The SIS Epidemic Model Based On Complex Networks With Communities Structure

It has very important realistic significance to study the epidemic model based on com-plex network with two communities.In this paper,we establish a susceptible-infected-susceptible(SIS)model which has no individual adaptive behavior on a network with two communities structure and established a susceptible-infected-susceptible(SIS)model on an adaptive network with two communities structure,and the influence of parameters in the epidemic model on the basic reproductive number and the spread of disease are discussed.In Chapter 1,we mainly summarize the basic theoretical knowledge about the epidemic model on the complex network,and introduces the domestic and international research trends of the influence of information on disease spreading on complex network with two communities structure,basic ideas and research methods of the paper.In Chapter 2,we build dynamics model of disease on complex network with two com-munities structure,the model is established as follows:Firstly,the basic reproduction number R0 of disease can be calculated by means of the next generation matrix defined by van den Driessche and J.Watmough,and the conclusion obtained is that disease-free equilibrium is stable if R0<1;otherwise,it is unstable.Finally,the result obtained by numerical simulation is consistent with the result of theoretical analysis,and the influence of community structure parameter Q and final disease scale on the basic reproductive number is discussed by numerical simulations.In Chapter 3,we build the node dynamics model on adaptive network with two commu-nities structure,and obtained the basic reproductive number by the next generation matrix.The model is established as follows:Firstly,the basic reproduction number R0 of disease can be calculated by means of the next generation matrix defined by van den Driessche and J.Watmough,and the conclusion obtained is that disease-free equilibrium is stable if R0<1;otherwise,it is unstable.Finally,the result obtained by numerical simulation is consistent with the result of theoretical analysis,and the influence of broken edge and reconnection on the spreading of the epidemic,and the conclusion obtained is that the probability of broken edge and reconnection will suppress the spread of disease if R0>1;the probability of broken edge and reconnection will speed up the extinction of disease if R0<1.