Epidemic spreading on dualistic social networks

The rapid development of modern society continually transforms the social structure which leads to an increasing distinct dualistic social structure pattern that more people gather to large cities, resulting high population density area, and less people remain in the rural area, resulting low population density area. We study the epidemic spreading on such dualistic structure where the infectious disease could be described by SIRS model. We find that distinct from other disease model, the SIRS model has two epidemic threshold. A disease could not persist the spreading when the population density is too high or too low, which is verified both on theoretical analysis and numerical simulations. Moreover, we find that for two areas, one has high population density and the other has low population density such that a disease could not survive in each of them, when they are connected the disease could however spread over the whole system. This phenomenon indicates that the connection of the two areas could radically change the capability of the whole system to resist an infectious disease. Our finding may provide new understanding of epidemic spreading on dualistic structure of modern society and the corresponding immunization strategies.