Existence of exact solution of the Susceptible-Exposed-Infectious-Recovered (SEIR) epidemic model

TL;DR

This paper derives exact solutions for the SEIR epidemic model using Abel differential equations, providing explicit formulas and properties of the solutions to better understand disease dynamics.

Contribution

It introduces a novel method to obtain exact solutions of the SEIR model through Abel differential equations, which was not previously established.

Findings

Exact solutions expressed in closed form

Properties of solutions derived directly from the exact form

Representation of infected individuals via Abel differential equations

Abstract

Exact solutions of the SEIR epidemic model are derived, and various properties of solutions are obtained directly from the exact solution. In this paper Abel differential equations play an important role in establishing the exact solution of SEIR differential system, in particular the number of infected individuals can be represented in a simple form by using a positive solution of an Abel differential equation. It is shown that the parametric form of the exact solution satisfies some linear differential system including a positive solution of an Abel differential equation.