Study Of HIV Infection Based On Statistical Models

AIDS,since its discovery in 1981,has become a very harmful infectious disease.It is caused by HIV.HIV virus attacks human immune system,in which CD4 lymphocyte is the main target.At present,there is no specific drug for HIV treatment in the world,and antiviral treatment can only alleviate AIDS.Therefore,the study of AIDS prevention and prediction has important practical significance.A large number of scholars have studied AIDS.In the initial stage,qualitative analysis on AIDS was the main method.The rise of quantitative analysis and the popularity of data mining have enriched the means of AIDS research and made the prediction on the number of AIDS patients more accurate.In this thesis,differential equation theory and statistical methods are used to model for transmission and treatment of AIDS,and predict the related problems.Finally,some suggestions on the prevention and treatment of AIDS are put forward.Firstly,based on the SI model of AIDS transmission dynamics,this thesis classifies the infected population into diagnostic intervention group and non-diagnostic intervention group,establishes differential equation model,obtains the basic reproduction number and equilibrium point,and carries out stability analysis.In the second part,according to the data provided by Hunan CDC,the variable coefficient regression model is used to predict the number of AIDS cases among college students in Hunan Province.Compared with the traditional grey prediction method,the 95%confidence interval of the new reported cases of AIDS among college students in Hunan Province in 2017 is[209,231].In the third part,a quantile regression model is established with CD4 as the response variable and marital status,route of infection,gender,duration of treatment and stage of illness as the explanatory variables.According to the data of antiviral treatment provided by Hunan CDC,the number of CD4 of HIV carriers in Hunan Province was obtained at different loci,which is different from the mean regression model.This model provides a theoretical basis for targeted antiviral therapy for different populations.Finally,the thesis makes a brief summary on modeling and prediction of HIV infected population and puts forward new prospects for the shortcomings of the thesis.