Parameter Estimation Of Two Kinds Of Stochastic Differential Equation Biological Models

In recent years,people have a deep understanding of mathematical models,and the analysis of random and complex systems have been involved in financial,physics,biological,materials and many other fields.Stochastic differential equation models are established for the complex systems,combined with software simulation,studying the dynamic system of these models,and then the system represented by the model can be predicted and controlled.In this paper,we introduce a prey-predator model with foraging arena scheme and a SIS model with two independent Brownian motions.Based on the previous studies,Euler-Maruyama method,Tamed-Euler method and Truncated Euler-Maruyama method are mainly used to discretize the stochastic differential equation model.Then the pseudo-maximum likelihood method is used to estimate the parameters of these two new bio-mathematic models,and the software is used to simulate the data to verify the estimation value.The results of numerical simulation show that for the predator-predator model with foraging arena scheme,when the three Euler methods converge,the estimation of the traditional EM method and the Truncated EM method is better than that of the Tamed-Euler method.When the EM method is divergent,the estimation of the Truncated EM method is better than that of the Tamed-Euler method.For the SIS model with two independent Brownian motions,when the three Euler methods converge,the estimation of the traditional EM method and the Truncated EM method is better than that of the Tamed-Euler method.When the traditional EM method diverges,the Truncated EM method and the Tamed-Euler method can estimate the value,but the estimation effect is not satisfactory.This paper has five chapters.The first chapter briefly introduces the research background and significance,the structure of the paper and its main contributions.The second chapter introduces the preparatory knowledge involved in this paper.The third chapter introduces the prey-predator model with foraging arena scheme,and a new prey-predator model was formed.Then the parameters of the new predator-predator model were estimated.The fourth chapter introduces the SIS model and considers the influence of environmental factors on the model.Introduce two independent Brownian motions and estimate the parameters of the new SIS model.The fifth chapter is the summary and prospect of the full text.