Abstract—In this paper, we consider an epidemic model with the infectious force in the latent and recovered period and establish the SEIR epidemic model with standard incidence rate. Then, we find the basic reproduction number R₀ which determines whether the disease exists. By using Liapunov function method, we prove that the disease-free equilibrium E₀ is globally asymptotically stable and the disease goes away when R₀ <1. By Hurwitz criterion, we also prove that E₀ is unstable and the unique endemic equilibrium E* is locally asymptotically stable when R₀ <1 . It is shown that when disease-induced death rate and elimination rate are zero, E* is globally asymptotically stable and the disease persists. Finally, we give numerical simulation to illustrate the theoretical analysis.

Index Terms—Basic reproductive number, equilibrium, stability, SEIR epidemic model, numerical simulation.

Yanli Ma is with Department of Common Course, Anhui Xinhua University, Hefei Anhui 230088, China (email: Linda-mayanli@163.com).

Cite: Yanli Ma, "Global Dynamics of an SEIR Model with Infectious Force in Latent and Recovered Period and Standard Incidence Rate," International Journal of Applied Physics and Mathematics vol. 7, no. 1, pp. 1-11, 2017.