Mathematical Biosciences and Engineering, 2013, 10(5&6): 1399-1417. doi: 10.3934/mbe.2013.10.1399.

Primary: 37N25, 37G10; Secondary: 92B05.

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection

1. Department of Mathematics, Shaanxi University of Science & Technology, Xi'an, 710021
2. Department of Mathematics, Xi'an Jiaotong University, Xi'an, 710049
3. Department of Mathematics, Xi’an Jiaotong University, Xi’an, 710049

A discrete SIS epidemic model with the bilinear incidence depending on the new infection is formulated and studied.The condition for the global stability of the disease free equilibrium is obtained.The existence of the endemic equilibrium and its stability are investigated.More attention is paid to the existence of the saddle-node bifurcation, the flip bifurcation, and the Hopf bifurcation.Sufficient conditions for those bifurcations have been obtained.Numerical simulations are conducted to demonstrate our theoretical results and the complexity of the model.
  Figure/Table
  Supplementary
  Article Metrics

Keywords Hopf bifurcation.; bilinear incidence; flip bifurcation; saddle-Node bifurcation; Discrete SIS model

Citation: Hui Cao, Yicang Zhou, Zhien Ma. Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection. Mathematical Biosciences and Engineering, 2013, 10(5&6): 1399-1417. doi: 10.3934/mbe.2013.10.1399

References

  • 1. Math. Biosci., 124 (1994), 83-105.
  • 2. Math. Biosci., 163 (2000), 1-33.
  • 3. J. Differ. Equ. Appl., 14 (2008), 1127-1147.
  • 4. Available from: http://mtbi.asu.edu/files/Discrete_time_SEIS_Models_with_Exogenous_Reinfection_and_Dispersal_between_Two_Patches.pdf.
  • 5. Numer. Funct. Anal. Optimiz., 9 (1987), 381-414.
  • 6. Math. Model. Appl., 1 (2012), 33-37.
  • 7. INT. J. Bio., 5 (2012), 61-76.
  • 8. Math. Comput. Model., 55 (2012), 385-395.
  • 9. Discrete Cont. Dyn. Sys. B, 18 (2013), 37-56.
  • 10. Discrete Dyn. Nat. Soc., (2011), Art. ID 653937, 21 pp.
  • 11. Nonliear Anal. TMA, 47 (2001), 4753-4762.
  • 12. in "Mathematical Approaches for Emerging and Reemerging Infectious Diseases: A introduction" (eds. C. Castillo-Chavez with S. Blower, P. van den Driessche, D. Kirschner and A. A. Yakubu), Springer-Verlag, New York, (2002), 153-163.
  • 13. Chaos Soliton. Fract., 40 (2009), 1956-1962.
  • 14. SIAM J. Appl. Math., 66 (2006), 1563-1587.
  • 15. MTBI technical Report, 2000.
  • 16. Research in Economics, 62 (2008), 120-177.
  • 17. Springer, New York, 1983.
  • 18. J. Anim. Ecol., 44 (1975), 283-289.
  • 19. Nonlinear Anal. RWA, 13 (2012), 2017-2033.
  • 20. Nonlinear Anal. RWA, 12 (2011), 2356-2377.
  • 21. Appl. Math. Comput., 216 (2010), 1226-1234.
  • 22. Chaos Solution. Fract., 26 (2005), 947-958.
  • 23. J. Theor. Biol., 51 (1975), 511-524.
  • 24. Nature, 256 (1975), 165-166.
  • 25. Nature, 261 (1976), 459-467.
  • 26. J. Math. Biol., 30 (1992), 755-763.
  • 27. Comm. Appl. Nonl. Anal., 3 (1996), 43-66.
  • 28. in "A Survey of Mathematical Biology, Fields Communications Series" (ed. S. Sivaloganathan), 57, A co-publication of the AMS and Fields Institute, Canada, (2010), 83-112.
  • 29. J. Theor. Biol., 254 (2008), 215-228.
  • 30. Math. Biosci. Eng., 6 (2009), 409-425.
  • 31. Math. Comput. Model., 40 (2004), 1491-1506.
  • 32. Discrete Cont. Dyn. Sys. B, 4 (2004), 843-852.

 

This article has been cited by

  • 1. Yingying Zhang, Yicang Zhou, The Bifurcation of Two Invariant Closed Curves in a Discrete Model, Discrete Dynamics in Nature and Society, 2018, 2018, 1, 10.1155/2018/1613709
  • 2. Wei Tan, Jianguo Gao, Wenjun Fan, Bifurcation Analysis and Chaos Control in a Discrete Epidemic System, Discrete Dynamics in Nature and Society, 2015, 2015, 1, 10.1155/2015/974868
  • 3. S.M. Salman, E. Ahmed, A mathematical model for Creutzfeldt Jacob Disease (CJD), Chaos, Solitons & Fractals, 2018, 116, 249, 10.1016/j.chaos.2018.09.041
  • 4. Jianglin Zhao, Yong Yan, Stability and bifurcation analysis of a discrete predator–prey system with modified Holling–Tanner functional response, Advances in Difference Equations, 2018, 2018, 1, 10.1186/s13662-018-1819-0

Reader Comments

your name: *   your email: *  

Copyright Info: 2013, Hui Cao, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved