Epidemic outbreaks are often accompanied by the unconfirmed information propagation Especially in the early stages of an epidemic outbreak, because of the lack of adequate verification, some ...unconfirmed information appears, which has a significant impact on the epidemic. Meanwhile, individuals under different emotions can also have different response to epidemics. In the paper, an interplay between epidemic spreading and unconfirmed information propagation model is established considering individuals’ emotional factors in multilayer networks. The mean-field method is used to analyze the interaction dynamic propagation process and the threshold of epidemic is obtained. Finally through the theoretical analysis and numerical simulations of scale-free network, the validity of the results is verified. The results show that the information, although unconfirmed, is still conducive to curb the spread of the epidemic. In addition, individuals with different emotions will adopt different self-protective behaviors, so as to further affect the spread of the epidemic.
•An interplay between unconfirmed information propagation and epidemic spreading model is proposed.•The individuals’ emotional factors are considered in multilayer network.•The mean-field method is used to analyze the interaction dynamic propagation process.•The unconfirmed information propagation have an effect on the spread of the epidemic.•The individuals with anxious make less favorable for the epidemic control.
In the Internet age, rumors bring great panic, research on the mechanism of propagation will help mitigate the bad influence of rumors. In this paper, we propose a modified rumor propagation model ...with consideration of scientific knowledge level and social reinforcement, and derive the mean-field equations that describe the dynamics of rumor propagation process. We obtain the rumor propagation threshold, which is closely related to scientific knowledge level and social reinforcement. The threshold of rumor propagation is increased by the scientific knowledge level, and the critical threshold of scientific knowledge level is also affected by the rumor propagation probability The results show that rumor propagates more quickly and more widely in people without scientific knowledge, while rumor propagates more slowly and the final size of the rumor is smaller in people with scientific knowledge. Positive social reinforcement will reduce the propagation threshold of rumor propagation, increase the propagation rate, and finally increase the rumor scale. Negative social reinforcement has the opposite effect on rumor. These results are verified by numerical simulations on scale-free networks. Research results also provide a good reference for future studies on how to control rumor propagation.
•We introduce a modified ISR rumor propagation model on heterogeneous networks.•The modified model considers the scientific knowledge level and social reinforcement.•The modified model reshapes the critical threshold of spreading dynamics.•It brings a nonlinear impact on propagation speed and final size of the rumor propagation.
In recent years, as the COVID-19 global pandemic evolves, many unprecedented new patterns of epidemic transmission continue to emerge. Reducing the impact of negative information diffusion, calling ...for individuals to adopt immunization behaviors, and decreasing the infection risk are of great importance to maintain public health and safety. In this paper, we construct a coupled negative information-behavior-epidemic dynamics model by considering the influence of the individual's self-recognition ability and physical quality in multiplex networks. We introduce the Heaviside step function to explore the effect of decision-adoption process on the transmission for each layer, and assume the heterogeneity of the self-recognition ability and physical quality obey the Gaussian distribution. Then, we use the microscopic Markov chain approach (MMCA) to describe the dynamic process and derive the epidemic threshold. Our findings suggest that increasing the clarification strength of mass media and enhancing individuals' self-recognition ability can facilitate the control of the epidemic. And, increasing physical quality can delay the epidemic outbreak and leads to suppress the scale of epidemic transmission. Moreover, the heterogeneity of the individuals in the information diffusion layer leads to a two-stage phase transition, while it leads to a continuous phase transition in the epidemic layer. Our results can provide favorable references for managers in controlling negative information, urging immunization behaviors and suppressing epidemics.
•A coupled information-behavior-epidemic model is proposed to describe the co-evolution process in multiplex networks.•The influence of the individual's self-recognition ability and physical quality are considered in the coupled model.•Microscopic Markov Chain Approach is used to analyze the evolutionary process and conduct the epidemic outbreak threshold.•Enhancing the individuals' self-recognition ability can promote them to adopt the immunization behavior.•Improving individuals' physical ability will have a continuous impact on reducing epidemic outbreak threshold.
