The Research On Application Of K-means Clustering Algorithm In SIR Infectious Disease Model

K-means clustering algorithm is a kind of classical clustering algorithm,which is applied to biology,astronomy,environment,economy,medical treatment and other aspects.SIR epidemic model(Susceptible Infected Recovered Model)is the important foundation of the epidemic model.Cellular Automata is discrete in state,time and space,which has been widely used in computer science,mathematics,sociology,physics,ecology and medicine.Based on the cellular automata model and K-means clustering algorithm as the important tool,established is K-means clustering algorithm of SIR cellular automata simulation model.Based on the obey Gaussian distribution and uniform distribution random respectively two kinds of initial analysis and simulation of the source of infection,infection is given radius and the radius of isolation effect on the spread of the disease,and the application research of K-means clustering algorithm with feature weight on the SIR cellular automata model with age structure and random walk,and further discusses the influence of age structure and random walk on the prevention and control of infectious diseases.This paper is mainly divided into the following four chapters:The first chapter is the introduction,which summarizes the proposal,development process and related applications of k-means clustering algorithm in the field of biological mathematics.Meanwhile,the cellular automata model and infectious disease model both are briefly summarized.The second chapter firstly introduces the k-means clustering algorithm,including the definition,features,ideas and related concepts of the k-means clustering algorithm.Secondly,the basic theory and concept of SIR warehouse model based on cellular automata are established,and the idea and method of establishing SIR cellular automata model with k-means clustering algorithm are given.The third chapter is the first part of the main work of this paper,the application research of k-means clustering algorithm in SIR basic infectious disease model,aiming to give the influence of infection radius and isolation radius on disease transmission through the analysis and simulation of two types of initial infection sources subject to Gaussian distribution and random uniform distribution.The results show that: Under the first distribution of two different types,a maximum of infected with disease transmission radius and isolation of radius were positively correlated with negative correlation,the number of infected people over time and the rate of change of rendering the same change rule.The different distribution of the initial data type affects only the positive and negative correlation between growth.And according to the Gaussian distribution and uniform distribution random contrast experimental results,explain the biological significance in the actual infectious diseases and the corresponding prevention and control measures.The fourth chapter is the second part of this paper work,K-means clustering algorithm based on feature weighting in the age structure and random walk SIR infectious disease model,the application of cellular automata,analyses the three layers of children,young adults and older age structure effects on infectious diseases.Also,in obedience to Gaussian distribution and uniform distribution random mode of two classes of the initial infection sources,the study found that: K-means clustering with characteristic weight was used to analyze the two distributions.Among the three age structures,the young adults with a large number of people and strong infectivity had a significant impact on the maximum value of infected people.The infection radius,the initial isolation time and the moving radius were positively correlated with the maximum value of infected people,while the isolation radius was negatively correlated with the maximum value of infected people.In addition,the method of map generation and initialization for all random uniform distribution and gaussian distribution,as well as the problem of gauss migration of non-adjacent body are provided.To some extent,the completion of this paper makes up for the deficiency of K-means clustering algorithm in epidemiological research.In the future,the simulation process of K-means algorithm in epidemic disease can be further concretized in combination with actual epidemic cases,so as to obtain more feasible research results.