Nonintegrability of the SEIR epidemic model

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