猩红热和流脑流行过程的混沌分维研究

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

以辽宁省本溪市 1 955～ 1 996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 .本溪流脑数据的混沌迭代模型是 Xt+1=r X2texp{ -0 .0 0 3394 ( Xt-1 4 .4 1 0 96) 2 } ,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移 ,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 .82 1 .为时间序列的分析研究提供了一种新方法 .

On the basis of the monthly reported cases of scarlet fever and epidemic cerebrospinal meningitis in Benxi city in the periods 1955～1996, and the reconstruction technique of phase space of Chaotic Dynamics, the time series the phase portrait and Poincare section was made. Found that epidemic of scarlet fever was periodic, and epidemic cerebrospinal meningitis was chaotic. The epidemic model of epidemic cerebrospinal meningitis was X t+1 =rX 2 t exp {-0 003394(X\-t-14 41096) 2}. The correlation dimension was 2 821.