Imitation and social pressure are usually observed in the aggregate behavior of populations, and they are responsible for the appearance of trends, herd effects, discontinuities and crashes. To account for these phenomena, interactions networks must be included in the modeling of social systems, and measured from data. We present a recent analysis on an extensive dataset from adhesion to cancer screening campaigns, where a modeling, based on statistical mechanics and multi-species mean field spin models, allows for a quantitive estimate of average interaction effects through an inverse problem and leads to a forecast of effective social policies to enhance participation.