Researches On The Spread Of Infectious Diseases With Immunization Based On Percolation Theory

The epidemic and outbreak of infectious diseases not only make human beings suffer from illness and separation,but also cause the depression social economy and the pollution of human living environment.In the prevention,control and elimination of infectious diseases,immune prevention plays an important role.Among them,vaccination is the most important means of immune prevention,which can enhance human immunity,improve resistance to infectious diseases,and thus reduce the probability of transmission of infectious diseases.In today's society,the convenience of transportation and the wide use of social networks make the contact relationship between people become closer and closer,which leads to the more and more complex contact network structure between people.Different contact network structures have different effects on the threshold and final scale of disease prevalence.In summary,it is undoubtedly an important topic to study the network topology and the spread of infectious diseases and formulate a reasonable and effective immunization strategy.Based on the above background and inspired by the percolation theory,we regard the disease transmission process in the network as a percolation process,and combine site percolation with bond percolation to construct a new percolation model of disease transmission with immunization in a complex network.By using the method of probability generation function,the accurate solution of the threshold and the average outbreak size before the epidemic related to the immune probability,as well as the analytical solution of the size of the giant component after the epidemic,is obtained.In addition,given the specific degree distribution network structure,the effects of different network structures and the probability of nodes being immunized on disease transmission are studied.The specific contents of this paper are as follows:In the second chapter,considering that the real-life population will generally get immunity through vaccination,the general SIR percolation model is extended to the site-bond percolation model with immunization.By using the method of probability generation function,the accurate expression of the epidemic threshold and the average outbreak size related to immune probability is obtained.The results show that when the threshold is less than 1,the disease is not prevalent,and when the threshold is greater than 1,the disease erupts and the giant component appears.The effects of different network structures and the probability of nodes being immune on disease transmission are discussed by numerical simulations.In the third chapter,considering the heterogeneity of population contact structure,the percolation model with immunization in the previous chapter is applied to the transmission of immune diseases in the bipartite network of this chapter.By using the method of probability generation function,the accurate solution of the threshold of the epidemic that depends on the immune probability,the average outbreak size before the epidemic,and the analytical solution of the size of the giant component after the epidemic are obtained for the two types of nodes.They are applied to Poisson-Poisson network,Poisson-power-law network,and power-law-power-law network respectively.The theoretical results are verified by numerical simulations,and the effects of the probability of the two types of nodes being immune and the homogeneity of different network structures on disease transmission are analyzed.