Model Development and Model Validation for Pandemic Influenza

人们早就知道，流感在冬季更为流行，但尚不清楚这是由于学年期间接触率增加，还是由于环境对病毒传播性的影响。这种季节性造成了在大流行性流感中可见的春季/秋季双波性。目前的流感模型试图将疾病的季节性纳入模型，通常假设一个和谐的强迫感染率。然而，我们的初步探索性研究表明，周期性的强迫感染率会导致混乱的动力学，因此，对周期性性质的不同假设可能导致疾病在人群中传播的短期动态预测发生巨大变化，特别是在大流行性流感的情况下。因此，如果模型被用来协助决策者在新的大流行爆发时进行疾病控制和干预，那么对模型中感染率的时间行为使用不正确的假设可能会造成相当大的破坏。因此，我们的研究旨在通过开发准确描述人口动态和疾病季节性的现实模型来了解大流行性流感的短期动态。我们用常微分方程（ODE’s）对疾病建模。我们将检验模型预测对模型参数变化的敏感性；由于系统的混沌性质，当使用该模型评估疾病干预策略（如疫苗接种运动）时，此类研究对于确定模型预测的稳健性非常重要。我们的工作将为迄今尚未得到充分研究的大流行性流感可能出现的复杂短期动态提供新的线索。通过模型复杂性的分层推进，我们将确定最合适和最实用的模型，避免开发过于复杂和深奥的方法。此外，通过明确地将数学模型与现有数据联系起来，我们确保这些模型将产生可靠的结果，用于制定大流行病防范方面的公共卫生政策。

Influenza has long been known to be more prevalent in winter, although it is unknown whether this is due to increased contact rates during the school year, or due to environmental effects on the transmissibility of the virus. This seasonality is responsible for the spring/autumn dual wave nature that can be seen in pandemic influenza. Current models of influenza that attempt to incorporate the seasonality of the disease into the model generally assume a harmonically forced infection rate. However, our preliminary exploratory studies have shown that a periodically forced infection rate leads to chaotic dynamics, and that different assumptions of the nature of the periodicity can thus lead to dramatic changes in the predictions of the short term dynamics of the spread of the disease in a population, particularly in the case of pandemic influenza. Using an incorrect assumption for the time behavior of the infection rate in the model can thus be quite damaging if the models are employed to assist policy-makers in disease control and interventions in the event of a new pandemic outbreak. Our research thus aims to understand the short-term dynamics of pandemic influenza through the development of realistic models that accurately describe population dynamics and the seasonal nature of the disease. We model the disease through ordinary differential equations (ODE's). We will examine the sensitivity of the model predictions to changes in the model parameters; because of the chaotic nature of the system, such studies are important to ascertain the robustness of the model predictions when disease intervention strategies (such as vaccination campaigns) are assessed using the model. Our work will shed new light on the complex short term dynamics possible with pandemic influenza, which has hitherto not been well studied. Through a hierarchical advancement of model complexity, we will identify the most appropriate and pragmatic models, avoiding the development of overly complex and abstruse methods. Further, by explicitly linking the mathematical models with existing data, we ensure that the models will produce reliable results for use in the development of public health policy in pandemic preparedness.