We report on our continuing efforts between our group at NCSU and ecologists at California State University, Monterey Bay and the Swedish University of Agricultural Sciences, Uppsala. To provide a tool for projecting and testing sensitivity of growth and death of populations under contrasting and combined pressures, we developed a non-linear, non-autonomous delay differential equation (DDE) model of bumblebee colonies and resources model that describes bumble bee population dynamics. We explain the usefulness of delay differential equations as a natural modeling formulation, particularly for bumble bee modeling. We then introduce a specific spline-based numerical method that approximates the solution of the delay model. We demonstrate that the model satisfies sufficient conditions to assure the subsequent theoretical developments therein in order to attain convergent approximate solutions. We report on our continuing efforts on studies of response to toxic substances, in particular our simulations related to growth, death and sublethal responses to neonicotinoid exposure.