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arXiv · 2006.09818

Analytic solution of the SEIR epidemic model via asymptotic approximant

Steven J. Weinstein·Morgan S. Holland·Kelly E. Rogers·Nathaniel S. Barlow
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Abstract

An analytic solution is obtained to the SEIR Epidemic Model. The solution is created by constructing a single second-order nonlinear differential equation in $\ln S$ and analytically continuing its divergent power series solution such that it matches the correct long-time exponential damping of the epidemic model. This is achieved through an asymptotic approximant (Barlow et. al, 2017, Q. Jl Mech. Appl. Math, 70 (1), 21-48) in the form of a modified symmetric Pad\'e approximant that incorporates this damping. The utility of the analytical form is demonstrated through its application to the COVID-19 pandemic.

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Steven J. Weinstein, Morgan S. Holland, Kelly E. Rogers, Nathaniel S. Barlow. 2020-06-12. Analytic solution of the SEIR epidemic model via asymptotic approximant. https://doi.org/10.1016/j.physd.2020.132633

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