Numerous studies have investigated the various stressors that can cause the collapse of honeybee colonies. Given the challenges in directly observing honeybee population dynamics, it is essential to construct mathematical models to gain insight into the factors that significantly affect bee populations. Several models have been proposed to capture the dynamics of honeybee populations and the effects of human-induced stressors, such as pathogens, parasites, and nutritional deficiencies, on the colony’s long-term survival. However, these models generally overlook the death rate of brood, concentrating instead on the mortality rates of foraging bees. We consider a model of a nonlinear system of ordinary differential equations with main unknowns the brood B and the hive bees H. We formulate an optimization problem for recovering coefficients in the system that satisfies the state constraints and minimize the cost functional. The nature of the algorithm is to numerically reconstruct the unknown parameters, i. e. they are fitted with a good accuracy, although not exactly. We develop a computational approach to solve the problem. Numerical experiments with synthetic and real data are analyzed.