Study On The Interplay Between Local Information Based Awareness And Epidemic Dynamics In Complex Networks

With the rapid development of the complex network theory, the research on epidemic dynamics has also been paid more and more attention. People often use classical SIS and SIR models to study the spread of the epidemic dy-namics in the past. However, when facing the outbreaks of epidemics, people can obtain information related to the epidemics, which may induce individuals to take self-initiate protective measures to lower the probability of being infect-ed, which essentially forms the subject about the interplay between epidemic and information spreading dynamics in complex networks.This dissertation mainly introduces the related concepts of complex net-work and illustrates several classical models of complex networks. In view of this, we analyze a model with alert state, and then study the interplay be-tween local information based awareness and epidemic dynamics in complex networks. In addition, we quantitatively study the impact of asymptomatic in-fection on the interplay between diseases and behavioral responses in complex networks. In this dissertation, the main research results are as follows:First, to illustrate the impacts of the human behavioral responses, a new class of individuals, SF,is introduced to the classical SIR model. In the model, SFstate represents that susceptible individuals who take self-initiate protective measures to lower the probability of being infected, and a susceptible individual may go to SF state with a response rate when contacting an infectious neighbor. Via the percolation method, the theoretical formulas for the epidemic threshold as well as the prevalence of epidemic are derived. The analytical results are also verified by the numerical simulations. Our finding indicates that, with the increasing of the response rate, the epidemic threshold is enhanced and the prevalence of epidemic is reduced. In addition, we demonstrate that, because the mean field method neglects the dynamic correlations, a wrong result based on the mean field method is obtained-the epidemic threshold is not related to the response rate.Second, we quantitatively analyze the impacts of asymptomatic infection on the diseases spread, then considering this mechanism into the improved SIS model (SAUIS) and the improved SIR model (SAUIR), respectively. Using the mean field method and the percolation theory to derive the theoretical formulas for the epidemic threshold as well as the prevalence of epidemic, re-spectively. Combining with theoretical analysis and simulations, we found that the local information behavioral responses to SAUIS model as well as SAUIR model can obviously increase the epidemic threshold and reduce the prevalence of epidemic. Moreover, the existence of the U-state causes the delayed and i-naccurate responses from susceptible individuals, leading to the suppression effects of behavioral responses on diseases control are weakened. In addition, because of the irreversible process of the SAUIR model, the suppression effect of behavioral responses on disease control is not as good as the case of the SAUIS model.Finally we conclude the work we have done and present outlook of further researches in this field.