During epidemics, individual responses to prevention and control information vary significantly, affecting the execution of preventive measures. This paper introduces a novel model to analyze the ...co-evolution of the information-behavior-epidemic dynamic, accounting for the heterogeneity in individual behavioral adoption thresholds and network structures. The model consists of three layers: the upper layer, utilizing scale-free social networks to represent the diffusion of information; the middle and lower layers, employing community networks, to illustrate individuals’ decision-making and epidemic transmission processes, respectively. We applied the Heaviside step function to depict the effects of information and local environmental factors on individuals’ decisions. Through the microscopic Markov chain approach (MMCA), we determined the epidemic threshold. Our methodology also included extensive Monte Carlo (MC) simulations to validate our theoretical predictions. Our results reveal several key insights: (i) reducing community mobility and the threshold for adopting preventive behaviors can significantly restrain the scale of the epidemic and delay outbreaks; (ii) the level of individual activity in the physical contact network has a significant influence on epidemic transmission; (iii) integrating individuals’ behavior adoption thresholds induces a two-stage phase change, deviating from the continuous phase transition typically observed in epidemic transmission.
•Integrated model predicts epidemic dynamics accurately.•Lowering thresholds reduces epidemic risk significantly.•Community structures exert significant influence on transmission dynamics.•Individual activity levels play a crucial role in epidemic transmission.•Effective vaccination campaigns bolster outbreak control efforts.
The widespread propagation of rumors has become a serious challenge today, posing a serious threat to public trust and social stability. To comprehensively examine the dynamics of rumor propagation, ...in this paper, we propose a multi-scale mathematical model that couples the intra-individual information discrimination process and the inter-individual rumor propagation process using nested modeling approach. Subsequently, we conduct a detailed mathematical analysis of the intra-and inter-individual dynamics process to obtain the basic regeneration number and the equilibrium points of the systems, respectively, and then prove the stability of the equilibrium point by using the Lyapunov stability theory. Numerical simulations reveal that during the initial stages of rumor propagation, individuals are more likely to be converted into spreaders due to their insufficient knowledge reserves. Enhancing the learning ability of individuals can enable individuals to identify rumors more quickly and transform into stiflers, thus reducing the scale of rumor propagation. In addition, we find that the greater the heterogeneity in the rumor's retention duration in the information base, i.e., the more scattered the time of rumor uploading by spreaders, which makes the rumor keep emerging in the information base, the wider the scale of rumor propagation will be. In addition, we find that the greater the heterogeneity in the rumor's retention duration in the information base, i.e., the more scattered the time of rumor uploading by spreaders, the wider the scale of rumor propagation will be. This is because rumors are constantly emerging in the information base. It is worth noting that the decreasing trend in the popularity of the rumor gradually slows down, which indicates that the effect of intervening on the rumor at the early stage of propagation is more significant.
•A new multi-scale rumor propagation model based on a nested modeling approach is proposed.•The model is used to describe the integrated propagation dynamics at the macro level and the micro level.•A detailed mathematical analysis of intra- and inter-individual rumor propagation dynamics is presented.•The stability of the equilibrium points is demonstrated using the Lyapunov stability theory.•Intervening in the early stages of rumor spreading has been proven to be effective.
Propagation of rumor, as one of the most important aspects of spreading dynamics on networks, which is often accompanied by the self-growth of individuals and indiscernible degree of events, and the ...analysis of this phenomenon can help us to better understand the information dissemination in the social network. Here, with the wiseman supplemented to the classical ignorant–spreader–stifler ( ISR) rumor spreading model, a modified ignorant–wiseman–spreader–stifler (IWSR) model is established with self-growth mechanism by considering indiscernible degree of events. By mean-field equations of IWSR model, the spreading thresholdλc is calculated to describe the theory of steady state dynamics of the rumor spreading. Numerical simulation is performed to assess the influence of self-growth of individual and indiscernible degree of events on dynamic spreading process. The results show that when the spreading rate λ is smaller than the threshold λc, the rumor will not spread in the population; the stronger the self-growth ability of the individual is, the smaller the range of rumor will be; the higher the indiscernible degree of events is, the greater influence of the rumor; These obtained findings in the present study could not only elaborate our understandings of spreading dynamics in network, but also provide us with an insight to develop effective strategies of inhibiting rumor propagation.
