Research On Transmission Dynamics And Prevention And Control Strategies Of Sudden Infectious Diseases Based On Vaccination

Outbreaks of infectious diseases have seriously affected the food,clothing,shelter and transportation of most people around the world,and have even caused countless deaths.Infectious diseases have reshaped the focus of global scientific attention and efforts,and researchers around the world have done much to analyze the dynamics of infectious diseases in response to current and future outbreaks.Among them,the capture of the outbreak dynamics of complex diseases can provide a guidance role for public health.Firstly,a nonlinear differential equation dynamic model is established to model and analyze the real-time dynamics of infectious diseases.The nonnegative,bounded and disease-free equilibria of the model solutions under certain meaningful sets are given.The basic reproduction number is derived by the next generation matrix method,and on this basis,the global stability and consistent persistence of disease-free equilibrium are studied strictly.We observed that the disease-free equilibrium point is globally asymptotically stable when the basic reproduction number is less than 1(the disease disappears from the population).However,when the basic reproduction number is greater than 1(the disease persists in society),there is a unique endemic equilibrium,which is globally asymptotically stable.Secondly,the COVID-19 data in Shanghai were fitted and predicted.Through the sensitivity analysis of the basic reproduction number,it was found that three parameters,namely vaccination,booster vaccine protection rate and the probability of isolation of asymptomatic patients per unit time,had a great impact on the transmission of COVID-19.Therefore,we carried out numerical fitting,and the results showed that if the vaccination rate of booster vaccine was increased by 1.8 times at the initial moment,the cumulative number of patients in Shanghai would be reduced to 260,000;if the protection rate of booster vaccine was 50%,the number of patients in Shanghai would eventually increase to2.4 million;meanwhile,if the nucleic acid test was conducted once every three days,the number of patients in Shanghai would eventually increase to about 1.6 million.This means that the high frequency of nucleic acid testing is also the key to timely control of the epidemic.Therefore,the government should call on the public to receive booster vaccine as soon as possible,allocate more health resources to Shanghai,establish more nucleic acid testing institutions,and carry out nucleic acid testing as soon as possible.Thirdly,in order to balance the loss of the number of patients and the social and economic cost,this paper will consider three different control strategies to prove the existence and uniqueness of the optimal control,and obtain the solution of the optimal system.Through the numerical simulation of the optimal system,the optimal control of the number of infections and the cost of the lowest is obtained.The results show that the optimal control plays an important role in the spread of the disease.Finally,the content of this paper is summarized.