Abstract—In this paper, the effect of time delay on an SEIR epidemic model with saturated incidence rate is investigated. The model has two equilibria, namely, a disease-free equilibrium and an endemic equilibrium. The threshold value of the model, which is called the basic reproduction number, is derived. The results show that for any time delay if the basic reproduction number is less than unity, the disease-free equilibrium is locally asymptotically stable whereas if it is greater than unity, the endemic equilibrium is locally asymptotically stable. Numerical simulations are presented to illustrate the analytical results.

Index Terms—SEIR model, saturated incidence, time delay, stability.

The authors are with the Department of Mathematics, King Mongkut’s University of Technology Thonburi, Bangkok 10140 Thailand (e-mail: sira.tjs@gmail.com, iwirwong@kmutt.ac.th).

Cite: Sirachat Tipsri and Wirawan Chinviriyasit, "Stability Analysis of SEIR Model with Saturated Incidence and Time Delay," International Journal of Applied Physics and Mathematics vol. 4, no. 1, pp. 42-45, 2014.