Application Of Bayesian Parameter Estimation Methods In Infectious Disease Models

In the study of complex systems or natural phenomena that are difficult to understand directly,researchers can always abstract the most essential factors,and then establish a model on this basis.Then evaluate,modify and integrate the established model according to the observed real data,so as to obtain the certainty of the unknown system.In the framework of Bayesian estimation,the solution of unknown parameters requires the operation of likelihood function.However,in complex systems,the likelihood function is often difficult to be presented in analytical form.In this case,the Approximate Bayesian Computation(ABC)with likelihood-free methods and the Sequential Neural Estimation methods based on simulation came into being.These methods have achieved good results in dealing with such problems.Bayesian framework has great advantages in solving small batch data and realtime updated data.Starting from the estimation of Bayesian posterior distribution,this paper uses several efficient algorithms based on Approximate Bayesian calculation and Sequential Neural estimation method based on forward simulation to explore the solution method of complex model parameters.Firstly,these methods are applied to the Lorenz equation of the known parameter model to compare the efficiency of each algorithm.We find that the Neural estimation method achieves the highest accuracy,but its computational cost is much higher than the Adaptive Population Monte Carlo(APMC)method based on Approximate Bayesian calculation.We further applied these methods to the dynamics model of infectious diseases and found that in the absence of data in reality,the comprehensive performance of Sequential Neural Posterior estimation(SNPE)is the best.On the basis of this method,we complete the parameter estimation of the SEIR model of the COVID-19 epidemic in Iceland at different stages,and complete the prediction of the epidemic in Iceland with the help of the estimated parameters.In addition,according to the data experiment,the similarities and differences of the above two kinds of algorithms in solving this kind of problem are discussed,and some calculation strategies are provided for solving this kind of problem.