Modeling for heterogeneous multi-stage information propagation networks and maximizing information**Project supported by the National Natural Science Foundation of China (Grant No. 61873194).

Abstract

In this paper, we propose a heterogeneous multi-stage model to study the effect of social reinforcement on information propagation. Both heterogeneity of network components and the heterogeneity of individual reinforcement thresholds are considered. An information outbreak condition is derived, according to which the outbreak scale and individual density of each state under specific propagation parameters can be deduced. Monte Carlo experiments are conducted in Facebook networks to demonstrate the outbreak condition, and we find that social reinforcement effects generally inhibit the propagation of information though it contributes to the emergence of certain hot spots simultaneously. Additionally, by applying Pontryagin’s Maximum Principle, we derive the optimal control strategy in the case of limited control resources to maximize the information propagation. Then the forward–backward sweep method is utilized to verify its performance with numerical simulation.