小巢虫的侵染率可以在恒定的季节性条件下将所有种群稳定在独特的内部平衡状态，而在考虑到季节性因素时可能会驱使螨种群灭绝；(c) 根据恒定和季节性条件下的初始种群规模，高繁殖率会破坏种群动态，导致种群崩溃；(d) 敏感性分析的结果表明，蜂王产卵可能对群体规模的影响最大。育雏死亡率和育雏存活率为最大一半时的菌落大小也被证明是高度敏感的，与菌落种群大小呈负相关。我们的结果提供了关于季节性对动态影响的见解。