Multiple Epidemic Spreading On Complex Networks

Complex networks depict a wide range of systems in nature and society. Fre-quently cited examples include the social network, biological network, Internet, neural network,transportation networks and so on. In the past decade many significant results have been achieved about epidemic spreading on complex networks. The study was first focused on the static networks where each node represents an immobile agen-t and the contagion occurs only between the neighboring nodes through links.It was revealed that for scale-free networks,there is no epidemic threshold in the thermody-namic limit.Then the study was moved to the reaction-diffusion model where agents can move to their neighboring nodes by a possibility.In this model,the links are used only for diffusion.Later on,the random diffusion of epidemics was replaced by the objective traveling of human being.Recently,the study is moving to the case of two-layered networks.In this case,epidemic spreading may be transmitted from one lay-er(e.g. animals)to the other (e.g. human beings) such as the SARS epidemic of 2003, 2009H1N1 influenza pandemic,and 2013 H7N9 avian influenza etc.A two-layered net-work may also consist of one layer for physical network and the other for online in-formation network.In this case,the obtained information will influence the epidemic spreading.All these studies on two-layered networks are focused only on the epidemic spreading of one pathogen. However, the actual situation about epidemic spreading is often much more complicated including the interaction of two or more pathogens, such as the interaction between tuberculosis and HIV.Our thesis mainly consider the case of two interacting pathogen on a two -layer network. We have made two work in this thesis.In the first work we present a model to unify all the kinds of interaction into a unified framework.The model in-corporates the mutual influences between two pathogens into a state-dependent infec-tious rate.comparing with the constant infectious rate in the previous studies.We con-struct a new two-layer independent random Erdos-Renyi networks and two pathogen-s spread on the two networks,respectively.We here consider the pathogen-I with the SIS model and the pathogen-II with the SIR model.We find that the stabilized epi-demics depends on the range of parameters in the infectious rate and may result in an interesting phenomenon,i.e.initial cooperation(suppression)induced final suppres-sion(acceleration),We also discuss the effect of time delay.In the second work,we present a two-layer network model without fixed links between the two layers,but with dynamic propagators to connect the two layers.By this model we show that (i)the propagators take the key role to transmit pathogens from one layer to the other and significantly influence the stabilized epidemics;(ii)the epidemic thresholds will be changed by the propagators,resulting in an interesting phe-nomenon that the epidemic can outbreak even when the infective rate is smaller than its threshold of isolated spreading.This model thus paves a way toward a description of the dynamics of interacting pathogens by propagators.