Study On Spread Of Infectious Diseases In Complex Networks

Infectious diseases have always posed a threat to human beings and have attracted widespread attention from scientists.Therefore,how to prevent infectious diseases has been the focus of researchers worldwide.Preemptive vaccination is the most effective way to prevent and control infectious diseases.However,not all people involved in public health administration choose vaccination.Whether people are vaccinated will be affected by their economic conditions,risks,living environment,and other factors.In the case of infectious diseases with serious consequences,people usually adopt measures of vaccination.In the case of other infectious diseases,people may adopt self-protection methods such as paying attention to personal hygiene,and in the case of diseases with minor consequences,such as seasonal colds,most people adopt laissez-faire measures and may thus be protected from these diseases without incurring any costs.The choice of a personal strategy is usually a trade-off between the cost of taking measures and the outcome of being infected.On this basis,previous studies have input the strategies taken by individuals facing infectious diseases into a game model for analysis.Game theory has been applied to predict the strategy of an individual from the costs and payoffs of actions and outcomes.Many papers have been put forward to review and analyze the processes by which epidemics spread in complex networks.The epidemic transmission process is studied using an evolutionary game model of complex networks.It is assumed that individuals choose their strategies by comparing their payoff with their neighbors’ payoff in the process of disease transmission.The majority of models of disease spread are based on disease statuses,such as the susceptible–infected(SI)model,the susceptible–infected–removed(SIR)model,and the susceptible–infected–susceptible(SIS)model.With the development of research,a number of quantitative complex networks have been introduced to reveal the relationships between individuals.The structure of an interacting population can be represented by a complex network.Connected structures have been devised to demonstrate the framework.The decisions of individuals are directly or indirectly influenced by their neighbors.The behavior of an individual is affected by the course of an epidemic in a complex network.1.Facing infectious diseases,the actions taken by individuals play an important role in the prevention and control of these diseases.The prevention and control of infectious diseases have attracted much attention from human beings.Human behavior plays an important role in the propagation of epidemics.Chapter 3 discusses the process of epidemic propagation in the cases of different imitation principles and network topology.Previous studies have shown that there is a counter-intuitive phenomenon in the spread of disease.A higher success rate of selfprotection may not reduce the epidemic size.As the success rate of the self-protection strategy rises,the fraction of individuals in the removed state increases at first and then decreases.It has been shown that the counter-intuitive phenomenon in the process of epidemic propagation is affected not only by human reactions and imitation principles but also by the network topology.In networks with community structure,no matter which imitation principle individuals adopt,the counter-intuitive phenomenon exists.This suggests that in a social community with close ties the risk of infection is not reduced as the success rate of the selfprotection strategy increases.At this point,an individual should choose the vaccination strategy or reduce contact with others.However,if individuals are in a network without community structure,the counter-intuitive phenomenon is influenced by imitation principles for updating strategies,and hence they can choose different imitation principles to reduce the risk of infection.In Chapter 3,four different imitation principles for updating strategies are defined and analyzed on well-mixed(WM)networks,square-lattice(SL)networks,Erd?s–Rényi(ER)networks,Barabási–Albert(BA)networks,Lancichinetti– Fortunato–Radicchi(LFR)networks,and Facebook networks.Not only are the effects of different imitation principles on disease transmission compared,but also the effects of community structures are studied.It is found that different strategies affect the scope and intensity of counter-intuitive phenomena.Firstly,we study more imitation principles and introduce different imitation principles into an epidemic process in complex networks.The three strategies of vaccination,self-protection,and laissezfaire are taken into account in the SIR model.Moreover,we investigate the effects of the model parameters,network topologies,and imitation principles on the epidemic size of the disease.We employ more types of networks.It is shown that the spread sizes of infectious diseases in networks with community structures are more sensitive to imitation principles than that in networks without community structures.Furthermore,the influences of the same imitation principle on different networks are compared.The effects of different imitation principles are also studied.Specifically,the counter-intuitive phenomenon always exists in a network with community structures,but not necessarily in a network without community structures,where the existence of the counter-intuitive phenomenon is affected by imitation principles.We study more imitation principles and more types of networks,reaching more conclusions which are valuable.2.According to the network topology,the single-layer network and the multi-layer network are studied.In the multi-layer network,the network model comprises different layers;each layer has the same node,but the connection edge may be different.It is significant to study the spread using the multi-layer network.On the one hand,different kinds of relationships exist among people,and the connection of relationships