Analytic solution of the SEIR epidemic model via asymptotic approximant

An analytic solution is obtained to the SEIR Epidemic Model. The solution is created by constructing a single second-order nonlinear differential equation in lnS 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) in the form of a modified symmetric Padé approximant that incorporates this damping. The utility of the analytical form is demonstrated through its application to the COVID-19 pandemic. •An accurate analytic solution is obtained to the SEIR Model.•The SEIR model is recast as a single 2nd order nonlinear ODE in ln(S).•The power series solution to the ODE in ln(S) is analytically continued beyond its radius of convergence.