Bauch Chris T, Earn David J D
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada.
Proc Biol Sci. 2003 Aug 7;270(1524):1573-8. doi: 10.1098/rspb.2003.2410.
Historical records of childhood disease incidence reveal complex dynamics. For measles, a simple model has indicated that epidemic patterns represent attractors of a nonlinear dynamic system and that transitions between different attractors are driven by slow changes in birth rates and vaccination levels. The same analysis can explain the main features of chickenpox dynamics, but fails for rubella and whooping cough. We show that an additional (perturbative) analysis of the model, together with knowledge of the population size in question, can account for all the observed incidence patterns by predicting how stochastically sustained transient dynamics should be manifested in these systems.
儿童疾病发病率的历史记录揭示了复杂的动态变化。对于麻疹,一个简单的模型表明,流行模式代表了一个非线性动态系统的吸引子,不同吸引子之间的转变是由出生率和疫苗接种水平的缓慢变化驱动的。同样的分析可以解释水痘动态的主要特征,但对风疹和百日咳却不适用。我们表明,对该模型进行额外的(微扰)分析,再结合所研究人群规模的信息,通过预测这些系统中随机持续的瞬态动态应如何表现,就能够解释所有观察到的发病率模式。