Exact solution for a discrete-time SIR model
Dynamical Systems
2024-09-17 v1 Physics and Society
Populations and Evolution
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.
Cite
@article{arxiv.2409.09157,
title = {Exact solution for a discrete-time SIR model},
author = {Márcia Lemos-Silva and Sandra Vaz and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:2409.09157},
year = {2024}
}
Comments
This is a preprint published Open Access in 'Applied Numerical Mathematics' [https://doi.org/10.1016/j.apnum.2024.09.014]