Parameter Estimation Of Noise-driven Stochastic Differential Equation Biological Models With Correlations

Stochastic differential equations are widely used in various fields,especially in the field of biological models.The research and application of stochastic differential equation biological models have played a positive role in the prevention and suppression of infectious diseases.In this paper,we select a stochastic differential biological model with correlated Brownian motion.Use the Euler-Maruyama method,the tamed-Euler method and the Milstein method to discretize them,respectively.Then use the least squares estimate,the pseudo-maximum likelihood estimate to estimate the parameters,and carry out interval estimation.The Matlab is also used for numerical simulation to compare the estimated values and the true values.This article simulates and discusses the two cases of the model.Through numerical simulations,it can be concluded that the pseudo-maximum likelihood method is better than the least-squares method in the case of persistence,and the pseudo-maximum likelihood method with the Milstein discretization has the best effect.In the case of extinction,the estimation errors of the least squares method with Euler-Maruyama method and Milstein method discretization are both too large,and the pseudo maximum likelihood estimation perform well.The pseudo-maximum likelihood estimate with the tamed-Euler method is better.In addition,the estimation error will be reduced when a smaller step size is used,and the estimation will be better when the longer time interval is used.