Stability Of SIS Model Based On Awareness And Individual Activity Potential In Complex Networks

Infectious disease dynamics model is good for the research on the rules of the spread of infec-tious diseases,for the prevention of disease and control provides an important theoretical basis.In this paper,considering disease awareness and active effect on the spread of the disease of the dis-ease,the SIS model is established,and analyzes the stability of the disease-free equilibrium and the threshold.First chapter,the paper introduces the domestic and foreign research dynamic,on the con-sciousness for the spread of disease in the complex network dynamic model of the influence of the establishment of thought and research methods,and introduce the main work of this article is simple.Second chapter,this paper studies three kinds of consciousness(local,global awareness,con-tact)effect on the spread of the disease,the SIS model on complex networks is established,and the model are obtained the stability of the disease-free equilibrium and the transmission threshold.where ?k = Ik/Nkis the density of infected nodes with degree k,?(t)=1/(k)?k=1nkp(k)?k(l)a sus-ceptible node from all sides of the probability of one connected to the infected node,a,b,?k respectively represent the local consciousness and the strength of the global consciousness,contact consciousness.Using the stability theory to solve the model,the stability of the disease-free equilibrium and propa-gation threshold.The results show that local and contact can improve the transmission rate threshold,full consciousness on the stability of the disease-free equilibrium and the propagation threshold.Fi-nally by using numerical simulation to verify the theoretical results.Third chapter,in the SIS model of a complex network,the following model is established by considering that the active state of the infected person affects the spread of the disease.where activity degree ? represents the probability that nodes in the network will be converted into active nodes within a unit of time.Using the stability theory to solve the model,the stability and propagation threshold of the disease-free equilibrium are obtained.The results show that the indi-vidual activity can be Changing the threshold of infectious disease,the lower the activeness is,the higher the threshold is.The numerical results are used to verify the theoretical results.Summarizes the results of this study and puts forward some opinions on the follow-up work.