The Prediction Of SARS Epidemic Based On Modern Control Theory

Exploring epidemic spreading and predicting its development trend are important aspects for epidemic study, and they are the basis of control policy adopted by the government and medical department. Sever Acute Respiratory Syndrome (SARS), which emerged in 2003 spreaded abroad thirty-tow countries in the world. Although SARS don't prevail now, to research scientific and exact prediction method is the basis of preventing other epidemic from prevailing.Many mathematics models have been set up to research the spread of SARS since SARS broke out. So far, the methods based on models are not scientific prediction. They are only simulations of numbers with computer. What this paper research is a really scientific prediction method based on modern control theory. It has strong academic foundation, and makes the result more exact.Firstly, a differential equation model with time delay is set up based on the characteristic of SARS. Based on traditional SIR model, a new group named free infective people is added to differential equation. Free infective people are the origin of the epidemic, so controlling them can prevent the transmission of SARS. Simulation result proves this model is reasonable. Then a kind of functional observer with internal delay is designed to predict epidemic, and the necessary and sufficient condition for the existence of the functional observer is given, too. Then the design of the unknown matrices of the functional observer is converted to the design of a parameter matrix using the theory of generalized inverse. Meanwhile, a sufficient condition for the time-delay independent stability of the functional observer is derived using the linear matrix inequality technique. To predict the epidemic of SARS on line, a basal Kalman Filter is designed. And the stability of the Filter is analyzed based on the stability criterion. The Filter is proved steady. The simulated result agrees well with the reported epidemic data, which shows that the tow methods have higher precision. They are new methods for SARS epidemic prediction.