Stability analysis of infectious diseases model in a dynamic population

Abstract

The stability analysis of infectious disease model in a dynamic population is studied.The recruitment rate into the susceptible
population is introduced since the population is dynamic thereby allowing a varying pouplation as a result of migration and birth.The
model exhibited two equilibria: the disease free and endemic. The local stability of the model is asymptotically stable when R0 < 1 and
unstable when R0 > 1. The global stability analysis of the disease free shows that the system is globally stable when the first derivative
of Lyapunov function is negative.

Keywords

• Basic Reproduction Number,dynamic population,asymptotically stable,Lyapunov function

Kaynakça

1. [1] A.A Momoh, M.O Ibrahim and B.A Madu (2011): Stability Analysis of an infectious disease free equilibrium of Hepatitis B model.Res.J. Applied sc,Eng and Tech 3(9):9005-9009.
2. [2] Chunqing Wu and Zhongy Jiang (2012): Global Stability for the Disease Free Equilibrium of a Delayed Model for Malaria Transmission:int J.Math anal;v (6)38 1877-1881.
3. [3] C. Vargas-De-Leon (2013): On the global stability of infectious diseases models with relapse ; Abstraction & Application 9 pp 50-61.
4. [4] Guihua Li, Zhan Jim (2005): Global Stability of a SEIR epidemic model infectious rate in latent, infected and immune period.Elsevier:25 1177-1184.
5. [5] Hongbin Guio, Micheal Y Li and Zhisheng S (2006): Global Stability of the Endemic Equilibrium of Multigroup SIR Epidemic Models Cen.App.Math V(14).
6. [6] Rajinder Sharma (2014): Stability Analysis of Infectious Diseases with Media coverage and Poverty: Mathematical Theory and Modelling V(4).
7. [7] XiaMa, Y cang Zhou and Hui Cao (2013): Global Stability of the endemic equilibrium of a discrete SIR epidemic Model. Advance difference equation 42.
8. [8] Yu Zhang Lequan MIN. YuJi. Yongmei Su, Yang K (2010): Global Stability of Endemic Equilibrium point of Basic virus Infection model with Application to HBV infection, Journal of Systems Science and Complexity, December 2010, Volume 23, Issue 6, pp 1221–1230.

9. [9] Zack Yarus (2012): A Mathematical look at the Ebola virus. Published online. May 11 2012.