Mathematics to Save Honeybees: Modeling Colony Dynamics and Survival

Honeybees (Apis mellifera) are essential to biodiversity and agriculture, pollinating nearly 85% of flowering plants and contributing an estimated $15–20 billion annually to U.S. crop production. Yet, recent widespread colony declines pose serious threats to both ecosystems and food security. In this talk, I will demonstrate how mathematical modeling offers powerful tools to uncover the mechanisms shaping honeybee colony growth, persistence, and collapse. Building on tractable frameworks—including nonlinear, nonautonomous, and delay differential equations—we integrate empirical data with theory to analyze the impacts of parasites, environmental variability, and pesticide exposure. These models reveal key drivers of colony collapse and provide actionable insights for mitigating Varroa infestations in changing environments and improving colony management. If time permits, I will discuss how mathematics powered with AI extend beyond honeybees to broader questions in complex adaptive systems, including information flow in social insect colonies and parallels in human collective decision-making.