Trophallaxis-inspired model for distributed transport between randomly interacting agents

Trophallaxis, the regurgitation and mouth to mouth transfer of liquid food between members of eusocial insect societies, is an important process that allows the fast and efficient dissemination of food in the colony. Trophallactic systems are typically treated as a network of agent interactions. This approach, though valuable, does not easily lend itself to analytic predictions. In this work we consider a simple trophallactic system of randomly interacting agents with finite carrying capacity, and calculate analytically and via a series of simulations the global food intake rate for the whole colony as well as observables describing how uniformly the food is distributed within the nest. Our model and predictions provide a useful benchmark to assess to what level the observed food uptake rates and efficiency in food distribution is due to stochastic effects or specific trophallactic strategies by the ant colony. Our work also serves as a stepping stone to describing the collective properties of more complex trophallactic systems, such as those including division of labor between foragers and workers