Dynamics Analysis Of Rumors Propagation Mechanism And Control Strategy In Emergency

Due to the natural conditions, economic development level, population and other factors, China is a country with many emergencies such as natural disasters and accidents which feature various types, high frequency, and great losses. By looking back into some major emergencies in the history, we can find that almost every emergency came with many rumours. The rumour propagation is harmful to the society because it will not only affect people's daily life, but also greatly influence normal social order and political stability, or even turn into public events. After emergencies, government departments usually immediately start the emergency response plan, take corresponding measures to control the situation and organize and carry out emergency rescue and treatment measures to reduce losses. The propagation of rumours will pose a threat to the organization of emergency treatment and logistics. Thus the research on the rumour propagation process can help control the rumour propagation. In this case, the researches on the propagation mechanism,spread and diffusion channels and influential factors, as well as the way of controlling and guiding the dynamic evolution of rumours have become the focus of current academic field.These research results are of great theoretical and practical significance for the emergency decision-making departments to deeply understand the evolution rules of rumour propagation, make precautions for rumours, improve judging ability and take timely and effective intervening and controlling actions in case of emergencies.Rumours after emergencies are taken as the research subject, systematic dynamics theories and methods adopted, and various factors including media influence, time-delay,limitation of government control ability and reaction-diffusion, etc. taken into consideration,to establish more practical time-delay rumour propagation models and study their dynamical features. The details are as follows:(1) Dynamics analysis of a delayed rumor propagation model in an emergency-affected environment.The time needed for transforming a rumour propagator into a non-propagator, and the government control time-delay are taken into consideration to propose the time-delay SIR rumour propagation model that takes the media influence after emergencies into account and study its dynamical features. By using time-delay as the bifurcation parameter, local stability of the boundary equilibrium point and positive equilibrium point is discussed to obtain the conditions for Hopf bifurcation. Then, according to the canonical form method and the center manifold theorem, the stability formula to determine the Hopf bifurcation direction and bifurcating periodic solutions is put forward. At last, some numerical simulations are offered to illustrate the theoretical results. Through theoretical analysis and numerical simulation, it is found that government control time-delay has a significant influence on the stability of the system because it can cause disequilibrium, Hopf bifurcation and periodic vibration. When time-delay overpasses a certain threshold value, the system will produce the periodic solution. In addition, when the system is stable, as time-delay increases, the convergence speed of the system will slow down gradually. Therefore, the rumour propagation can be controlled by adjusting the media influence and government control time-delay.(2) Dynamics analysis of a delayed rumor propagation model with saturated control function.Resources and ability limitations of the government control in rumour propagation governance are taken into consideration and saturated control function is adopted to establish the time-delay rumour propagation model with saturated control function and study its dynamical features. Time-delay is taken as the bifurcation parameter to study the stability of the system and Hopf bifurcation. Local stability of the boundary equilibrium point and positive equilibrium point is discussed to obtain the conditions for Hopf bifurcation.According to the canonical form method and center manifold theorem, the stability formula to determine the Hopf bifurcation direction and bifurcating periodic solutions is put forward.Some numerical simulations are offered to illustrate the theoretical results. The simulation results show that: when the number of the infected people is small and the resources controlled by the government is enough, the rumour control results are satisfactory;otherwise, there might be the risk of social public events. The government's controlling actions can change the scale of rumour propagation when it is in equilibrium state, which means that if the rumour propagation causes any social instability, the government control can help assure social stability. Appropriate government control can also make the periodic vibration become stable, thus improving the balance of social system; when the government control is strengthened, the rumours may probably be ended. In short, effective methods to control rumour propagation include timely influencing and interfering with the propagators,improving the government control level and ability and reducing the propagation coefficient.(3) Dynamic analysis of a spatial diffusion rumor propagation model with delay.Two parameters of time-delay and reaction-diffusion are at the same time introduced into the rumour propagation research, and the space diffusion factors, time delay effects and government control are taken into acount to establish time-delay and reaction-diffusion rumour propagation model with government control parameter. According to the partial differential equation theory, stability of the model is discussed. Time-delay is taken as the bifurcation parameter to study the Hopf bifurcation of the system. The theoretical analysis and numerical simulation results show that time-delay can change the stability of the system.When time-delay overpasses a certain threshold value, Hopf bifurcation will be generated.Under certain conditions, the positive equilibrium point can reach a global asymptotical stability. Then numerical simulation is adopted to discuss the influences of time-delay,diffusion and government control on the system dynamics. It is found that, regarding the time model, there is a threshold for time delay. When time delay is less than the threshold,the positive equilibrium point is close to asymptotical stability; when time delay exceeds the threshold, the positive equilibrium point is unstable and small amplitude periodic solutions will be produced. Regarding the space-time model, it is found that through mathematical analysis, the node movement has effectively relieved the vibration of rumour propagation,which means that the reaction-diffusion can reduce the possibility of social instability and that our introduction of diffusion is important. Control intensity of the government has a great influence on the stability of the system. If the government intensifies the control, the number of rumour propagators can be remarkably reduced and the number of susceptible people and rational groups will be obviously increased. Besides, as the government control intensifies, the stability domain of the system also expands.Internal mechanism of rumour propagation is explored to study the influence of important parameters (such as time-delay, government control, and reaction-diffusion) on the model dynamics properties and corresponding control strategies, and further enrich the existing theoretical achievement of rumour propagation, which has provided theories,methods and decisions support for effectively controlling and guiding public behaviours.