Marshall University Math Colloquium
October 30, 2013
Filtered LeapFrog Time Integration with Enhanced Stability Properties
The Leapfrog method for the solution of Ordinary Differential Equation initial value has been historically popular for several reasons. The method has second order accuracy, requires only one function evaluation per time step, and is non-dissipative. Despite the mentioned attractive properties, the method has some unfavorable stability properties. The absolute stability region of the method is only an interval located on the imaginary axis rather than a region in the complex plane. The method is only weakly stable and thus exhibits computational instability in long time integrations over intervals of finite length. In this work the use of filters is examined for the purposes of both controlling the weak instability and also enlarging the size of the absolute stability region of the method.
Agent-based Modeling of Pandemic Influenza
A striking characteristic of influenza pandemics is the multiple peaks of infection. For example, the United States has experienced two peaks of infection in each of the past four influenza pandemics, one peak during the summer months and a second peak during the typical flu season. In contrast, the number of infected individuals peaks only once during a seasonal flu. The mechanisms that cause the multiple peaks of infection during pandemic influenza seasons are not well understood. The goal of this project is to use agent-based modeling to investigate mechanisms that can generate two peaks of infection.
In this talk I will describe the susceptible-exposed-infectious-recovered (SEIR) agent-based model developed in Netlogo for simulating the 2009 H1N1 influenza pandemic. The incubation and infectiousness periods are drawn from gamma distributions. The model is calibrated by matching known average daily contacts and key epidemiological quantities, such as the basic reproduction number, the number of new infections generated from one infectious person at the beginning of the outbreak. Also, I will discuss the results of model simulations that include waning immunity, which is one potential mechanism for generating multiple peaks of infection.