Recurrent Epidemics Outbreak On Complex Networks

Complex network has been studied in depth for recent two decades.However,it is still a hot topic in scientific research nowadays.Not only the mathematicians and physicists are attracted to this research area,but also the researcher of biology,engineering and systematics are interested in this field.Complex network has become a fascinating interdiscipline.Driven by complex network,epidemic spreading has been well studied and many significant results have been achieved.The study was first focused on the static networks.It was revealed that for scale-free networks,the epidemic threshold will be vanishingly small in the thermodynamic limit.Then,the study was moved to the reaction-diffusion model where agents can move to their neighboring nodes by a possibility.In this framework,people can ob-serve the spatio-temporal pattern of global epidemic.Later on,the research interest was concentrated on how the human activities and concrete factors influence the epi-demic spreading,such as the objective traveling,adaptive networks,the traffic-driven epidemic spreading and temporal networks,and so on.In recent years,the research interest has turned to the case of epidemic spreading on multilayer networks.All these studies are focused on the increasing branch of epidemic outbreak,especially on the epidemic threshold.However,most of the studies are lacking the supports of real epi-demic data and are just based on the phenomenological models.Thus,based on the real data,we are wondering whether we can escape this framework to make a fresh start.For this purpose,we collected a large number of real epidemic data from differ-ent cities.In the spirit of "talking based on data",we find that besides the traditional epidemic features,there are also many neglected new characteristics,such as the recur-rence of epidemic,the asymmetry of growing and recovering processes,synchronized and mixed outbreak patterns on adjacent regions and the pattern of multi-peaks in an outbreak process,and so on.In order to understand the underlying mechanisms of these features,we presented some new models on complex network,which can repro-duce these features of real data very well.Specifically,the main contributions of this thesis can be summarized as following:1.Based on a large number of real data from different cities,we find that besides the seasonal periodic outbreaks of influenza,there are also non-periodic outbreaks,i.e.non-seasonal or non-annual behaviors.To understand how the non-periodicity shows up,we present a network model of SIRS epidemic with both time-dependent infection rate and a small possibility of persistent epidemic seeds,representing the influences from the larger annual variation of environment and the infection generated sponta-neously in nature,respectively.Our numerical simulations reveal that the model can reproduce the non-periodic outbreaks of recurrent epidemics with the main features of real influenza data.Further,we find that the recurrent outbreaks of epidemic depend not only on the infection rate but also on the density of susceptible agents,indicating that they are both the necessary conditions for the recurrent epidemic patterns with non-periodicity.A theoretical analysis based on Markov dynamics is presented to explain the numerical results.This finding may be of significance to the control of recurrent epidemics.2.Based on a large number of real epidemic spreading data from coupled re-gions or cities,we find that epidemic spreading shows either synchronized outbreak pattern where outbreaks occur simultaneously in both networks or mixed outbreak pat-tern where outbreaks occur in one network but do not in another one.To reveal the underlying mechanism,we present a two-layered network model of coupled recurrent epidemics to reproduce the synchronized and mixed outbreak patterns.We show that the synchronized outbreak pattern is preferred to be triggered in two coupled networks with the same average degree while the mixed outbreak pattern is likely to show for the case with different average degrees.Further,we show that the coupling between the two layers tends to suppress the mixed outbreak pattern but enhance the synchronized outbreak pattern.A theoretical analysis based on microscopic Markov-chain approach is presented to explain the numerical results.This finding opens a new window for studying the recurrent epidemics in multilayer networks.3.A common point in all previous contributions is that epidemic presents a single peak outbreak pattern in an epidemic period.However,based on a large number of real data from different cities,we find that besides the pattern of single peak,there are also the patterns of two or multiple peaks in an epidemic period.To understand how the pattern of two peaks shows up,we introduce a standard SIR epidemic model on multilayer networks to reproduce the two peaks outbreaks pattern.Our numerical simulations reveal that the model can reproduce both a single and two peaks outbreak patterns with the main features of real epidemic data.Further,we find that the long time delay of epidemic outbreak in each network is the main reason for the emergence of the pattern with two peaks.Specially,the phenomenon of two peaks outbreaks tends to be triggered with weakly coupling strength(i.e.small average degree and infected rate between the two layers).Moreover,this pattern is likely to show on the coupled networks with different degree distribution.An edge-based compartmental theory is developed to explain the numerical results.This finding may be of significance for epidemic outbreak detection and control in different regions.4.In metropolis,traffic congestion has been becoming a more and more serious problem,especially in rush hours.This congestion process makes people have more chance to contact each other and thus will accelerate epidemic spreading.To explain this observation,we present a reaction-diffusion model with a periodic varying diffu-sion rate to represent the daily traveling behaviors of human beings and its influence to epidemic spreading.By extensively numerical simulations,we find that the epidem-ic spreading can be significantly influenced by traffic congestion where the amplitude,period and duration of diffusion rate are the three key parameters.Furthermore,a brief theory is presented to explain the effects of the three key parameters.These findings suggest that except the normal ways of controlling contagion in working places and long-distance travelings,controlling the contagion in daily traffic congestion may be another effective way to reduce epidemic spreading.Based on all these results,we find that our research framework opens a new window for studying the epidemic spreading.It means that the studying of epidemic spreading is far from the ending and many new challenging problems are waiting for us to further explore.