Nonparametric Estimation Of Infectious Disease Infection Curve Based On Full Smoothing Method

With the development of economy and the convenience of transportation,the increasing exchanges and contacts among people all over the world have provided favorable conditions for the global spread of infectious diseases.Infectious diseases,as a major killer of human health,constantly threaten people's lives.In the process of spread of infectious diseases,its infection trend determines the severity of the epidemic.And predicting the future epidemic trend of infectious diseases depends on the current number of infections.This paper will focus on the estimation of infection curve.In this paper,we propose a non-parametric estimation method of infectious disease infection number based on full smoothing method.The large sample attributes of the estimator,including consistency and asymptotic normality,are also studied.The numerical simulation and case analysis show that this estimation is feasible and has some advantages over the existing methods for estimating infectious disease infection curve.The main contents of this paper include the following chapters:In the first chapter,we introduce the background and content of this study,analyze the urgency and necessity of estimating infectious disease infection curve,and briefly describe some existing methods of estimating infectious disease infection curve.In chapter 2,we introduce some basic symbols and hypotheses according to the intrinsic characteristics of infectious disease data.we introduce the research progress of infectious disease infection curve by scholars at home and abroad,mainly introduce the theory and estimation process of one-step estimator and local smoothing estimator,and analyze some drawbacks of infectious disease infection estimation methods.In chapter 3,a new infectious disease infection model based on full smoothing method and an effective algorithm for estimating the parameters in the model are described.The selection of kernel function and bandwidth is discussed,mainly the theoretical and practical selection methods of optimal bandwidth,and the definition of leave-one-out cross-validation score is given.In chapter 4,this chapter mainly establishes the large sample properties of full smoothing estimator,including consistency and asymptotic normality,and gives a detailed proof process.In chapter 5,a simulation study is carried out.The risk function is selected to simulate the transmission process of an infectious disease under human intervention.The differences of bias,variance and root mean square error between one-step estimator,local smoothing estimator and full smoothing estimator are compared and discussed.It shows that the new full smoothing estimator has some advantages.In chapter 6,this paper provides real data analysis.According to the number of infectious disease cases published on the relevant official websites of the health department,the infectious curve of SARS epidemic in Hong Kong in 2003 is reconstructed and the number of new infections of hepatitis C in ZheJiang Province from January2015 to June 2018 is estimated,respectively.The infectious situation and trend of infectious diseases are analyzed.In the last chapter,this chapter mainly summarizes and prospects.Firstly,the full smoothing estimation method proposed in this paper is summarized,and its advantages over the existing methods of infectious disease infection estimation are pointed out.Finally,the shortcomings of this paper are prospected and some suggestions are put forward.