Population Dynamics Characteristics Of The Network Model Of Infectious Diseases

With the development of the society, it is increasingly apparent to the network charac-teristics formed of the population structure because of regional diferences and populationfowing. The research of infectious disease model has certain practical signifcance based onthe characteristics of such network. The dynamics of network infectious diseases use networkto describe this system of infectious disease. we establish the mathematical model that canrefect its variation law, according to the happening of the disease, development and envi-ronmental change an so on. Then we research it carefully, seek to the optimal strategy ofprevention and control. Prevention of decision for people, we can provide the theory basisand quantity basis.In order to prevent and control of infectious diseases. In this paper, according to thestudy of systems both at home and abroad in recent years, we carefully studied the followingthree dynamic models, which are established to consider the disease spread on networksby means of the theory of epidemic dynamics, complex networks and diferential equationqualitative and stability method.Some networks in real world often evolve over time, for example, by network rewiringor network growth. According to the features of this kind of networks, we develop anSEIRS epidemic models on evolving networks using a general ordinary diferential equation(ODE) model, and further the basic reproduction number is obtained. Then we also get thatdiferent rewiring process can get diferent thresholds of system in evolving networks. Theanalysis of this temporal evolution is not only important for understanding what happensto the network itself, but also it can be of great relevance to the phenomena occurring onthe network.Second, according to the character of sexually transmitted diseases (STDs), we consideran SIRS model with multi-type on scale-free networks. The absence of a threshold in inf-nite scale-free network is proved using the critical value theory of spreading. For a hard cutof scale-free network, we also analysis the stability of the equilibrium by means of stability theory. Two immunization schemes are studied and compared. We fnd that targeted strat-egy is more efective in this model on SF networks. Theory gets that an appropriate condomusing has prominent efect to control STDs spread on scale-free networks.