doi: 10.17706/ijapm.2017.7.1.1-11
Global Dynamics of an SEIR Model with Infectious Force in Latent and Recovered Period and Standard Incidence Rate
Yanli Ma
- Department of Common Course, Anhui Xinhua University, Hefei Anhui 230088, China
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 R<sub>0</sub> which determines whether the disease exists. By using Liapunov function method, we prove that the disease-free equilibrium <em>E</em><sub>0</sub> is globally asymptotically stable and the disease goes away when <em>R</em><sub>0</sub> <1. By Hurwitz criterion, we also prove that <em>E</em><sub>0</sub> is unstable and the unique endemic equilibrium <em>E</em>* is locally asymptotically stable when <em>R</em><sub>0</sub> <1 . It is shown that when disease-induced death rate and elimination rate are zero, <em>E</em>* is globally asymptotically stable and the disease persists. Finally, we give numerical simulation to illustrate the theoretical analysis.
Keywords
- Basic reproductive number
- equilibrium
- stability
- SEIR epidemic model
- numerical simulation
How to 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. https://doi.org/ 10.17706/ijapm.2017.7.1.1-11
Copyright & License
Copyright © 2017 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).