Global stability and optimal control analysis of a knowledge transmission model in multilayer networks

Abstract

Knowledge dissemination plays an important role in many aspects. The control strategy to improve the performance of knowledge transmission in couple networks is a meaningful work, which is little consideration in the existing work. This paper addresses the problem of optimal control for a class of knowledge transmission models. Firstly, the multilayer complex networks are built according to how knowledge is acquired. Secondly, inspiration from the spread of a disease, a model of knowledge transmission is established. Moreover, the basic reproduction number R0, knowledge-free equilibrium (KFE), and knowledge endemic equilibrium (KEE), as well as their stability, are deduced. Then, the imposition of optimal control, including improving the digestion and absorption of knowledge contacts and increasing the review rate of knowledge-forgotten persons, can increase the number of knowledge communicators. Afterward, Pontryagin’s maximum principle is used to deal with the nonlinear optimal control problem. Finally, through numerical simulations, the stability of the equilibriums are confirmed, the effect of knowledge dissemination is the best and the range of the knowledge dissemination is widest when two control strategies are applied at the same time.