Infectious Diseases Spreading on an Adaptive Metapopulation Network

When an emerging acute infectious disease occurs, travel restrictions, one-way or two-way, are often taken to prevent its global spread. In order to investigate the impact of two-way travel restrictions in the global spread of infectious diseases, this paper defines a risk indicator according to the relative infection density. Based on this risk indicator and an intervention time on two-way travel restrictions, we define an adaptive metapopulation network. Then a susceptible-infectious-removed (SIR) metapopulation model on this network is proposed. The mathematical analysis shows that the basic reproduction number is independent of human mobility. Furthermore, this essay compares the effects of one-way travel restrictions and two-way travel restrictions on the global spread of infectious diseases. It is shown that the adaptive metapopulation network under two-way travel restrictions can effectively suppress the global spread of infectious diseases. We also obtain a threshold of risk indicator to prevent the global spread of infectious diseases by simulations. The earlier the intervention time on two-way travel restriction is, the better to curb the global spread of the disease. Even if two-way travel restrictions are not implemented, controlling the mobility of infectious persons would help prevent the global spread of the disease. This work will throw lights on the prevention and control of the globally spreading of an emerging infectious disease.