Community-distributed compartmental models

Abstract

[EN] A framework that allows the incorporation of community structure into epidemiological compartmental models has been developed. The models resulting from this process are compartmental models as well, which are related to the base models. This work includes an existence and uniqueness theorem, showing that, under certain conditions on the mobility, epidemiological models in which f(t, X) is continuous in time and Lipschitz continuous on the compartments induce unique community models; and a homogeneous mixing limit, showing that under high mobility conditions the base model is recovered in the global population. Applications of the SIR model and the impact of the community structure on the estimation of their effective parameters are discussed in detail. An open computational implementation of this framework is available to the scientific community. It allows modeling community distribution using mobility data, as shown with Spain data during the 2020 state of alarm.