Dynamics of the Rumor-Spreading Model with Control Mechanism in Complex Network

The spread of rumors has a great impact on social order, people’s psychology, and life. In recent years, the application of rumor-spreading models in complex networks has received extensive attention. Taking the management and control of rumors by relevant departments in real life into account, the SIDRQ rumor-spreading model that combines forgetting mechanism, immune mechanism, and suspicion mechanism and guides on a uniform network is established in this paper. Then, the basic reproductive number of the system and the unique existence of the solution are discussed, and the stability of the system is analyzed using the basic reproductive number, Lyapunov function, and Lienard and Chipart theorem; furthermore, the basic reproductive number may not be able to deduce the stability of the system and a counterexample is given. Finally, the influence of different parameters on the spread of rumors is studied, and the validity of the theoretical results is verified.

The Impact of the Global and Local Awareness Diffusion on Epidemic Transmission Considering the Heterogeneity of Individual Influences

In this paper, we propose a coupled awareness - epidemic spreading model considering the heterogeneity of individual influences, which aims to explore the interaction between awareness diffusion and epidemic transmission. The considered heterogeneity of individual influences are threefold: the heterogeneity of individual influences in the information layer, the heterogeneity of individual influences in the epidemic layer and the heterogeneity of individual behavioral responses to epidemics. In addition, the individuals' receptive preference for information and the impacts of individuals' perceived local awareness ratio and individuals' perceived epidemic severity on self-protective behavior are included. The epidemic threshold is theoretically established according to the microscopic Markov chain approach and mean-field approach. Results indicate that the critical local and global awareness ratios have two-stage effects on the epidemic threshold. Besides, either the heterogeneity of individual influences in the information layer or the strength of individuals' responses to epidemics can influence the epidemic threshold with a nonlinear way. However, the heterogeneity of individual influences in the epidemic layer has few effect on the epidemic threshold, but can affects the magnitude of the final infected density.

A new spreading model in the environment of epidemic-related online rumors

This paper takes COVID-19-related online rumors as the research object, and explores the law of spreading public opinion in social networks. The paper also conducts empirical research on the relationship between rumor spreading, user characteristics and subject interest differences, and analyzes the common influence of individual factors and social environment. In the process of public opinion dissemination, measures that can effectively regulate the dissemination of public opinion are proposed. Based on the susceptible-exposed-infected-recovered (SEIR) model, this paper analyzes the influence of individual differentiation characteristics, friend factors, and time-dependent decline on user status changes. The study found that the user’s environment can affect the spread and popularity of public opinion information, and prolong the survival time of public Controlling the propagation threshold and exit threshold of the platform helps to control the large-scale dissemination of online public opinion. The extinction of public opinion is affected by the decline of time and heat rather than certain probability.

Panic Spreading Model with Different Emotions under Emergency

Emotion plays an important role in decision making. In an emergency, panic can spread among crowds through person-to-person communications and can cause harmful effects on society. The aim of this paper is to propose a new theoretical model in the context of epidemiology to describe the spread of panic under an emergency. First, according to divisions in personality in the context of psychology, groups are divided into a level-headed group and an impatient group. Second, individuals in the two groups have unique personalities. Thus, the level-headed group only infects within the group, while the impatient group considers emotional infection within the group and cross infection between the groups. Then, a nonlinear infection rate is used to describe the probability of infection after an infected person contacts a susceptible person, which is more in line with the real situation. After that, the level-headed group–impatient group nonlinear SIRS panic spreading model is developed. Stable analysis of the model is obtained using the Lyapunov function method to study the stability of the panic-free equilibrium and panic-permanence equilibrium. Finally, simulations are carried out to dynamically describe the spread process of group emotional contagion.

ILSHR Rumor Spreading Model by Combining SIHR and ILSR Models in Complex Networks

Rumor is an important form of social interaction. However, spreading harmful rumors can have a significant negative impact on social welfare. Therefore, it is important to examine rumor models. Rumors are often defined as unconfirmed details or descriptions of public things, events, or issues that are made and promoted through various tools. In this paper, the Ignorant-Lurker-Spreader-Hibernator-Removal (ILSHR) rumor spreading model has been developed by combining the ILSR and SIHR epidemic models. In addition to the characteristics of the lurker group of ILSR, this model also considers the characteristics of the hibernator group of the SIHR model. Due to the complexity of the complex network structure, the state transition function for each node is defined based on their degree to make the proposed model more efficient. Numerical simulations have been performed to compare the ILSHR rumor spreading model with other similar models on the Sina Weibo dataset. The results show more effective ILSHR performance with 95.83% accuracy than CSRT and SIR-IM models.

Numerical Investigations through ANNs for Solving COVID-19 Model

The current investigations of the COVID-19 spreading model are presented through the artificial neuron networks (ANNs) with training of the Levenberg-Marquardt backpropagation (LMB), i.e., ANNs-LMB. The ANNs-LMB scheme is used in different variations of the sample data for training, validation, and testing with 80%, 10%, and 10%, respectively. The approximate numerical solutions of the COVID-19 spreading model have been calculated using the ANNs-LMB and compared viably using the reference dataset based on the Runge-Kutta scheme. The obtained performance of the solution dynamics of the COVID-19 spreading model are presented based on the ANNs-LMB to minimize the values of fitness on mean square error (M.S.E), along with error histograms, regression, and correlation analysis.

Susceptible-Infectious-Critical-Recovered rumor spreading model in social networks

As an important area of social networks, rumor spread has attracted the attention of many scholars. It aims to explore the rumor propagation, and to propose effective measures to curb the further spread of rumors. Different from some existing works, this paper believes that susceptible persons affected by rumor-refuting information will first enter the critical state, while ones who related to rumors will directly turn into the spread state. Therefore, this paper proposes a Susceptible-Infectious-Critical-Recovered (SICR) rumor model. In addition, considering that infectious persons with high levels of refuting rumors may cause emotional resonance among individuals, this model adds a connecting edge from the recovered to the infectious who are triggered by the information of refuting the rumors. First, the basic regeneration number [Formula: see text] is obtained by using the next generation matrix method. Then, the global stability of the rumor-free equilibrium [Formula: see text] and the persistence of rumor propagation are proved in detail in theoretical analysis. The simulation results show that the existence of a critical state can reduce the influence of rumors. Rumor refutation mechanism, as soon as possible to curb the spread of rumors, is an effective measure.