Modeling And Analysis Of Network Infectious Diseases Integrating Individual Game Behaviors

Infectious diseases affect the life style of individuals and threaten their lives.Since no infective vaccines,in the early spread of infectious diseases,non-drug interventions such as isolation,wearing masks,reduce gatherings and others can effectively control the spread of infectious diseases.Due to cultural differences and cognitive limitations,not all individuals are willing to take these measures voluntarily.Vaccination can make the main body produce antibodies,thus effectively controlling the spread of infectious diseases.People will consider the difference between the cost of vaccination and the cost of infection,making it difficult to reach the level of group immunization.In order to analyze the influence of human behavior on infectious diseases,this essays establishes four kinds of mathematical models: the infectious disease model combined with vaccination and isolation on the uniform mixed network,the discrete model combined with non-drug intervention measures and infectious diseases on the complex network,the continuous model combined with non-drug intervention measures and infectious diseases on the complex network,and the defense model considering the infectious diseases of undiagnosed infected persons.These models include the game model of voluntary protective measures.Details are as follows :Considering the transmission of infectious diseases under the combined action of quarantine and vaccination,a model combining the transmission of infectious diseases and individual behavior is established on a homogeneous mixed network to study the effects of quarantine of susceptible individuals,quarantine of infected individuals,vaccination of susceptible individuals and quarantine of vaccination individuals on the control and prevention of infectious diseases.Through theoretical analysis,the disease-free equilibrium and its stability,the basic reproduction number and endemic equilibrium are obtained.Through numerical simulations,the theoretical results are verified and the influence of the two protection measures on the spread of infectious diseases is analyzed.The results show that when the basic reproduction number is less than 1,quarantine individuals and increasing vaccination rate can effectively reduce the number of infected people.When vaccination is not available,the number of voluntary quarantine individuals will increase.Combined with incompletely effective nonpharmacologic interventions during the spread of infectious diseases,a discrete model combining infectious diseases and behavioral games on complex networks is established.Through theoretical analysis,the transmission threshold of infectious diseases and the stability of the disease-free equilibrium are obtained.According to the optimal control theory,the optimal proportion of protective measures of infected individuals are obtained.Through numerical simulations,the accuracy of the optimal control strategy is verified.In the case of optimal control,the proportion of infected people will decrease rapidly and the cost will be the least.We also analyze the impact of voluntary protective measures for the susceptible and compulsory protective measures for the infected on the spread of infectious diseases.The results show that compulsory protection measures have a greater impact on infectious diseases.With the increase of control,the final epidemic size will be reduced and the average social cost will be reduced.According to the different situations of payoff in behavioral game,we divide the payoff matrix into fixed value and time-varying.Based on the quenched mean field theory,a model combining classical SIS epidemic model and behavior dynamics on complex networks is established.Through theoretical analysis,the disease-free equilibrium and its local and global stability are obtained.Through numerical simulation,the stability of the disease-free equilibrium is verified,and the influence of behavior dynamics on the spread of infectious diseases under different payoff matrices are analyzed.The results show that reducing the relative cost of protective measures can effectively reduce the number of infected individuals and increase the number of individuals taking protective measures.Increasing the effectiveness of protection measures will increase the number of free riders.For unconfirmed infected individuals such as latent and asymptomatic infected in the spread of infectious diseases,their behavior cannot be separated from the behavior of susceptible people.We model their behavior in combination with the spread of infectious diseases.The disease-free equilibrium and its stability were obtained by theoretical analysis.The basic reproduction number is obtained by the next generation matrix method.Through numerical analysis,the sensitivity of each parameter is analyzed.The results show that as the relative cost of protection measures increases,the peak of the infected individuals will increase and the peak of the individual taking protection measures will decrease.When the rate of change in behavior is greater than the rate of transmission of infectious diseases,the time series of the number of infected individuals and individual behavior dynamics will have multiple peaks.By analyzing the influence of individual game behavior on the spread of infectious diseases,this essays concludes that reducing the cost of protection measures can effectively control infectious diseases.The research in this essays establishes a theoretical framework for the behavioral game on the network and provides theoretical guidance for the prevention and control of infectious diseases.