Abstract
Rumor spreading is a typical form of social communication and plays a significant role in social life. A nonlinear rumor mathematical model is proposed to describe the impact of awareness programs by media report on rumor spreading. It exists a nonlinear proportional relationship between the ignorant individuals and media report. Then, the feasible equilibriums and their stability properties are analyzed based on theory of Routh–Hurwitz, and the existence of the optimal control is proved by using Pontryagin’s Maximum principle. Numerical simulation shows that the proposed optimal control strategies are efficient method to reduce the number of rumor spreaders and to maximize social utility.
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