Analysis of infected population threshold exceedance in an SIR epidemiological model

TL;DR

This paper derives precise conditions on the basic reproduction number in an SIR model to prevent the infected population from surpassing a specified threshold, using advanced mathematical tools.

Contribution

It introduces a parametric solution approach and utilizes Lambert W function to establish exact criteria for threshold exceedance in epidemic modeling.

Findings

Necessary and sufficient conditions on R0 for threshold control

Mathematical characterization of epidemic peak behavior

Quantitative measures for threshold exceedance

Abstract

We consider an epidemiological SIR model and a positive threshold $M$. Using a parametric expression for the solution curve of the SIR model and the Lambert W function, we establish necessary and sufficient conditions on the basic reproduction number $\mathcal{R}_0$ to ensure that the infected population does not exceed the threshold $M$. We also propose and analyze different measures to quantify a possible threshold exceedance.