Epidemic Spreading Dynamics And Vaccination Dynamics On Networks

Throughout history,infectious diseases,such as the smallpox and the bubonic plague,brought huge disaster to human beings repeatedly.For example,the black death pandemic in Europe from 1346 to 1350,reduced the population of Europe by nearly a quarter and made the average life of people(which is 30 years old before the epidemic decreasing)to just 20 years old.Though the development of economy,science,and technology provide the human the economic guarantee and the technical support to conquest the diseases,it also makes many regional diseases spreading more easily.For example,the SARS in 2003,the H1N1 in2009,the H7N9 in 2013,and the Ebola in 2014,which spread from a local area to the most regions and countries and caused heavy losses in people and economic.Therefore,it is a vital important topic for scientists and countries to study the mechanism and characteristics of epidemic spreading on complex networks.One of the most important problems is the prediction of epidemic prevalence and epidemic threshold.In this doctoral dissertation,the first research line focuses on the theoretical analysis.In 2001,Pastor-Satorras and Vespignani studied the computer viruses spreading in the Internet network,and proposed a heterogeneous mean-field method which can solve the prediction of epidemic prevalence and epidemic threshold in the annealed networks.From here on,the static network had gradually became a hot issue in the theoretical analysis of epidemic spreading.In the past decade,by means of the ordinary differential equations which came from the master equation idea,the researchers proposed many significative method to understand the mechanism of epidemic spreading on static networks,such as quenched mean-field method,effective degree theory,pair-approximation method,three-site approximation theory,heterogeneous pair-approximation,pair quenched mean-field theory,etc.Vaccination is an important and effective measure for the corresponding infections disease prevention,control and even eradication in local or global population.Achieving widespread vaccine coverage by voluntary vaccination is also a hot issue of the epidemic spreading on complex networks.For example,in the last few years,some researchers combine the epidemic spreading process and the evolution game theory to explore how the individual behavior will affect the dynamics of epidemic spreading.In this doctoral dissertation,our second research line follows the physical modeling area which we focus on the imitate vaccination dynamics model.In the following,we will briefly introduce the framework and innovation of our doctoral dissertation.Chapter 1: In this chapter,we first introduce the historical background of complex networks and some recent important progress.Meanwhile,we introduce the construction method of the various empirical networks and artificial networks.In the last,we introduce the basic knowledge of the classical epidemiological models in detail.Chapter 2: According to the introduction of relevant theoretical analysis method of previous work,we propose our theoretical analytical method–effective degree markov-chain approach and detailed balance method–in a skillful way.Based on the disadvantages of the microscopic markov-chain approach(MMCA)which is a popular method in the discrete time epidemic processes,we propose an effective degree Markov-chain approach(EDMA)which keeps track of the number of susceptible and infected neighbors instead of tracking the degree to treat the classical SIS and SIR epidemic processes on complex networks.By comparing with the method of MMCA,we note that the EDMA has three advantages:(i)the EDMA is more accurate in accordance with the simulation results of the time series of infected individuals;(ii)the EDMA is of more general,which can be extended easily to the SIR epidemic process;and(iii)it is not necessary to know the adjacency matrix of the network of contagion for the EDMA.Moreover,we have studied the impact of dynamic correlations,naturally arising in spreading processes on static networks,on the SIS epidemics.In particular,we take into account the dynamic correlation from infected pairs,but ignore those from other node pairs and higher-order network structure,to derive the master equations governing the state evolution of the system.By combining the idea of the heterogeneous mean-field theory with the effective degree approach,we are able to obtain the epidemic prevalence and epidemic threshold of the SIS process in uncorrelated static networks with arbitrary degree distributions.Chapter 3: To understand the physical mechanism of imitation vaccination dynamics deeply and make some steppingstones on the future researches such as intervention policy,we study the imitation vaccination dynamics model in the diversity of the infection rate,interaction frequency,and vaccination strategies.The results are as follows:· To be more specific,the heterogeneity in infection rate can always give rise to a decrease of the final epidemic size provided the individuals from different groups interact with equal likelihood.Nonetheless,as the individuals become more inclined to interact mainly with others from the same group,the heterogeneity in infection rate can hinder the epidemic spreading only in the situation that the fraction of individuals vaccinated is low enough.Very surprising,this just facilitates the epidemic spreading in a regime with the presence of a large fraction of vaccinated individuals.· When individuals are allowed to change their vaccination decisions according to their experience and observations,we find that as the heterogeneity in infection rate for the two types of individuals becomes more noticeable,the final epidemic level in randomly arranged population changes much more evidently than that in the case of a regularly arranged population.· In lattice population,we found an unexpected phenomenon that a lower level of vaccination in the population leads to a lower level of spreading of disease in the continuous-strategy case at low c.And the qualitative properties of the results obtained on ER network and BA network are the same as the results on square lattice.Our results show that the diversity of the infection rate,interaction frequency,and vaccination strategies play some important roles in epidemic spreading dynamics on complex networks.