Abstract
An Innocents-Spreaders-Calmness-Removes (ISCR) rumor propagation model is established with nonlinear incidence and time delay on complex networks in this paper. Based on the mean-field theory, the spreading dynamics of the ISCR model are discussed in detail. Firstly, the basic reproduction number R 0 is obtained by the next generation matrix method to ensure the existence of rumor-prevailing equilibrium. Secondly, by utilizing the Routh–Hurwitz criterion and LaSalle’s invariance principle, the local stability and global stability of rumor equilibria are proved. Moreover, the optimal control is presented via Pontryagin’s minimum principle, which is to effectively restrain rumor diffusion. Finally, the theoretical results are verified by numerical simulations.
Highlights
Rumors are usually defined as unproven words and may damage personal reputation, affect financial markets, cause social panic and instability, and severely disrupt people’s normal and orderly life
An ISCR rumor propagation model with nonlinear incidence and time delay is presented on complex networks
According to the mean-field theory, the ISCR model is discussed in detail
Summary
Rumors are usually defined as unproven words and may damage personal reputation, affect financial markets, cause social panic and instability, and severely disrupt people’s normal and orderly life. Based on the above discussion, the nonlinear incidence c〈k〉I(t)S(t)/1 + αS(t) is used in this paper to describe the influence of the psychological changes of Innocents on rumor propagation, where c represents the spreading ability of rumors and α represents the impact of population crowding or changes on Innocents. This is more in line with the reality. (1) A novel ISCR rumor propagation model is proposed with nonlinear incidence and time delay on complex networks. This paper analyzes the influence of time delay on optimal control in numerical simulation
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