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Stability analysis of infectious diseases model in a dynamic population

Year 2018, Volume: 3 Issue: 3, 37 - 43, 31.12.2018

Joseph A. Akinyemi Micheal O. Adeniyi Angela U. Chukwu

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

References

  • [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] 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] C. Vargas-De-Leon (2013): On the global stability of infectious diseases models with relapse ; Abstraction & Application 9 pp 50-61.
  • [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] 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] Rajinder Sharma (2014): Stability Analysis of Infectious Diseases with Media coverage and Poverty: Mathematical Theory and Modelling V(4).
  • [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] 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] Zack Yarus (2012): A Mathematical look at the Ebola virus. Published online. May 11 2012.

Year 2018, Volume: 3 Issue: 3, 37 - 43, 31.12.2018

Joseph A. Akinyemi Micheal O. Adeniyi Angela U. Chukwu

Abstract

References

  • [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] 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] C. Vargas-De-Leon (2013): On the global stability of infectious diseases models with relapse ; Abstraction & Application 9 pp 50-61.
  • [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] 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] Rajinder Sharma (2014): Stability Analysis of Infectious Diseases with Media coverage and Poverty: Mathematical Theory and Modelling V(4).
  • [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] 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] Zack Yarus (2012): A Mathematical look at the Ebola virus. Published online. May 11 2012.
There are 9 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Joseph A. Akinyemi This is me

Micheal O. Adeniyi This is me

Angela U. Chukwu This is me

Publication Date December 31, 2018
Published in Issue Year 2018 Volume: 3 Issue: 3

Cite

APA Akinyemi, J. A., Adeniyi, M. O., & Chukwu, A. U. (2018). Stability analysis of infectious diseases model in a dynamic population. Communication in Mathematical Modeling and Applications, 3(3), 37-43.
AMA Akinyemi JA, Adeniyi MO, Chukwu AU. Stability analysis of infectious diseases model in a dynamic population. CMMA. December 2018;3(3):37-43.
Chicago Akinyemi, Joseph A., Micheal O. Adeniyi, and Angela U. Chukwu. “Stability Analysis of Infectious Diseases Model in a Dynamic Population”. Communication in Mathematical Modeling and Applications 3, no. 3 (December 2018): 37-43.
EndNote Akinyemi JA, Adeniyi MO, Chukwu AU (December 1, 2018) Stability analysis of infectious diseases model in a dynamic population. Communication in Mathematical Modeling and Applications 3 3 37–43.
IEEE J. A. Akinyemi, M. O. Adeniyi, and A. U. Chukwu, “Stability analysis of infectious diseases model in a dynamic population”, CMMA, vol. 3, no. 3, pp. 37–43, 2018.
ISNAD Akinyemi, Joseph A. et al. “Stability Analysis of Infectious Diseases Model in a Dynamic Population”. Communication in Mathematical Modeling and Applications 3/3 (December 2018), 37-43.
JAMA Akinyemi JA, Adeniyi MO, Chukwu AU. Stability analysis of infectious diseases model in a dynamic population. CMMA. 2018;3:37–43.
MLA Akinyemi, Joseph A. et al. “Stability Analysis of Infectious Diseases Model in a Dynamic Population”. Communication in Mathematical Modeling and Applications, vol. 3, no. 3, 2018, pp. 37-43.
Vancouver Akinyemi JA, Adeniyi MO, Chukwu AU. Stability analysis of infectious diseases model in a dynamic population. CMMA. 2018;3(3):37-43.
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