Abstract
BackgroundPandemic is a typical spreading phenomenon that can be observed in the human society and is dependent on the structure of the social network. The Susceptible-Infective-Recovered (SIR) model describes 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.MethodsWe have developed a spreading phenomenon simulator that can input the epidemic parameters and network parameters and performed the experiment of disease propagation. 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.ResultsWe 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 degree-based model respectively in the mathematical function form for the insights on the relationship between experimental simulation and theoretical consideration.ConclusionsWe discover the coupling effect between SIR spreading and SF network through devising novel marker VRTP which reflects the shifting effect and relates to entropy.
Highlights
Pandemic is a typical spreading phenomenon that can be observed in the human society and is dependent on the structure of the social network
As we see the relationship in the SIR model, the number of infected changes depending on the recovery parameter, which means that both curves are not independent
Where rTP is Value of recovered on turning point (VRTP) and R0 is reproduction number, s0 is the initial value of the susceptible population
Summary
Pandemic is a typical spreading phenomenon that can be observed in the human society and is dependent on the structure of the social network. The Susceptible-Infective-Recovered (SIR) model describes 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. The pattern of spreading differs with the structure of the social network. The model expresses spreading in the form of differential equation among population compartments; susceptibles, infected, and removed. There are many types of research of spreading phenomena reflecting individual interactions through random network models. Keeling et al [6] review of this research with the basis of epidemiological theory and network theory and suggest how the two fields of network theory and epidemiological modeling can deliver an improved understanding of
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