# Inverting the SIR Model (IMUC 2009)

This is one of the talks I gave at the International Mathematica User Conference 2009.

Inverting the SIR Model to Study Origins of Novel H1N1

The wide spread of Novel H1N1 provides an invaluable lesson for data analysis and modeling of a pandemic. A study based on analyzing case and mortality numbers using the SIR, or Kermack-McKendrick, model to provide an estimate of how long an outbreak has lasted in a population is discussed. The presentation used map images and geographic data from Wolfram|Alpha.

• The SIR Model (aka Kermack-McKendrick Model) is a set of 3 coupled ordinary differential equations that track the three major groups of an epidemic (Susceptible, Infected, and Recovered)
• Question: Can the SIR model be used to extrapolate backwards and estimate the origin of a pandemic?
• Hypothesis: Given data about a pandemic’s spread in individual countries, the SIR Model can be used to solve for the amount of time the pandemic has been present in the country, yielding an estimation as to when and therefore where the pandemic started.
• Data from 132 countries as published by the World Health Organization on July 6th, 2009 was used to to test this hypothesis
• Mathematica was used to solve for how long the epidemic has been present in each country by trying to match up the number of case numbers or number of deaths to the SIR Model

What is the value of the research?

• It is plausible to use the SIR model to extrapolate backwards and forwards, making it an option to investigate pandemics when data is still limited; only one-day snapshot of case & mortality number are needed.
• Can be used to track new pandemics when only numbers are available before pathological studies are possible.
• Can also be used to analyze historic pandemics when data sets do not contain details about time.

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