{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,28]],"date-time":"2026-08-28T11:43:50Z","timestamp":1787917430245,"version":"build-2784847793"},"reference-count":57,"publisher":"World Scientific Pub Co Pte Ltd","issue":"13","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2022,10]]},"abstract":"<jats:p> Accurate predictions for the spread and evolution of epidemics have significant societal and economic impacts. The temporal evolution of infected (or dead) persons has been described as an epidemic wave with an isolated peak and tails. Epidemic waves have been simulated and studied using the classical SIR model that describes the evolution of susceptible (S), infected (I), and recovered (R) individuals. To illustrate the fundamental dynamics of an epidemic wave, the dependence of solutions on parameters, and the dependence of predictability horizons on various types of solutions, we propose a Korteweg\u2013de Vries (KdV)\u2013SIR equation and obtain its analytical solutions. Among classical and simplified SIR models, our KdV\u2013SIR equation represents the simplest system that produces a solution with both exponential and oscillatory components. The KdV\u2013SIR model is mathematically identical to the nondissipative Lorenz 1963 model and the KdV equation in a traveling-wave coordinate. As a result, the dynamics of an epidemic wave and its predictability can be understood by applying approaches used in nonlinear dynamics, and by comparing the aforementioned systems. For example, a typical solitary wave solution is a homoclinic orbit that connects a stable and an unstable manifold at the saddle point within the [Formula: see text]\u2013[Formula: see text] space. The KdV\u2013SIR equation additionally produces two other types of solutions, including oscillatory and unbounded solutions. The analysis of two critical points makes it possible to reveal the features of solutions near a turning point. Using analytical solutions and hypothetical observed data, we derive a simple formula for determining predictability horizons, and propose a method for predicting timing for the peak of an epidemic wave. <\/jats:p>","DOI":"10.1142\/s0218127422501991","type":"journal-article","created":{"date-parts":[[2022,11,3]],"date-time":"2022-11-03T06:40:11Z","timestamp":1667457611000},"source":"Crossref","is-referenced-by-count":16,"title":["A KdV\u2013SIR Equation and Its Analytical Solutions for Solitary Epidemic Waves"],"prefix":"10.1142","volume":"32","author":[{"given":"Wei","family":"Paxson","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, San Diego State University, 5500 Campanile Drive, San Diego, CA, 92182, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0750-0625","authenticated-orcid":false,"given":"Bo-Wen","family":"Shen","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, San Diego State University, 5500 Campanile Drive, San Diego, CA, 92182, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2022,11,3]]},"reference":[{"key":"S0218127422501991BIB001","unstructured":"Anderson, R. 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