Models of Information Diffusion in a Social Group: Construction of Optimal Programs

Resumo

We investigate modified models of information diffusion (or propagation) in a social group. The process dynamics is described by a one-dimensional controlled Riccati differential equation. The models in this article differ from the original model [2] by the choice of the optimand functional. Two variants of the optimand functional are considered. The optimal control problems are solved by the Pontryagin maximum principle [1]. We show that the optimal control program is a bang bang function of time with at most one switching point. Easily checked conditions on the problem parameters are derived, guaranteeing the existence of a switching point in the optimal control. Our theoretical analysis of the problem leads to the construction of a one-dimensional convex minimization problem to find the optimal control switching point. We also describe an alternative approach (without invoking the maximum principle) for the construction of the optimal solution that utilizes a special representation of the optimand functional and analyzes the reachable sets independent of the functional.