Modeling And Analysis Of The Propagation Dynamics Of Complex Networks

The transmission dynamics of infectious diseases on a network is the evolution of different types of nodes caused by infectious diseases over time,depending on both the topology in the network and the form of transmission of infectious diseases.In recent years,the propagation dynamics of network infectious diseases have attracted widespread attention,and the transmission patterns of infectious diseases in networks have been explored by qualitative analysis of infectious disease models.In this thesis,we focus on the infectious disease models on complex networks and discuss the influence of individual responses and network structure on the transmission of infectious diseases and analyze their dynamical behavior.Firstly,taking into account the impact individual alertness,we propose a new infectious disease synchronization model on complex dynamic networks.According to the Lyapunov stability theory and LeSalle invariant set principle,the global stability of disease-free equilibrium points and local equilibrium points is systematically studied.Moreover,we obtain the the global stability conditions of synchronization of infectious diseases.In the following,numerical simulations are implemented to investigate the relationship between the spread rate and synchronization error,and individual alertness and infectious disease transmission.Our results show that the collective behavior induced by individual alertness interacts with the spreading behavior,and the individual alertness can inhibit the spread of infectious diseases,while the spread of infectious diseases also promotes individual alertness.It was also found that network size affects the spread rate and synchronization effect,i.e.,the larger the network size,the better the error synchronization effect.Then,considering the time delay of the behavioral responses of individuals,we present the SIQR infectious disease model with alertness period and quarantine delay on the space subnetwork.The basic reproduction number of the infectious disease model is calculated by mean field theory,and the results conclude that the individual alertness period is negatively correlated with the basic reproduction number,and the quarantine time lag does not affect the basic reproduction number,and the sensitivity of the parameters to the basic reproduction number is analyzed by using sobol sensitivity analysis.Also,the local and global stability of the equilibrium point is discussed,and the stability results of the theoretical part are verified using numerical simulations.In addition,the numerical simulation results show that the increase of individual alertness and alertness period inhibits the spread of infectious diseases.In contrast,the increase of quarantine delay leads to a large-scale spread of infectious diseases in social networks.Finally,based on the topology of community networks,we construct the contagion model on community networks with different connected edges of individuals.The basic regeneration number of the model is calculated by the next-generation matrix method,and it is found that the connection rate of individuals inside and outside the communities has an impact on the basic regeneration number.Then,the relationship between the size of infected nodes and the connection rate and the number of connected edges of nodes inside and outside the community is investigated,and the results show that the difference in the number of connected edges of individuals within different communities leads to different trends in the spread of infectious diseases,i.e.,the infection density of communities with a higher number of connected edges of individuals will continue to increase until it reaches a steady state.The infection density curve of associations with a lower number of individual connected edges will gradually decrease to a steady state.On the other hand,community strength affects the basic reproduction number of the infectious disease model and thus the final shape of infectious disease transmission.