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Magal, P. and Ruan, S. (2014) Susceptible-Infectious-Recovered Models Revisited: From the Individual Level to the Population Level. Mathematical Biosciences, 250, 26-40.
https://doi.org/10.1016/j.mbs.2014.02.001

has been cited by the following article:

• TITLE: The Spreading Profile for an Emerging Infectious Disease and Its Resemblance to the KdV Solution

  AUTHORS: Zach Fendler, Valipuram S. Manoranjan

  KEYWORDS: SIR Model, Second-Order Approximation, Korteweg-de Vries Equation, Nonlinear PDE, Solitary Wave

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.8, August 18, 2025

  ABSTRACT: Modern times have shown that understanding infectious diseases is imperative to our survival. In this study, we gain an understanding of the SIR model for novel or emerging infectious diseases by deriving time-dependent solutions for the spreading profiles using a second-order approximation. We noticed that we got a solution that resembles the well-known soliton solution of the Korteweg-de Vries (KdV) equation. The KdV equation is a deterministic nonlinear partial differential equation that possesses a solitary wave solution known as a soliton. Using phase portrait analysis, we can show that the graphical time profile of the number of infected in the SIR model is qualitatively the same as the KdV wave profile.