Research On The Coupling Of Disease Spreading Model SIH And Scale-free Network

Infectious diseases have always been a major threat to the public health of human society.And Whether it was the plague that once raged in Europe,or the SARS that had a profound impact on the world,it has done great harm to people's property and life.The study of infectious diseases is an indispensable link of the natural sciences,and it is also a practical problem that human society urgently needs to solve.As a means of modeling real complex systems,complex networks have been used by researchers to study the dynamic mechanism of infectious diseases in the population.Human society,as a complex interconnected system in the real world,can be expressed as a network of interconnected individuals,and these networks usually have scale-free feature.Through the assignment of node states,the problem of disease spreading can be abstracted into a network dynamics problem in which the state of each node in a complex network affects and spreads.Existing infectious disease models,such as SI(Susceptible-Infected),SIR(SusceptibleInfected-Recovered)and SIS(Susceptible-Infected-Susceptible),are disease spreading models obtained by distinguishing the "susceptible","infection" and "normal" status of nodes,and specifying a certain spreading mechanism.Researchers have studied whether disease and human social networks can coexist for a long time by modeling disease spreading on scale-free networks.The theoretical research shows that diseases cannot coexist with human social networks(ie,diseases are difficult to couple with scale-free networks),but this theory conflicts with the real situation.By reviewing the research status of the coupling between scale-free networks and disease spreading,the existing research has two shortcomings:(I)From the perspective of network modeling,it will be found that the real social network is a dynamic evolution process,and the nodes in the network will be randomly attacked by disease and result in the change of network structure.However,the traditional static network evolution model cannot resist random attacks.Once a large number of nodes are deleted,the scale-free features of the static network will disappear.(II)From the perspective of the infectious disease model,the classic infectious disease model will destroy the scale-free network due to the lack of propagation threshold restrictions.Under a dynamically evolving environment,scale-free networks will speed up the spread of disease,which will hinder the formation of scale-free networks,resulting in the inability of coupling scale-free networks and infectious diseases to coexist.In order to address the above two problems,this thesis first proposes a dynamic evolutionary immune and highly random life-and-death scale-free network generation model(SNGMD).This model abandons the traditional rules and improves the design model of margin.During the evolution process,by continuously optimizing the margins of the network to maximize it,the structure of the control network is always maintained as a scale-free network.Theoretical and experimental results show that the SNGMD model can always guarantee the scale-free characteristics of the network under the condition of high random life and death.Secondly,in the actual process of disease spreading,there will be patients who carry the virus but do not show symptoms,who are called "invisible communicators" or "asymptomatic infected people.",and these patients are difficult to be found.Therefore,it is also an important route of disease spreading.According to this feature,this thesis proposes a disease spreading model SIH(Susceptible-Infected-Hidden)with invisible communicators.The model describes that only S(susceptible nodes),I(sick nodes),and H(hideen communicators)exist in the network,then theoretically analysis the correctness of SIH model.Experiments in this thesis show that when SNGMD is combined with SI and SIR models,neither disease nor scale-free networks can coexist.Under the SI model,disease will infect the entire network;and under the SIR model disease disappears;when SNGMD is combined with SIS,disease and scale-free The conditions under which the network can coexist are harsh.The conditions for coexistence depend on the size of the recovery rate.The recovery rate is too large or too small to not coexist,and only when the recovery rate is close to the infection rate.Therefore,none of SI,SIR,and SIS can coexist with scale-free networks.In order to analyze whether the SIH model can co-exist with the scale-free network,we will discuss the two situations without the immune strategy and the immune strategy.(1)Without the immune strategy,the experimental results show that the SIH model can be coupled with the scale-free network;(2)With the addition of health immune strategies,the SIH model was combined with N = 500,N = 2000,and N = 5000 networks to conduct experiments.The experimental results show that in three networks of different scales,the disease can be coupled with the scale-free network,and in the case of high and low spreading rates,the disease can coexist with the network,and shows that the level of infection and lethality is not the key to the coexistence of disease and the scale-free networks,the invisible spreading mode is the key.So far,this thesis theoretically and experimentally demonstrates that the key to the coexistence of both Internet and infectious diseases lies in invisible infectors.Because of the existence of invisible infectors,even if all the diseased nodes are identified and removed,the disease cannot be eliminated.When infectious viruses are widely distributed,the disease will be coupled with human social structure,which makes it difficult for people to completely eliminate the virus.In the early stages of the outbreak of infectious diseases,timely isolation was the only known and feasible method,and the price paid was relatively small.