Numerical Simulation Of SARS Epidemic In Beijing In 2003

SARS(Sever acute respiratory syndrome) is the most wide-spread infectious disease that man encountered in recent years.The study of the development of SARS in Beijing has great significance,since the SARS cases in Beijing occupy a very high proportion in China.This thesis analysed the observed statistical data of SARS in Beijing.The apparent development of SARS in Beijing was divided into three periods according to the observed statistical data: the initial developing period,the high and steady-developing period and the declining period.The intrinsic development of SARS is assumed to contain two stages. In the first stage, no measure to prevent SARS from spreading was taken and SARS spreads naturally with its intrinsic infectious speed. In the second stage, all the measures by the government and other relevant organizations took effect and SARS spreads in a controlled manner with a slow infectious rate. The mathematical model involves five important parameters, initial numbers of patients in the infectious period (the numbers of patients in the infectious period on March 19), and the infectious rates outside hospitals and inside hospitals, during the first stage, and second stage. Four groups of patients related to the spread of the SARS epidemic were discussed.They are patients in the latent period, patients in the infectious period, patients in hospital and patients who are recovered or died in hospital.Then a mathematical model was established to simulate the SARS development in Beijing by difference equations,and an objective function was also established which mainly consists of the sum of squares of the differences between the simulated and observed statistical data of SARS in Beijing. Relevant Fortran programs was compiled.The parameters estimation shows that the initial numbers of patients in infectious period equal to 7.45,the infectious rates outside hospitals during the first and second stage equal to 0.88(1/day) and 0.27(1/day),respectively, 0.04(1/day) and 0.00(1/day),inside hospitals. Both the total patient number and the sum of the numbers of recovered and died patients in hospital were simulated. The simulation describes the three stages of the SARS development in Beijing satisfactorily. The relative error between the simulated and observed values of the total patient numbers is less than 2%, and so is that of the sum of numbers of recovered and died patients in hospital.