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arXiv · 0912.3225

The SIR epidemic model from a PDE point of view

Fabio A. C. C. Chalub·Max O. Souza
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Abstract

We present a derivation of the classical SIR model through a mean-field approximation from a discrete version of SIR. We then obtain a hyperbolic forward Kolmogorov equation, and show that its projected characteristics recover the standard SIR model. Moreover, we show that the long time limit of the evolution will be a Dirac measure. The exact position will depend on the well-know $R_0$ parameter, and it will be supported on the corresponding stable SIR equilibrium.

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Fabio A. C. C. Chalub, Max O. Souza. 2009-12-16. The SIR epidemic model from a PDE point of view. https://doi.org/10.1016/j.mcm.2010.05.036

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