Coupling equation based models and agent-based models: example of a multi-strains and switch SIR toy model

Modeling in ecology or epidemiology generally opposes two classes of models, Equation Based Models and Agent Based Models. Mathematical models allow predicting the long-term dynamics of the studied systems. However, the variability between individuals is difficult to represent, what makes these more suitable models for large and homogeneous populations. Multi-agent models allow representing the attributes and behavior of each individual and therefore provide a greater level of detail. In return, these systems are more difficult to analyze.These approaches have often been compared, but rarely used simultaneously. We propose a hybrid approach to couple equations models and agent-based models, as well as its implementation on the modeling platform Gama [8]. We focus on the representation of a classical theoretical epidemiological model (SIR model) and we illustrate the construction of a class of models based on it