•A IWSR model is established with self-growth mechanism by considering indiscernible degree of events.•The spreading threshold λc is calculated to describe the theory of steady state dynamics of the rumor spreading.•The influence of self-growth of individual and indiscernible degree of events on dynamic spreading process.•The stronger the self-growth ability of the individual is, the smaller the range of rumor will be.•The higher the indiscernible degree of events is, the greater influence of the rumor.
Rumor is defined as an unconfirmed public opinion or gossip, which can be propagated through various channels, causing serious economic losses and disturbing the normal order of life. Therefore, ...studying the rumor propagation mechanism is helpful to implement effective rumor propagation control strategies. In this paper, the wise man is involved in the dynamic process of rumor propagation, and the modified rumor propagation model is established with consideration of social reinforcement and forgetting factors in heterogeneous network. The theories analysis of the model is carried out based on the mean field equation. The rumor propagation threshold is obtained, which is closely related to dual social reinforcement, wisdom conversion rate and forgetting factors. The final size of the rumor is related to positive social reinforcement and negative social reinforcement. Numerical simulations indicate that, the social positive reinforcement promotes rumor propagation and social negative reinforcement suppresses rumor propagation. And the addition of wise men reduces the number of spreaders, thus affecting the process of rumor propagation.
•We firstly introduce a modified ISWR rumor propagation model on heterogeneous networks.•We derive the mean field equations with considering the wise man and social reinforcement.•The wisdom conversion rate and the social reinforcement reshapes the critical threshold of spreading dynamics.•The social reinforcement brings a nonlinear impact on propagation speed and final size of the rumor propagation.
In this paper, we propose a new model for supply chain risk propagation considering herd mentality and risk preference under warning information on multiplex networks, in which one layer is used to ...denote the risk propagation and the other one represents the warning information propagation network. In this model, the enterprises can be divided into two types, namely with warning information or without warning information. Meanwhile, the herd mentality and risk preference are considered to discuss their influence on the supply chain risk propagation. We build the probability transition tree to establish the state transition equation in detail through the microscopic Markov chain approach (MMCA) and analyze the established equation and derive the propagation threshold of supply chain risk. The analysis results are shown that the propagation threshold has been correlated with the network topology, the herd mentality and the risk preference under warning information diffusion Finally, the simulation results further verify the feasibility of the model.
•We proposed a new model for supply chain risk propagation.•The model considering herd mentality and risk preference on multiplex networks.•We built the probability transition tree to establish the state transition equation through MMCA.•We analyzed the equation and derive the propagation threshold of supply chain risk.
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.
•A rumor model is proposed to describe the impact of awareness programs by media report.•It exists a nonlinear proportional relationship between the ignorant individuals and media report.•The feasible equilibriums and their stability properties are analyzed based on theory of Routh–Hurwitz.•Optimal control strategies are efficient method for reducing the number of rumor spreaders and maximizing social utility.
The diseases dissemination always brings serious problems in the economy and livelihood issues. It is necessary to study the law of disease dissemination from multiple dimensions. Information quality ...about disease prevention has a great impact on the dissemination of disease, that is because only the real information can inhibit the dissemination of disease. In fact, the dissemination of information involves the decay of the amount of real information and the information quality becomes poor gradually, which will affect the individual's attitude and behavior towards disease. In order to study the influence of the decay behavior of information on disease dissemination, in the paper, an interaction model between information and disease dissemination is established to describe the effect of the decay behavior of information on the coupled dynamics of process in multiplex network. According to the mean-field theory, the threshold condition of disease dissemination is derived. Finally, through theoretical analysis and numerical simulation, some results can be obtained. The results show that decay behavior is a factor that greatly affects the disease dissemination and can change the final size of disease dissemination. The larger the decay constant, the smaller final size of disease dissemination. In the process of information dissemination, emphasizing key information can reduce the impact of decay behavior.
