The SIR epidemic model from a PDE point of view
Populations and Evolution
2013-01-21 v1
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 parameter, and it will be supported on the corresponding stable SIR equilibrium.
Keywords
Cite
@article{arxiv.0912.3225,
title = {The SIR epidemic model from a PDE point of view},
author = {Fabio A. C. C. Chalub and Max O. Souza},
journal= {arXiv preprint arXiv:0912.3225},
year = {2013}
}