SIS Model of Rumor Spreading in Social Network with Time Delay and Nonlinear Functions**Project supported by the National Natural Science Foundation of China (Grant No.11571170), the Natural Science Research of the Jiangsu Higher Education Institutions of China (Grant No.19KJB110001) and the Natural Science Foundation of Jiangsu Province, China (Grant No.SBK2019040208).

Abstract

With the advent of the information age of networks, the study about rumor propagation in social networks has become increasingly significant. In this paper, a rumor propagation model with nonlinear functions and time delay in social networks is proposed. First, according to the next-generation matrix method, we work out the basic reproduction number. Second, we discuss the existence of the rumor-prevailing equilibrium points. Third, we demonstrate the stabilities of equilibrium points and analyze the sufficient conditions for Hopf bifurcation. Finally, the correctness of the theory is verified and several vital conclusions are obtained by numerical simulations.