Analytic solution of the SEIR epidemic model via asymptotic approximant

TL;DR

This paper derives an explicit analytical solution to the SEIR epidemic model using an asymptotic approximant, enabling better understanding of epidemic dynamics and application to COVID-19 data.

Contribution

It introduces a novel method to solve the SEIR model analytically by constructing a nonlinear differential equation and applying an asymptotic approximant for divergence control.

Findings

Analytical solution matches long-time exponential damping.

Method applied successfully to COVID-19 data.

Provides a new tool for epidemic modeling and analysis.

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.