Exact solution for a discrete-time SIR model

TL;DR

This paper introduces an exact solution for a discrete-time SIR model using a nonstandard finite difference scheme, ensuring consistency with the continuous model and providing biologically sound results.

Contribution

The paper presents a novel discrete-time SIR model with an exact solution, improving mathematical and biological validity over existing models.

Findings

Exact solution derived for the discrete-time SIR model

Model demonstrates long-term behavior consistent with continuous models

Ensures mathematical and biological soundness of the discrete model

Abstract

We propose a nonstandard finite difference scheme for the Susceptible-Infected-Removed (SIR) continuous model. We prove that our discretized system is dynamically consistent with its continuous counterpart and we derive its exact solution. We end with the analysis of the long-term behavior of susceptible, infected and removed individuals, illustrating our results with examples. In contrast with the SIR discrete-time model available in the literature, our new model is simultaneously mathematically and biologically sound.