Epidemic Spreading In Complex Networks Based On Human Behaviors

In the real world, epidemic spreading usually causes different human behavioral responses, such as reducing out, seeking medical care, vaccinations, and releasing information of virus existing. Also, the changing of human behavior can influence epidemic spreading. The interplay between epidemic spreading and human behavior in complex network can cause richer dynamical behavior. In this dissertation, in order to reflect the process of epidemic spreading, the human behavior is taken into account epidemic spreading by using the mean-field approach, nonlinear differential dynamics theory, continuous-time Markov processes, and the impact of human self-protection behavior and vigilance behavior on epidemic spreading are studied. The main contents and contributions of the dissertation are as follows:1. For heterogeneity of scale-free networks, the heterogeneous vigilance awareness behavior is characterized by infected node neighbors and awareness intensity, and a susceptible-infected-removed (SIR) epidemic model with heterogeneous awareness is proposed on scale-free networks based on the mean-field theory, to study the effect of heterogeneous vigilance awareness on epidemic spreading. It is shown that the existence of heterogeneous vigilance awareness can significantly enhance the epidemic threshold, reduce the risk of virus outbreaks, slow down the epidemic spreading speed and delay the arrival of epidemic spreading peak. Moreover, the total number of infections reduces with awareness intensity increasing.2. Considering the case that the alert individual may relax their alert and forget the alert information because the alert individual can’t become infected after a period of time in actual human networks, a modified susceptible-alert-infected-susceptible (SAIS) model with forgetting responses of alert information is presented to study the impact of forgetting alertness response on epidemic dynamics and analyze the local stability and forward bifurcation and backward bifurcation behavior of the system. The epidemic threshold and existing condition of equilibrium are derived. It is found that forgetting alert information can slow down epidemic spreading when the alerting of the alert individual is less than the alerting of the susceptible individual, otherwise, forgetting alert information will promote epidemic spreading. It means that the alertness responses are important to control epidemic spreading and should been paid more attention. In addition, as the emphasis of alert information becomes stronger, the inhibition on epidemics is more effective.3. Considering limited treatment capacity for infected individuals of country or city, a susceptible-infected-susceptible (SIS) epidemic model with limited treatment capacity on adaptive networks is presented. The impact of the treatment on epidemic spreading is studied by using nonlinear differential dynamic system. The existing condition of equilibrium and occurring condition of backward bifurcation or forward bifurcation are derived. The local stability of the equilibrium in this network model is investigated by analyzing its corresponding characteristic equation of Jacobian Matrix of the nonlinear system. It is found:(i) if a backward bifurcation occurs at the disease-free equilibrium of the system, then bistability exists regardless of the size of the capacity, (ii) if a forward bifurcation occurs at the disease-free equilibrium of the system, then bistable endemic equilibria exists when the capacity is low. It is also shown that the range of bistability becomes smaller as the capacity increases when the capacity is smaller, otherwise unchanged for larger treatment capacity. Epidemic spreading considering treatment can reduce the risk of virus outbreaks and range of bistability.4. Epidemic spreading usually accompanies with the dissemination of information, and the diffusion mechanism of information is different from propagation mechanism of diseases. Based on the continuous time Markov chain process, a new epidemic model accounting for the spreading of information on multiple networks is proposed to study the interplay between information spreading and epidemic spreading. The process of epidemic spreading is described in social contact networks, and the cycle process of information spreading is simulated in social networks. Epidemic threshold associated with information spreading is derived in multiple networks. It is shown that the epidemic threshold not only depends on dynamics of information spreading, but also network structure of social networks. The spreading of information in networks can slow down the spreading of epidemic and reduces the scale of epidemic outbreak...