Qualitative Analysis of Unpredictability: A Case Study from Childhood Epidemics

摘要: The unpredictability of the recurrent outbreaks childhood epidemics has been a matter scientific dispute. At first sight deterministic SEIR model, which divides host population into four classes (Susceptible, Exposed, Infectious, Recovered), fails to explain unpredictability, because realistic parameter values lead periodic attractors. We show that these attractors coexist with chaotic transients. detailed geometrical analysis this phenomenon suggests transients have underestimated in their importance for dynamics on observable time scales. A second problem model is high extinction probability finite populations. argue immigration infectives from outside an essential context. Immigration and process infection itself are sources demographic fluctuations, undergo subtle interaction stochastic simulation shows permanently revisited. noise integrates intermittent episodes.