Nonlinear Analysis and Optimal Control of an Improved SIR Rumor Spreading Model

摘要

Based on the classic SIR model, this paper proposes a new rumor spreading model which considers the transition probability of nodes from S to I as a variable instead of a constant. This paper firstly studies the nonlinear phenomena in the new model, such as balance node, Hopf bifurcation, limit cycle. Secondly, this paper studies how to control the range of limit cycle. Finally, this paper studies the optimal control method, which can minimize the people who spread rumors.