The first integrals and closed-form solutions of a Susceptible-Exposed-Infectious epidemic model

The closed-form solutions of Susceptible-Exposed-Infectious (SEI) epidemic model are constructed for two different scenarios. The SEI model is governed by a dynamical system of three first-order ordinary differential equations (ODEs). The dynamical system of three ODEs converts to a second-order ODE in terms of only one variable for the specific restrictions on the parameters. Two scenarios are considered. For both scenarios, the multiplier approach yields two first integrals. We utilize these first integrals to establish the closed-form solutions of SEI model for these two scenarios.