肝炎和伤寒流行过程的混沌分维研究

Viral Hepatitis and Typhoid

以辽宁省本溪市 １９５５－１９９６年的肝炎、伤寒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．发现伤寒的流行过程是混沌的，混沌迭代模型是Ｘｔ＋１＝ｒＸｔｅｘｐ｛－０．００００９２８７（Ｘｔ－３３．２５３５２）２）；肝炎的流行过程是非混沌的．在模型参数变化范围内，经历了周期状态、混沌状态之间的转换，这表明伤寒的流行过程是复杂的，给出了流行病的“阈值”，以控制它们的流行涨落，求出伤寒的关联分维是３．

On the basis of the monthly reported cases of viral hepatitis and typhoid 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 viral hepatitis was periodic, and epidemic of typhoid was chaotic. The epidemic model of typhoid was Xt+l = rXt exp{-0.0009287(Xt - 33.25352)2}. The correlation dimension of typhoid was 3.087.