Evolutionary Game Study Of Public Vaccination And Government Prevention And Control

The emergence of infectious diseases in recent years has caused a huge disaster to human beings,not only seriously threatening the safety of people’s lives and properties,but also bringing enormous pressure on government departments for prevention and control.With the improvement of science and technology,the successful development of vaccines for infectious diseases has played an extremely important role in the prevention,control and extinction of infectious diseases.However,within a certain period of time,the choice of vaccination strategy and epidemic prevention and control strategy became a social dilemma problem.At the early stage of vaccine emergence,the public tended to have a wait-and-see attitude and a generally low willingness to receive vaccines due to its high price cost and unclear effectiveness.As for government departments,the spread of the epidemic reduced government economic revenue.If economic production is to be restored as soon as possible,it is necessary to increase the financial expenditures needed to undertake vaccine research and development,vaccination,and implementation of prevention and control policies.Therefore,it is important to study the behavior of the social public’s vaccination strategy and the government’s choice of prevention and control strategy to actively promote vaccination and the extinction of the epidemic.On the basis of evolutionary game theory,this paper integrates three aspects of the public’s loss of income from vaccination cost,and personal physical and mental loss,and four aspects of public trust in government departments,financial subsidies for vaccines,cost of prevention and control,and loss of government income.This paper takes the government and the public as finite rational game subjects,and establishes an asymmetric evolutionary game model based on the traditional symmetric evolutionary game model.And it combined with the specificity and complexity of the strategic gains of the government and the public in reality.Then,we explore the replication dynamics of the game subject’s strategy and get five equilibrium points and their existence conditions.The equilibrium points are judged to be unstable,saddle point,center and stable point through numerical calculations such as Jacobi matrix.In particular,the article analyzes the conditions for the existence of the center of the replication dynamic system and the evolutionary stabilization strategy {voluntary vaccination,strict prevention and control}.It is found that,when this evolutionary stable strategy exists,the proportion of voluntary vaccination of the public is lower and the prevention and control intensity of government departments grows faster.The cost of the government under different prevention and control intensity will directly affect the credibility of the government and the speed of its strategy change.In the presence of the center,the behavior of the game strategy evolves with a certain periodicity,the closer to the center,the smaller the change and the shorter the period,the more distant from the center,the larger the change and the shorter the period.The closer the distance from the center,the smaller the change and the shorter the cycle,and the farther the distance from the center,the larger the change and the longer the cycle.Based on the asymmetric evolutionary game model,the model further takes into account that the public can not only know the information of social vaccination in time,but also can quickly transmit it to the government department.The asymmetric evolutionary game model with parameter payments is constructed by taking the public’s strategy state vaccination ratio as the payment matrix parameter of the game model.Further,the article explores the replication dynamics of the strategies of the two sides of the game.And we obtain five equilibrium points and their existence conditions through computational derivation.The evolutionary stable strategies and conditions of existence are obtained.It is found that,when very few people are vaccinated,everyone is reluctant to be vaccinated.When more people are vaccinated,the public is more willing to be vaccinated.The greater the prevention and control efforts of government departments,the less importance the public attaches to vaccination,and the smaller the prevention and control efforts,the faster the public is vaccinated.Further,the authors use MATLAB and Maple to verify the above theoretical models and conclusions by simulations.The evolutionary trend of each evolutionary stabilization point is visualized.Factors affecting the evolutionary rate and steady state are analyzed.The following recommendations are made: strengthen the government’s macro-control capacity and promote the modernization of social governance capacity;enhance the competitiveness of the vaccine market to increase market vitality and enhance the public’s willingness to vaccinate;increase the transparency of public information and accelerate the collaboration between the two parties to fight the epidemic.