Impact of Infection on Honeybee Population Dynamics in a Seasonal Environment

We studied a non-autonomous model for the spread of disease within a bee colony under the influence of seasonality where we consider time-dependent parameters to integrate the impact of the periodicity of weather on the Honeybee population dynamics. We proved that the system admits a unique bounded positive solution, and also a global attractor set. The basic reproduction number, R0, was defined as the spectral radius of a linear integral operator. We proved that the global dynamics is determined by this threshold parameter: If R0≤1, then the disease-free periodic solution is globally asymptotically stable, while if R0>1, then the disease persists. We confirmed the theoretical results trough an extensive numerical simulations.