Mathematical Analysis of a SEIR Model with Nonlinear Incidence Rate for COVID-19 Dynamics
Eid Alhmadi *
General Studies Department, Technical College, Technical and Vocational Training Corporation, Jeddah, Saudi Arabia.
*Author to whom correspondence should be addressed.
Abstract
In this paper, an SEIR epidemic model with nonlinear incidence is considered. First, we formulate the model and obtain its basic properties. Then, we find the equilibrium points of the model, the disease-free and the endemic equilibrium. The stability of disease-free and endemic equilibrium is associated with the basic reproduction number R. If the basic reproduction number \(\mathcal{R}\) < 1, the disease-free equilibrium \(\mathcal{E}\) is locally as well as globally asymptotically stable. Moreover, if the basic reproduction number \(\mathcal{R}\) > 1, the disease is uniformly persistent and the unique endemic equilibrium \(\mathcal{E}\) * of the system is locally as well as globally asymptotically stable under certain conditions. Finally, the numerical results justify the analytical results.
Keywords: SEIR epidemic model, nonlinear incidence rate, local stability, global stability, Lyapunov function, LaSalle's invariance principle