Parameter Estimation And Its Application To A Certain Type Of The Epidemic Model

Infectious diseases have become an important disease which is harmful to human health.With the development of the economy,the contact and communication between the peoples of all countries is increasing,and it provde a favorable condition for the spread of infectious deseases.More and more people are concerned about the spread,prevention and control of infectious diseases.In this paper,we will establish a stochastic differential equations(SDEs)on the basis of classical epidemic model,and estimate the parameters of the SIR epidemic model and the SIS epidemic model based on the real case.In this paper,we mainly study the mathematical theory of epidemic model.Through literature research,the research status of epidemic model at home and abroad,do a comparative literature review related the SIR epidemic model and stochastic SIS epidemic model.We base on complete observation and partial observation of the SIR model,analying the different observation by the use of different methods,and we give the parameters estimation respectively.Because in real life it is very difficult to do the completely observed,so we usually base on counting process to apply partial observation's sample.In practical case,we estimate the parameters through the counting process,and obtain an important threshold parameter.In this paper we estimate the parameters in the stochastic SIS epidemic model by using pseudo-maximum likelihood estimation(pseudo-MLE)and Bayes estimation.We obtain the joint confidence regions based on the likelihood ratio test statistic.We often have some information before data is collected,we estimate parameters by appling Bayesian approach.The Bayesian approach is another important way to estimate the parameters for epidemic model.Through the real case,we obtain the different parameters under given different estimation methods respectively and compare the different results under the two methods.In this paper,the SIR epidemic model and the SIS epidemic model are applied in the actual cases of tuberculosis,based on counting process and pseudo-maximum likelihood estimation method,we obtain parameters estimation.And wu use the conclusion of parameters estimation to reflect the actual situation of the disease,which provides reference for the prevention and control of the next step.