Abstract
We prove the nonintegrability of the susceptible–exposed–infected–removed (SEIR) epidemic model in the Bogoyavlenskij sense. This property of the SEIR model is different from the more fundamental susceptible–infected–removed (SIR) model, which is Bogoyavlenskij-integrable. Our basic tool for the proof is an extension of the Morales–Ramis theory due to Ayoul and Zung. Moreover, we introduce three new state variables and extend the system to a six-dimensional system to treat transcendental first integrals and commutative vector fields. We also use the fact that the incomplete gamma function Γ(α,x) is not elementary for α⁄∈N, of which a proof is included.
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