Study On Epidemic Spreading In Complex Networks Considering Individuals’ Behaviors

Complex network, a promising interdisciplinary science, attracts more and more attentions. Ithas covered many fields such as informatics, biology, physics, and sociology. At present, the studieson complex network include the following aspects: empirical study on network structure, networkevolution, modeling and control, and spreading dynamics process. Among these studies, epidemicspreading in complex networks has become one of the hot topics. In order to better understandepidemic behaviors, in this dissertation, epidemic spreading in complex networks are deeplyinvestigated with the impact of individual mobility and behavior response by using the mean-fieldapproach, differential dynamics theory, and Monte Carlo simulation. The main contents andcontributions of the dissertation are as follows:1. In the real world, people generally have awareness and reaction to epidemic to reduce therisk of infection. The awareness is characterized by two parameters of the awareness function andawareness period. An effective epidemic spreading rate is proposed which can be dynamicallyadjusted according to epidemic prevalence at awareness period, and a modified SIR(susceptible-infected-recovered) epidemic mathematical model is formulated in scale free networks.The impact of the awareness on epidemic spreading is studied by using a mean-field approach andMonte Carlo simulations. It is shown that individuals’ awareness cannot change the epidemicthreshold, but can mitigate the epidemic spreading speed and final infection size effectively, anddelay the arrival of epidemic infection peak. In addition, the higher the individuals’ awareness is,the better the effectiveness of the mitigation is.2. Considering that many real networks have mobility characteristics, an SEIRS(susceptible-infected-removed-susceptible) epidemic mathematical model in a dynamical networkof random mobile individuals is proposed. The epidemic evolution process and critical propertiesare analyzed from the perspective of differential dynamic system. The basic reproductive number ofepidemicR0is derived, and it is proved that the basic reproductive numberR0determines thestability of the system at equilibrium points. That is, ifR01, the epidemic always dies out and thedisease-free equilibrium is globally asymptotically stable; ifR01, the disease-free equilibrium isunstable, the epidemic is uniformly persistent, and the endemic equilibrium is globally asymptotically stable. By calculating the epidemic thresholds with respect to the individual’s actionradius, mobile velocity, and average density, it is found that the individual mobility has importanteffects on epidemic behaviors.3. Epidemic spreading in a social network is studied based on reaction diffusion process. Thesocial network is described by a heterogeneous metapopulation network, in which each noderepresents a city or an urban area that consists of any number individuals, and links connectingnodes correspond to the human traveling routes among cities. Individuals in nodes can move to theirneighboring nodes. A time-varying human mobility pattern is introduced to model the time variationof global human travels due to an epidemic outbreak. It is shown that the pattern does not alter theepidemic threshold, but can slightly lower the final average density of infected individuals as awhole. It is also found that there exists a critical node degree. For the nodes with degree smallerthan the critical value, the pattern can mitigate the epidemic spreading, but for the nodes withdegree larger than the critical value, it can aggravate the epidemic spreading.4. In view of the effects of social local properties, such as population density and individualhealth habits, on epidemic infectivity, a heterogeneous epidemic spreading rate in metapopulationnetworks is proposed. Furthermore, the positive-correlation infection regime (PIR)(i.e., thespreading rate is positively related to the node degree) and the negative-correlation infection regime(NIR)(i.e., the spreading rate is negatively related to the node degree) are respectively definedaccording to the relation between the spreading rate and the node degree. By using a mean-fieldapproach and Monte Carlo simulations, it is found that the two regimes both increase the thresholdby the same extent when only infected individuals move, and NIR increases the threshold and PIRdecreases it if both the infected and susceptible individuals move. It is also shown that theheterogeneity of the spreading rate has the significant impact on the temporal behavior of theprevalence above the epidemic threshold.