猩红热和流脑流行过程的混沌分维研究

以本溪市１９５５～１９９６年的猩红热和流脑逐月发病的数据为根据,利用混沌动力学中“相空间技术”,对流行病过程进行能量谱分析及混沌分析·发现流脑的流行过程是混沌的,猩红热的流行过程是周期的；并得到本溪流脑数据的混沌迭代模型·在模型参数变化范围内,经历了周期状态、混沌状态、吸引不动的稳定状态之间的转换,这表明流脑流行过程是复杂的,给出流行的“阈值”,以控制其流行涨落；求出流脑的关联分维是２８２１·为离散时间序列的分析研究提供了一种新方法·

Research of Correlation Fractal Dimension of Scarlet Fever Epidemic and Epidemic Cerebrospinal Meningitis

On the basis of the monthly reported cases of scarlet fever and epidemic cerebrospinal meningitis in Benxi city from 1955 to 1996, and the reconstruction technique of phase space of chaotic dynamics, epidemic was studied with power spectra and chaotic analysis. Chaos is found in the epidemic of epidemic cerebrospinal meningitis,and period is found in the epidemic of scarlet fever. The chaotic model of epidemic cerebrospinal meningitis was got. Within the extent of the model parameter r ,the epidemic of eqidemic cerebrospinal meningitis of Benxi traveled from periodic state to chaotic state,at last to stable state,so the epidemic is complicated. The threshold value of epidemic was given,the fluctuation of the epidemic of epidemic cerebrospinal meningitis would be controled,and the correlation dimension is 2 821.