Skip to main content
SpringerLink
Log in

Asymptotical Stability of an SEIS Epidemic Model with Latent Age Dependence and Generally Nonlinear Contact Rate

  • Conference paper
Advances in Neural Networks – ISNN 2011 (ISNN 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6675))

Included in the following conference series:

  • 1849 Accesses

Abstract

In this paper, an SEIS epidemic model with latent age and generally nonlinear contact rate is formulated. The existence and asymptotic stability of equilibrium are discussed, respectively. In the same time, a general condition is obtained by the similar method utilized in [12], under which the endemic equilibrium is exponentially asymptotically stable. At last, a special example is presented to verified this condition.

2000 Mathematics Subject Classifications: 34D20; 34D23; 45D05; 44A10. This work was supported by Mathematics Tianyuan Funds of NSFC (No:11026133);Scientific Research Plan Projects of Shaanxi Education Department (No.09JK601), National Science Foundation for Post-doctoral Scientists of China (No.20090461281), Training Fund of Xi’an University of Science and Technology under the contract 200836 and the Dr. Start-up Fund of Xi’an University of Science and Technology.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Castillo-Chavez, C., Hethcote, H.W., Andreasen, V., Levin, S.A., Liu, W.M.: Epidemiological models with age structure, proportionate mixing, and cross-immunity. J. Math. Biol. 27, 233–258 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  2. Hethcote, H.W., Yorke, J.A.: Gonorrhea transmission dynamics and control. LNCS (LNBI). Springer, Berlin (1984)

    Book  MATH  Google Scholar 

  3. Francis, D.P., Feorino, P.M., Broderson, J.R., Mccluer, H.M., Getchell, J.P., Mcgrath, C.R., Swenson, B., Mcdugal, J.S., Palmer, E.L., Harrison, A.K., et al.: Infection of chimpanzees with lymphadenopathy-associated virus. Lancet. 2, 1276–1277 (1984)

    Article  Google Scholar 

  4. Lange, J.M., Paul, D.A., Huisman, H.G., De Wolf, F., Van den Berg, H., et al.: Persistent HIV antigenaemia and decline of HIV core antibodies associated with transition to AIDS. British Medical J. 293, 1459–1462 (1986)

    Article  Google Scholar 

  5. Kermack, W.O., Mckendrick, A.G.: A contribution to the mathematical theory of epidemics. Proc. Roy. Soc. Lond Ser. A 115, 700–721 (1927)

    Article  MATH  Google Scholar 

  6. Mckendrick, A.G.: Applications of mathematics to medical problems. Proc. Edinburgh Math. Soc. 44, 98–130 (1926)

    Article  Google Scholar 

  7. Kermack, W.O., Mckendrick, A.G.: Contributions to the mathematical theory of epidemics.II. The problem of endemictity. Proc. Roy. Soc. Lond Ser. A 138, 55–83 (1932)

    Article  MATH  Google Scholar 

  8. Kermack, W.O., Mckendrick, A.G.: Contributions to the mathematical theory of epidemics.III. Further studies of the provlem of endemicity. Proc. Roy. Soc. Lond Ser. A 141, 94–122 (1932)

    Article  MATH  Google Scholar 

  9. Hoppensteadt, F.: An age dependent epidemic model. J. Franklin Inst. 297, 325–333 (1974)

    Article  MATH  Google Scholar 

  10. Hoppensteadt, F.: Mathematical theories of populations: demographics, genetics and epidemics. In: Regional Conference Deries in Applied Mathematics. Society for industrial and applied mathematics, Philadelphia (1975)

    Google Scholar 

  11. Kim, M.Y., Milner, F.A.: A mathematical model of epidmimcs with screening and variable infectivity. Mathl. Comput. Modelling 21, 29–42 (1995)

    Article  MATH  Google Scholar 

  12. Kim, M.Y.: Existence of steady state solutions to an epidemic model with screening and their asymptotic stability. Appl. Math. Comput. 74, 37–58 (1974)

    MathSciNet  MATH  Google Scholar 

  13. Thieme, H.R., Castillo-Chavez, C.: How infection-age-dependent infectivity affect the dynamics of HIV/AIDS? Siam J Appl. Math. 53, 1447–1479 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  14. Kribs-Zaleta, C.M., Martcheva, M.: Vaccination strategies and backward bifurcation in an age-since-infection structured model. Math. Biosci. 177/178, 317–332 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  15. Inaba, H., Sekine, H.: A mathematical model for Chagas disease wtih infection-age-dependent infectivity. Math. Biosci. 190, 39–69 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  16. Li, J., Zhou, Y.C., Ma, Z.Z., Hyman, M.: Epedemiological models for mutating pathogens. Siam J. Appl. Math. 65, 1–23 (2004)

    Article  MATH  Google Scholar 

  17. Fan, M., Li, M.Y., Wang, K.: Global stability of an SEIS epidemic model with recruitment and a varying total population size. Mathematical Biosciences 170, 199–208 (2001)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Sciences, Xi’an University of Science and Technology, Xi’an, Shaanxi, 710054, China

    Yeling Liu & Zhonghua Zhang

Authors
  1. Yeling Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhonghua Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Automation, Key Laboratory of Complex Systems and Intelligence Science, Chinese Academy of Sciences, 100190, Beijing, China

    Derong Liu

  2. College of Information Science and Engineering, Shenyang, Northeastern University, 110004, Liaoing, China

    Huaguang Zhang

  3. Department of Electrical and Computer Engineering, University of Cyprus, 75 Kallipoleos Avenue, 1678, Nicosia, Cyprus

    Marios Polycarpou

  4. Dipartimento di Elettronica, Politecnico di Milano, Piazza L. da Vinci 32, 20133, Milano, Italy

    Cesare Alippi

  5. Deptartment of Electrical, Computer and Biomedical Engineering, University of Rhode Island, RI 02881, Kingston, USA

    Haibo He

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Liu, Y., Zhang, Z. (2011). Asymptotical Stability of an SEIS Epidemic Model with Latent Age Dependence and Generally Nonlinear Contact Rate. In: Liu, D., Zhang, H., Polycarpou, M., Alippi, C., He, H. (eds) Advances in Neural Networks – ISNN 2011. ISNN 2011. Lecture Notes in Computer Science, vol 6675. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21105-8_42

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-21105-8_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21104-1

  • Online ISBN: 978-3-642-21105-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation