Skip to main content

Advertisement

Log in

Existence and Uniqueness of Endemic States for the Age-Structured Seir Epidemic Model

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

An age-structured SEIR epidemic model of a vertically as well as horizontally transmitted disease is investigated. Threshold results for the existence of endemic states are established for most cases. Under certain conditions, uniqueness is also shown. Threshold used are explicitly computable in term of demographic and epidemiological parameters of the model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P. E. M. Fine, Vectors and vertical transmission: An epidemiologic perspective, Annals N. Y. Academic Sci., 1979, 266: 173–194.

    Google Scholar 

  2. S. N. Busenberg and K. L. Cooke, Vertically Transmitted Diseases: Models and Dynamics, Biomathematics, V. 23, Springer-Verlag, Berlin, 1993.

  3. S. N. Busenberg and K. L. Cooke, The population dynamics of two vertically transmitted infections, Theor. Popul. Biol., 1988, 33(2): 181–198.

    Google Scholar 

  4. M. EI-Doma, Analysis of a general age-dependent vaccination model for a vertically transmitted diseases, Nonlinear Times and Digest, 1995, 2: 147–172.

    Google Scholar 

  5. R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford, 1991.

    Google Scholar 

  6. Y. Cha, M. Iannelli and E. Milner, Existence and uniqueness of endemic states for the age-structured SIR epidemic model, Math. Biosci., 1998, 150: 177–190.

    Article  Google Scholar 

  7. M. EI-Doma, Analysis of an age-dependent SIS epidemic model with vertical transmission and proportionate mixing assumption, Math. Comput. Model., 1999, 29: 31–43.

    Google Scholar 

  8. D. Greenhalgh, Analytical threshold and stability results on age-structured epidemic models with vaccination, Theor. Popul. Biol., 1988, 33: 266–290.

    Google Scholar 

  9. M. Iannelli, F. Milner and A. Pugliese, Analytical and numerical results for the age-structured S-I-S epidemic model with mixed inter-intracohort transmission, SIAM J. Math. Anal., 1992, 23(3): 662–688.

    Article  Google Scholar 

  10. M. Iannelli, M. Y. Kim and E. J. Park, Asymptotic behavior for an SIS epidemic model and its approximation, Nonlinear Analysis, 1997, 35: 797–814.

    Google Scholar 

  11. H. Inaba, Threshold and stability results for an age-structured epidemic model, J. Math. Biol., 1990, 28: 149–175.

    Article  Google Scholar 

  12. Xue-Zhi Li, Geni Gupur and Guang-Tian Zhu, Threshold and stability results for an age-structured SEIR epidemic model, Comput. Math. Appl., 2001, 42: 883–907.

    Google Scholar 

  13. D. W. Tudor, An age-dependent epidemic model with applications to measles, Math. Biosci., 1985, 73: 131–147.

    Article  Google Scholar 

  14. G. F. Webb, Theory of Nonlinear-Dependent Population Dynamics, New York and Basel, Marcel Dekker, 1985.

    Google Scholar 

  15. K. L. Cooke, P. Van Den Driessche, Analysis of an SEIRS epidemic model with two delays, J. Math. Biol., 1996, 35: 240–258.

    Article  Google Scholar 

  16. M. Y. Li, J. R. Graef, Liancheng Wang and J. Karsai, Global dynamics of an SEIR model with varying total population size, Math. Biosci., 1999, 160: 791–213.

    Article  Google Scholar 

  17. M. Y. Li and J. S. Muldowney, Global stability for the SEIR model in epidemiology, Math. Biosci., 1995, 125: 155–167.

    Article  Google Scholar 

  18. H. M. Yang, Directly transmitted infections modeling considering an age-structured contact rate, Math. Comput. Model., 1999, 29: 39–48.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xuezhi LI.

Additional information

Supported by the Natural Science Foundation of Henan Province (No. 0312002000 and No. 0211044800) and the National Natural Science Foundation of China (No. 10371105).

Rights and permissions

Reprints and permissions

About this article

Cite this article

LI, X., CHEN, J. Existence and Uniqueness of Endemic States for the Age-Structured Seir Epidemic Model. Jrl Syst Sci & Complex 19, 114–127 (2006). https://doi.org/10.1007/s11424-006-0114-4

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-006-0114-4

Key Words

Navigation