A Dynamic Epidemic Model for Rumor Spread in Multiplex Network with Numerical Analysis

Abstract

This paper focuses on studying and understanding of stochastic dynamics in population composition when the population is subject to rumor spreading. We undertake the study by first developing an individual Susceptible-Exposed-Infective-Removed (iSEIR) model, an extension of the SEIR model, for summarizing rumor-spreading behaviors of interacting groups in the population. With this iSEIR model, the interacting groups may be regarded as nodes in a multiplex network. Then various properties of the dynamic behaviors of the interacting groups in rumor spreading can be drawn from samples of the multiplex network. The samples are simulated based on the iSEIR model with different settings in terms of population scale, population distribution and transfer rate. Results from the simulation study show that effective control of rumor spreading in the multiplex network entails an efficient management on information flow, which may be achieved by setting appropriate immunization and spreading thresholds in individual behavior dynamics. Under the proposed iSEIR model we also have derived a steady-state result, named the "supersaturation phenomenon", when the rumor spreading process becomes equilibriumm, which may help us to make the optimal or better control of information flow in the practice.