Epidemic spreading on dual-structure networks with mobile agents

The rapid development of modern society continually transforms the social structure which leads to an increasingly distinct dual structure of higher population density in urban areas and lower density in rural areas. Such structure may induce distinctive spreading behavior of epidemics which does not happen in a single type structure. In this paper, we study the epidemic spreading of mobile agents on dual structure networks based on SIRS model. First, beyond the well known epidemic threshold for generic epidemic model that when the infection rate is below the threshold a pertinent infectious disease will die out, we find the other epidemic threshold which appears when the infection rate of a disease is relatively high. This feature of two thresholds for the SIRS model may lead to the elimination of infectious disease when social network has either high population density or low population density. Interestingly, however, we find that when a high density area is connected to a low density may cause persistent spreading of the infectious disease, even though the same disease will die out when it spreads in each single area. This phenomenon indicates the critical role of the connection between the two areas which could radically change the behavior of spreading dynamics. Our findings, therefore, provide new understanding of epidemiology pertinent to the characteristic modern social structure and have potential to develop controlling strategies accordingly.