For more information about this meeting, contact Kris Jenssen, Hope Shaffer, Yuxi Zheng.
| Title: | A New Conserved Quantity for the Kermack-McKendrick Epidemic Model |
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| Seminar: | Computational and Applied Mathematics Colloquium |
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| Speaker: | Warren Weckesser, Enthought, Inc. |
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| Abstract: |
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| 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: | MB106 |
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| Date: | 09 / 19 / 2008 |
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| Time: | 03:35pm - 04:25pm |
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