SIR Model with Stochastic Transmission

by   Christian Gourieroux, et al.

The Susceptible-Infected-Recovered (SIR) model is the cornerstone of epidemiological models. However, this specification depends on two parameters only, which implies a lack of flexibility and the difficulty to replicate the volatile reproduction numbers observed in practice. We extend the classic SIR model by introducing nonlinear stochastic transmission, to get a stochastic SIR model. We derive its exact solution and discuss the condition for herd immunity. The stochastic SIR model corresponds to a population of infinite size. When the population size is finite, there is also sampling uncertainty. We propose a state-space framework under which we analyze the relative magnitudes of the observational and stochastic epidemiological uncertainties during the evolution of the epidemic. We also emphasize the lack of robustness of the notion of herd immunity when the SIR model is time discretized.


page 1

page 2

page 3

page 4


Finite and Infinite Population Spatial Rock-Paper-Scissors in One Dimension

We derive both the finite and infinite population spatial replicator dyn...

Inference on Extended-Spectrum Beta-Lactamase Escherichia coli and Klebsiella pneumoniae data through SMC^2

We propose a novel stochastic model for the spread of antimicrobial-resi...

A stochastic SIR model for the analysis of the COVID-19 Italian epidemic

We propose a stochastic SIR model, specified as a system of stochastic d...

A linear noise approximation for stochastic epidemic models fit to partially observed incidence counts

Stochastic epidemic models (SEMs) fit to incidence data are critical to ...

STAMINA: STochastic Approximate Model-checker for INfinite-state Analysis

Stochastic model checking is a technique for analyzing systems that poss...

Inference, Learning, and Population Size: Projectivity for SRL Models

A subtle difference between propositional and relational data is that in...