We study a delayed SEIR epidemic model with constant recruitment by analysing the global stability of the disease-free via Lyapunov functional approach. For the endemic equilibrium, we adopt the geometric approach of Li and Muldowney and it is shown that this unique endemic equilibrium is stable. A disease threshold parameter  say, known as the basic reproduction number is derived: if  is less than or equal to unity, then by Lasalle invariance principle, the disease-free equilibrium  is globally asymptotically stable and the disease always dies out. Otherwise, if  is greater than unity, then a unique endemic equilibrium  exists and is globally asymptotically stable in the interior of the feasible region, and the disease persists if it is present initially.

SEIRepidemicmodel,globalstability,timedelay, Lyapunov function, equilibrium state, constant recruitment.