Model Development and Model Validation for Pandemic Influenza

Purdue University, West Lafayette IN

Investigators

Abstract

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.