Analysis Of Epidemic Model Based On Multiple Routes Transmission On Complex Networks

The traditional model of infectious disease dynamics suggest that the contacts between individuals are uniformly mixed,it constitutes a regular contact network.Although we can understand the dynamical behavior and the evolutionary trend of many diseases based on this hypothesis,it only suits for social groups that the space is relatively small and the frequent contact with staff.As for the contact-spreading network consists of a large-scale social groups,apparently,it is not a entirely regular network.A large number of empirical studies indicate that the contact between individuals generally constitute a complex network(small-world networks or scale-free networks).Therefore,the infectious diseases dynamic model of complex networks is more practical than that of conventional.The infectious diseases dynamics of complex networks are widely attentioned by scholars in recent years,but the majority of their work is studying the perspective of disease-spreading in a single way.However,in the real social network,it is can’t fully reflect the transmission mechanism of some diseases that only considering the disease-spreading in a single way.Therefore,in this paper we mainly investigate the multiple routes of disease transmission models on complex networks.In chapter 1,we provides an overview of the model and its relevant knowledge of dynamics,then describes the status of research on infectious disease dynamics of complex networks.Finally,the relevant theoretical knowledge of the paper need is given.In chapter 2,based on the transmission mechanisms of random and heterogeneous networks,we establish a new SIS epidemic model.Using the method of next generation matrix,the basic reproduction number of the model is derived.The global asymptotic stability of the disease-free equilibrium is obtained by using the comparison principle.In addition,we give the uniqueness of endemic equilibrium.In chapter 3,we use approximation method to establish a SIR Epidemic Models based on the edge-spread mechanism and spreading-contacts-random network,After add weight,we improve the traditional triad approximation formulas and calculate the basic reproduction number.Finally,the simulation of the model is conducted.