Optimal control for information diffusion over heterogeneous networks

In this paper, the optimal control problem for information diffusion over heterogeneous networks is inspected. First, the node-based susceptible-infected-susceptible (SIS) is introduced considering the heterogeneity of both network structure and diverse transition rates. Second, taking the scenario of campaigning and marketing as examples, an optimal control scheme is proposed aiming at information diffusion by a given final time with limited resources. The solution of the optimal control problem is proved to be existed and obtained by using Pontryagin Maximum Principle. Considering the computation problem of the analytical solution, a modified forward-backward sweep algorithm is provided to obtain a numerical solution. At last, the effectiveness of the proposed method is examined with several simulations.