English

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 R0R_0 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}
}