Optimal Control for Heterogeneous Node-Based Information Epidemics over Social Networks

In this article, we investigate the optimal control problems of heterogeneous node-based information epidemics. A node-based susceptible-infected-recovered-susceptible model is introduced to describe the information diffusion processes taking into account heterogeneities in both network structures and individual characters. Aiming at guiding information dissemination processes toward the desired performance, we propose an optimal control framework with respect to two typical scenarios, i.e., impeding the spread of rumors and enhancing the spread of marketing or campaigning information. We prove the existence of the solutions and solve the optimal control problems by the Pontryagin maximum principle and the forward-backward sweep method. Moreover, numerical experiments validate the use of the node-based SIRS model by comparing it with the exact 3N-state Markov chain model. The effectiveness of the proposed control rules is demonstrated on both models. Furthermore, discussion on the influence of the parameters provides insights into the strategies of guiding information diffusion processes.