Model Selection And Evaluation Based On Emerging Infectious Disease Data Set

Infectious diseases serious harmed to human health and hindered the develop-ment of social economy. The severe acute respiratory syndrome (SARS) in 2003, A/H1N1 in 2009, the outbreak of Ebola in West Africa in 2014 had brought huge disaster to the society. Therefore, the national health organization, experts of in-fectious disease control and disease susceptible populations were very concerned the control and prediction of infectious diseases. Many scholars established mathemati-cal models which can reflect the spreading process and combined with the reported data of disease, help to reveal its propagation of spreading, adopted measures to control and evaluated the effectiveness of control measures.Kermack and Mckendrick proposed classical mathematical model of the infec-tious diseases-SIR model (Susceptible Infective Removal model) using the method of dynamics in 1927. Later, it was widely used in the propagation characterization and other different types of infections disease. But when emerging epidemic disease broke out in some areas, public health department and people hope to understand the spread laws of the disease as soon as possible. In particular, to rapidly deter-mine the basic reproductive number, turning point and the ultimate infections of the disease, according to the existing information, including cumulative number of cases. The SIR model depicting the change law of the number of the susceptible, disease and remove people, and the population of the region need to be divided into three classes. When the data is limited, it can not meet the needs of model determination parameter estimation and prediction. Therefore, SIR model or other infections disease models are not the best choice in the early stage of the outbreak of the epidemic.Because the analytical solution and the model parameters are easy to be de-termined, the simple single population model is often used to study and evaluate the indicators of the outbreak of infectious diseases, such as, A/H1N1, SARS and dengue fever. But most of the works are to study on a specific diseases with a spe-cific model. However, the methods and the necessity of model selection for different disease without too much study. Therefore, the paper will based on the data of A/H1N1 and Ebola, use Bayes factor and MH algorithm to realize the model selec-tion and determine the optimal model. So as to explore the importance of model selection when estimate key factors of emerging infectious disease.First of all, the paper gives the method of model selection based on Bayes factor and MH algorithm. The paper's alternative models are four single population growth model that are common and have analytical solution. They are Logistic model, Gompertz model, Rosenzweing model and Richards model. The sources of data are the cumulative number of cases about A/H1N1 of Shaanxi Province in 2009 and Ebola of West Africa in 2014. Through the joint space of the model and parameters, we use MH algorithm to estimate the posteriori probability of each alternative model. And we selected the best model to fitting the data.Then, we estimate the basic reproductive number with, the turning point and the final number of infections use the best model, and then predict the intensity of infection and the time of disease be controlled and the final outbreak. For different data, get the best fitting model. Then compare the estimates of parameter of other models and the estimates of parameter of best model, we can get the uncertainty of model selection will lead to underestimate or overestimate parameters affecting the accuracy of the prediction of the epidemic. If randomly choose a model studying on disease data will make the prediction results and the actual results have large deviation. So, model selection is crucial when study the emerging infectious disease based on the valid data.