The SIR epidemic model from a PDE point of view

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.

References in corpus (1)

• From discrete to continuous evolution models: a unifying approach to drift-diffusion and replicator dynamics

Cited by in corpus (2)

• The frequency-dependent Wright-Fisher model: diffusive and non-diffusive approximations
• Predicting population extinction in lattice-based birth-death-movement models