Model Development and Model Validation for Pandemic Influenza

长期以来，人们一直知道流感在冬季更为普遍，尽管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。这种季节性导致了在大流行性流感中可以看到的春/秋双波性质。目前的流感模型试图将疾病的季节性纳入模型中，通常假定强制感染率协调一致。然而，我们的初步探索性研究表明，周期性强制感染率会导致混乱的动态，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，如果模型被用来帮助政策制定者在新的大流行爆发时进行疾病控制和干预，那么在模型中使用对感染率的时间行为的错误假设可能是非常有害的。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。我们通过常微分方程组(ODE‘s)对这种疾病进行建模。我们将检查模型预测对模型参数变化的敏感性；由于系统的混沌性质，当使用模型评估疾病干预策略(如疫苗接种活动)时，此类研究对于确定模型预测的稳健性非常重要。我们的工作将为大流行性流感可能的复杂短期动态提供新的线索，到目前为止，这一问题还没有得到很好的研究。通过对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，用于制定预防大流行的公共卫生政策。

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.