百日咳流行过程的关联分维研究

Research of Correlation Fractal Dimension of Pertussis Epidemic

以辽宁省本溪市１９５５ ～１９９６ 年的百日咳逐月发病数（ Ｘｔ） 为根据，利用混沌相图和递次振幅图，发现Ｘｔ 具有混沌分布的迭代模型·根据分形理论中关联分维的定义，得到本溪百日咳流行过程奇怪吸引子的分维值为２－６６７，其中计划免疫前分维值为２－７２２ ，计划免疫后分维值降为１－９３８ ，说明百日咳流行过程中，其相空间轨道存在有规则周期性或向平稳状态发展的趋势·通过对功率谱指数的分析， 证明百日咳的传染是混沌的，动力性态符合一个受噪声摄动的高－ 低４ 年循环·

On the basis of the monthly reported cases( X t ) of pertussis in Benxi city from 1955 to 1996, by the chaotic phase portrait and the poincare section, the iterated model of X t was estabilshed and found to be chaotic. For the strange attractor of pertussis epidemic in Benxi city, the correlation dimension from 1955 to 1996 is 2 667, before vaccination the correlation dimension is 2 722, after vaccination the correlation dimension is 1 938. The orbit of pertussis epidemic in Benxi city travels from chaotic to stable state. According to the power spectra analysis, the pertussis epidemic in Benxi city was proved to be chaos, and its dynamic corresponds to a high low 4 year cycle perturbed by noise.