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Mathematical modeling of disease spreading plays a crucial role inunderstanding, controlling and preventing epidemic outbreaks. In a microscopicdescription of the propagation of a disease over the complex network of humancontacts, the probability that an individual is in a given state (susceptible,infectious, recovered etc) depends on the state of its neighbors in thenetwork. Thus it depends on the state of pairs of nodes, which in turns dependson triples, in a hierarchy of dynamical dependencies. In order to producemodels that are at the same time reliable and manageable, one has to understandhow to truncate such a hierarchy, and how the chosen order of approximationaffects the ability of the model to forecast the real temporal evolution of anepidemics. In this paper we provide a systematic analysis of the reliability(under different hypotheses on the quantity and quality of available data) ofthe predictions obtained by truncating the hierarchy either at the level ofindividuals or at the level of pairs. We find that pair-based models arereliable tools both for estimating the epidemiological parameters and forforecasting the temporal evolution of the epidemics, under all conditions takeninto account in our work. However, a pair-based approach provides a much betterprediction of an individual-based one, only if better data, namely informationon the state of node pairs, are available. Overall, our results suggest thatmore refined mathematical models need to be informed by improved contacttracing techniques to better support decision on policies and containmentmeasures to adopt.

Individual- and pair-based models of epidemic spreading: master equations and analysis of their forecasting capabilities