Global Stability Analysis for a Generalized SEIR Epidemic Model with Vaccination and Treatment

The aim of this work is to propose and investigate the global stability of a delayed SEIR epidemic model with a generalized incidence function. The proposed model also includes general treatment function and vaccination term. Using the Lyapunov functions in the absence of delay, we show that the disease-free steady state is globally asymptotically stable if R-0 <= 1, and the disease-endemic steady state is globally asymptotically stable if R-0 > 1, where R-0 is the basic reproduction number. For specific functions which are given to the treatment function and the incidence function, we show that the vaccination and early treatment play an important role in healing. Moreover, numerical simulations are given to illustrate and confirm our main analytical results. (c) 2025 L&H Scientific Publishing, LLC. All rights reserved.