Toward a Quantitative Reduction of the SIR Epidemiological Model

Motivated by our intention to use SIR-type epidemiological models in the context of dynamic networks, we investigate in this framework possibilities to reduce the classical SIR model to a representative evolution model for a suitably chosen observable. For selected scenarios, we provide practical a priori error bounds between the approximate and the original observables. Finally, we illustrate numerically the behavior of the reduced models compared to the original ones. As a long-term goal, we would like to apply such techniques in the context of large-scale highly interacting inhomogeneous human crowds.