(A) study of epidemic disease spreading in complex networks

Abstract

Many epidemic diseases, such as the Black Death and Spanish flu, have threatened human through histories. But we do not know yet whether human will survive under the sudden and fast spread of epidemic diseases. It also does not know the characteristics of epidemic diseases that can lead to the extinction of humanity. Pandemic is a typical spreading phenomenon that can be observed in the human society and is dependent on the structure of the social network. In this research, we use the Susceptible-Infective-Recovered (SIR) model to describe spreading phenomena using two spreading factors

contagiousness (β) and recovery rate (γ). Some network models are trying to reflect the social network, but the real structure is difficult to uncover. We have developed a spreading phenomenon simulator that can input the epidemic parameters and network parameters and performed the experiment of disease propagation.

In PART I, we consider the coupling effect between epidemics and networks. The simulation result was analyzed to construct a new marker VRTP distribution. We also induced the VRTP formula for three of the network mathematical models. We suggest new marker VRTP (value of recovered on turning point) to describe the coupling between the SIR spreading and the Scale-free (SF) network and observe the aspects of the coupling effects with the various of spreading and network parameters. We also derive the analytic formulation of VRTP in the fully mixed model, the configuration model, and the moment closure model respectively in the mathematical function form for the insights on the relationship between experimental simulation and theoretical consideration. We discover the coupling effect between SIR spreading and SF network through devising novel marker VRTP which reflects the shifting effect and relates to entropy.

In PART II, we consider the threat of pandemics and present an important result from the epidemic simulation which shows the relation between the infectious diseases and the existence of human beings. In this simulation model, infectious diseases have two parameters, including the recovery time from infection and the spreading rate of infectious disease. From the result, we found two important things about the human safety against the threat of a pandemic. First, humans should be safe if the fatality rate is below 100%. Second, even though the fatality rate is 100%, humans would be safe when the average degree of human society network is below the threshold. Possibly, some diseases can infect all nodes and be candidates of human extinction when the average degree is over the threshold. In conclusion, humans are safe from the pandemics because the number of contacts is adjustable by humans.