may be different in the real social network.In addition,the disease spread needs certain physical contact,but awareness spread does not need physical contact.The transmission path of awareness information may not be the same with and the disease infection.On the other hand,because the epidemic disease may have different transmission paths,there may be different connections between the same nodes,and different topological structures lead to different diffusion results of the epidemic disease.Therefore,in the process of studying the disease spread model,it is necessary to distinguish the awareness transmission network from the epidemic spread network.The awareness transmission network is different from the physical contact network.It is significant to study the spread range of epidemic diseases by distinguishing the topological structure of awareness transmission network from that of the physical contact network.The multi-layer network coupling propagation models is proposed,which integrates the information diffusion and the disease spread.The relationship between different layers is the key element of the system model.On the network structure,the information transmission is simulated by the different strategy change mechanisms.SIR model is used to describe the epidemic-transmission process.Using the multi-layer network to describe the real world,Chapter 4 studies the interaction between epidemic diffusion and awareness propagation in the framework of multiple networks,and it also establishes strategy adjustment rules to study the awareness propagation dynamics in different networks.Considering the two-layer network,the first layer is described as the physical contact network,which the epidemic diseases spread through.The other layer is the awareness propagation network.The spread of epidemic diseases can trigger the spread of awareness information in another layer of network.The analysis based on the Markov chain method and a number of calculations show that once the network structure changes,the infection density will also change,following which the way of individual strategy change will also affect the results of the disease spread.It is an important task to study the complex interaction between human society and infectious diseases.3.Based on the proposed N-person threshold evolution game model,three different strategy imitation principle are innovatively proposed.The propagation networks with different topological structures are used for simulation.The proportion of individuals who choose cooperative strategies is calculated.The coverage of individuals who choose vaccination is analyzed under the balanced state.The vaccination cost,infection cost and population are explored.In Chapter 5,the spread model of infectious diseases is described based on the doublelayer network.In the awareness information transmission,not only four kinds of complex networks without community structure,i.e.regular network,random regular network,small world network and scale-free network are simulated,but also LFR network and Facebook network are simulated.Individuals are supposed to know the immune threshold.There is a structural population in awareness information transmission.Each individual can fully interact with each other,revealing the balance relationship between population size,basic regeneration quantity and vaccine coverage level,as well as the impact of initial setting of network community structure parameters on the final evolutionary stability.In the proposed N-person threshold game model,the results of vaccine coverage are simulated.The effects of infection cost,population structure and basic regeneration number on immune coverage are analyzed.At the level of network topology,the network without community structure and with community structure are simulated respectively,revealing the balance between each element and vaccine coverage level.In the case of free vaccination costs,it is not necessarily possible to achieve full coverage of vaccines in the population.However,as the relative cost of vaccination and infection increases,the balanced coverage of vaccines may decline rapidly.In addition,in the network with community structure,the larger the mixing parameter is,the slower the vaccine coverage rate decreases with the increase of the relative cost.The clarity of community structure has a great impact on the vaccine coverage rate of the whole population.The initial setting of community structure parameters of the network will affect the final evolutionary stability.The research of game model based on voluntary immunity shows that there is conflict between individual self-interest and group interest.According to different disease severity,the use of risk-free vaccine or close to risk-free vaccine can achieve comprehensive prevention of disease,but even if the use of risk-free vaccine,it is not necessarily to achieve full coverage of immune vaccine.Even if the use of vaccines is a costfree strategic model,there will be results that vaccines cannot be fully covered,resulting in the failure to eradicate a disease.When the cost of vaccination is greater than that of infection in the community structure,there will also be individuals who choose vaccination strategy.4.COVID-19 transmission are analyzed.In Chapter 6,the epidemic process is simulated.The parameters,control measures and network structures are analyzed.The disease severity and isolation prevention are studied.The simulation results are compared with the real data.In summary,the actual activities of human beings in real life are often more complex than is assumed.Their behavioral responses may be influenced not only by the structures of social networks and imitation principles,but also by factors such as the environment and policies.We pay attention to proposing models that integrate multiple factors,such as the influence between the epidemic spreading and awareness diffusion regarding epidemics in multiplex networks,so as to provide more reliable suggestions and opinions.