Mathematical Model and Dynamics Analysis of the Stingless Bee (Trigona sp.) in A Colony

Trigona sp. is a stingless bee species that is widely distributed in tropical countries. It has castes in thecolony, i.e. queen, worker, and male bee. Despite its size, Trigona sp. can produce high-quality commoditiessuch as honey, propolis, and bee pollen. However, it is a vulnerable species since it’s pretty easy to be predatedby several predators and has a relatively short lifespan. In addition, there are still few mathematical studiesthat discuss the population dynamics of Trigona sp. Thus, in this study, we construct a mathematical modelof the Trigona sp. population in the form of a dynamical system. The model is a nine-dimensional non-lineardifferential equation that is constructed based on the stages in the bee population, namely the stages of eggs,larvae, and adult bees from each colony except the queen colony. Coexistence analysis, stability of equilibria, and also the death parameter sensitivity analysis are carried out in two scenarios. The first scenario is a situation where none of the workers die so that the food supply at the larval stage is sufficient. Meanwhile, the second scenario is a more common situation where some worker bees die from exhaustion resulting in an insufficient food supply for the larvae stage. Stable coexistence of all sub-structures and structural dependence on the foraging behavior of the workers are shown. All the results will be presented in numerical simulation. From the results of the coexistence and stability analysis, bee farmers can maintain food availability by increasing the number of workers in a colony, or providing food sources with high contains nectar and propolis at a relatively close distance to reduce the death of worker bees.