麻疹流行过程的混沌分形

Chaotic and Fractal of Measles Epidemic

以辽宁省本溪市１９５５ ～１９９６ 年麻疹逐月发病数为根据，利用谱分析得出本溪麻疹的传染是混沌的，动力性态符合一个受噪声摄动的高低１ ～２ 年循环·利用混沌动力学相空间重构技术，给出本溪麻疹逐月发病数时间趋势图、混沌相图和递次振幅图，求出本溪麻疹逐月发病数混沌分布的迭代模型·并求出本溪麻疹流行过程奇怪吸引子的分维值为３－４２６ ６６７ ，其中计划免疫前分维值为３－４６２ ５０３ ，计划免疫后分维值降低为０－３３８ ４６１ ５ ，说明麻疹流行过程中相空间轨迹存在向平稳状态发展的趋势·

On the basis of the monthly reported cases of measles in Benxi city in the period 1955～1996, power spectra analysis shows that the epidemic of measles of Benxi is chaotic, and its outbreaks approximate to annual cycle and biennial cycle. According to the reconstruction technique of phase space of chaotic dynamics, the time series,the phase portrait and poincare section were made. The chaos distribution model of the monthly reported cases of measles of Benxi was given. The correlation dimension is 3 426?667, before vaccination the dimension is 3 462?503, after vaccination it changes to 0 338?461?5. The phase space locus of the epidemic of the measles in Benxi city tends to be stable.