EF45 – Multi-Agent Social Systems

Agent-based models have been proposed for modelling the spread of Covid-19 under implemented and candidate counter-measures. Since they are computationally very expensive, we propose a faster approach based on a coupled system of full ABMs and reduced sub-models that still allows to sample quantities of interest. Currently, we are working on a reduced hybrid PDE-ODE model that allows to approximate the dynamics of an ABM. Using this approach would allow to model larger regions, e.g., Berlin-Brandenburg or parts of Italy.

Motivated by [1], our initial focus is on modeling Lombardy, Italy, where we simulate the dynamics using a partial differential equation (PDE) model as a foundational reference to the hybrid model. The first results can be seen in Figures A and B. We choose the densely populated province of Milan to be represented by an ordinary differential equation (ODE) model, as this mirrors the dynamics of the corresponding PDE model more closely than other provinces.

The coupling of these two models is achieved through boundary conditions. This coupling results in infectious individuals from the PDE model coming into contact with susceptibles in the ODE model. Specifically, we introduce the infectious individuals from the PDE model into the ODE model by integrating over the boundary. This results in infectious individuals from the PDE model coming into contact with susceptibles in the ODE model. Conversely, infectious individuals from the ODE model can infect susceptibles in the PDE model at a specified rate. These interactions are captured through the use of Robin boundary conditions, creating a bridge between the two modeling approaches.