https://doi.org/10.1140/epjp/s13360-023-04005-1
Regular Article
Dynamical behaviors of a delayed SIR information propagation model with forced silence function and control measures in complex networks
1
School of Mathematical Sciences, Jiangsu University, 212013, Zhenjiang, People’s Republic of China
2
School of Mathematics, Hunan University, 410082, Changsha, People’s Republic of China
3
Jiangsu University Hospital, Jiangsu University, 212000, Zhenjiang, People’s Republic of China
Received:
29
December
2022
Accepted:
17
April
2023
Published online:
11
May
2023
Due to the advanced network technology, there is almost no barrier to information dissemination, which has led to the breeding of rumors. Intended to clarify the dynamic mechanism of rumor propagation, we formulate a SIR model with time delay, forced silence function and forgetting mechanism in both homogeneous and heterogeneous networks. In the homogeneous network model, we first prove the nonnegativity of the solutions. Based on the next-generation matrix, we calculate the basic reproduction number 
. Besides, we discuss the existence of equilibrium points. Next, by linearizing the system and constructing a Lyapunov function, the local and global asymptotically stability of the equilibrium points are found. In the heterogeneous network model, we derive the basic reproduction number 
through the analysis of a rumor-prevailing equilibrium point 
. Moreover, we conduct the local and global asymptotic stability analysis for the equilibrium points according to the LaSalle’s Invariance Principle and stability theorem. As long as the maximum spread rate 
is large enough, the rumor-prevailing point is locally asymptotically stable when 
. Additionally, it hits that the system exists bifurcation behavior at 
due to the newly added forced silence function. Later, after adding two controllers to the system, we research the problem of optimal control. Finally, aimed at authenticating the above theoretical results, a serious of numerical simulation experiments are carried out.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
