  The honeybee plays an extremely important role in ecosystem stability and
diversity and in the production of bee pollinated crops. Honey bees and other
pollinators are under threat from the combined effects of nutritional stress,
parasitism, pesticides, and climate change that impact the timing, duration,
and variability of seasonal events. To understand how parasitism and
seasonality influence honey bee colonies separately and interactively, we
developed a non-autonomous nonlinear honeybee-parasite interaction differential
equation model that incorporates seasonality into the egg-laying rate of the
queen. Our theoretical results show that parasitism negatively impacts the
honey bee population either by decreasing colony size or destabilizing
population dynamics through supercritical or subcritical Hopf-bifurcations
depending on conditions. Our bifurcation analysis and simulations suggest that
seasonality alone may have positive or negative impacts on the survival of
honey bee colonies. More specifically, our study indicates that (1) the timing
of the maximum egg-laying rate seems to determine when seasonality has positive
or negative impacts; and (2) when the period of seasonality is large it can
lead to the colony collapsing. Our study further suggests that the synergistic
influences of parasitism and seasonality can lead to complicated dynamics that
may positively and negatively impact the honey bee colony's survival. Our work
partially uncovers the intrinsic effects of climate change and parasites, which
potentially provide essential insights into how best to maintain or improve a
honey bee colony's health.
