A New Conserved Quantity for the Kermack-McKendrick Epidemic Model

Computational and Applied Mathematics Colloquium

Meeting Details

For more information about this meeting, contact Kris Jenssen, Hope Shaffer, Yuxi Zheng.

Speaker: Warren Weckesser, Enthought, Inc.

Abstract: In 1927, Kermack and McKendrick introduced a system of integro-differential equations that models the spread of a disease in a homogeneously mixed susceptible population. In this model, the duration for which an infected individual remains infectious can be interpreted as a random variable with an arbitrary probability distribution. (When the distribution is exponential, the integro-differential equations can be reduced to the well-known three-dimensional system of ordinary differential equations also known as the SIR model.) In this talk, I will show that the integro-differential equations have a conserved quantity that has not been previously observed. With this conserved quantity, we easily prove some well-known results on the threshold value and final size of an epidemic. I will also give new formulas for the basic reproduction number for very general multi-stage epidemic models with multiple susceptible classes in which the infected stages each have arbitrary probability distributions. These results generalize several previous results from the literature. This is joint work with Dan Schult of Colgate University.

Room Reservation Information

Room Number: 106 McAllister

Date: 09/19/2008

Time: 3:35pm - 4:25pm