In this work, we introduce a novel mathematical network model for community level preventative health interventions. We develop algorithms to approximately solve this novel formulation at large scale and we rigorously explore their theoretical properties. We create a realistic simulation environment for interventions designed to curb the prevalence of obesity occurring in the region of Montreal, Canada, and use this environment to empirically evaluate the performance of the algorithms we develop. We find that our algorithms significantly outperform all baseline interventions. Moreover, for fixed computational resources, our algorithms address problems of significantly greater size than the best existing alternative algorithm.