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Exact solutions of the SEIR epidemic model are derived, and variousproperties of solutions are obtained directly from the exact solution. In thispaper Abel differential equations play an important role in establishing theexact solution of SEIR differential system, in particular the number ofinfected individuals can be represented in a simple form by using a positivesolution of an Abel differential equation. It is shown that the parametric formof the exact solution satisfies some linear differential system including apositive solution of an Abel differential equation.

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