With the prevalence of online social networks, the potential threat of misinformation has greatly enhanced. Therefore, it is significant to study how to effectively control the spread of misinformation. Publishing the truth to the public is the most effective approach to controlling the spread of misinformation. Knowledge popularization and expert education are two complementary ways to achieve that. It has been proven that if these two ways can be combined to speed up the release of the truth, the impact caused by the spread of misinformation will be dramatically reduced. However, how to reasonably allocate resources to these two ways so as to achieve a better result at a lower cost is still an open challenge. This paper provides a theoretical guidance for designing an effective collaborative resource allocation strategy. First, a novel individual-level misinformation spread model is proposed. It well characterizes the collaborative effect of the two truth-publishing ways on the containment of misinformation spread. On this basis, the expected cost of an arbitrary collaborative strategy is evaluated. Second, an optimal control problem is formulated to find effective strategies, with the expected cost as the performance index function and with the misinformation spread model as the constraint. Third, in order to solve the optimal control problem, an optimality system that specifies the necessary conditions of an optimal solution is derived. By solving the optimality system, a candidate optimal solution can be obtained. Finally, the effectiveness of the obtained candidate optimal solution is verified by a series of numerical experiments.
An Optimal Control Problem Formulation for a State Dependent Resource Allocation Strategy
