Analysis Of Infectious Disease Models Based On Individuals On Complex Networks

In this paper,several kinds of individual-based epidemic models are studied using the quenched mean-field method and the pair quenched mean-field method.The first chapter introduces the preliminary knowledge.First,the three basic characteristics variables of the network are introduced.Then it introduces the analysis methods of infectious diseases based on individuals,including dynamic message-passing theory,Markov Chain method,the quenched mean-field method and the pair quenched mean-field method.From the second chapter to the fourth chapter,there are the derivation and theoretical analysis of individual-based infectious disease models on directed networks,weight networks,and cluster networks.According to different network characteristics,a continuous-time Markov chain method is used,and the SIS pair quenched mean-field model is derived using the total probability formula and different clustering approximation formula.The stability of the disease-free equilibrium point is analyzed by the stability theory of differential equations.Threshold analysis are performed using the second-order standard pair approximation formula,Then it derives threshold conditions for disease epidemics and thresholds in special cases,followed by numerical simulation,etc.Finally,the content of this paper is briefly summarized,and the future research ideas are proposed.This paper establishes dynamic models on different networks to make the model closer to the actual situation.It is found that the conditions of disease outbreaks on directed networks are closely related to infection parameters,and the influence level of the parameters varies.Through numerical simulation,it is also found that the weight of the edges in the network will affect the epidemic threshold of the disease on weight networks.On the clustering network,the pairwise approximation method based on individuals is derived and the existing models are generalized.