Coupling effects on turning points of infectious diseases epidemics in scale-free networks

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.

We 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.

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 degree-based 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.