Skip to main content

Numerical Simulation Method for the SIV Epidemic Model with Impulsive Vaccination and Infection-Age

  • Conference paper
  • 1816 Accesses

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 308))

Abstract

In the process of theoretical analysis of dynamic model of epidemic, using computers for simulation is also a vital research method. However, considering SIV epidemic model with impulsive vaccination and infection-age is a kind of model which has integro-differential initial-boundary value problem with pulse. Its theoretical analysis is relatively complicated. Therefore, taking advantage of implicit Euler, the low order formula of Newton-Cotes method and finite differences may lead to a new numerical simulation method. Numerical results show that this method is effective and possesses potential value of application.

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

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. World Health Organization: Global Tuberculosis Control, WHO report, World Health Organization. Geneva Switzerland (2006)

    Google Scholar 

  2. Brertta, E., Yang, K.: Geometric Stability Switch Criteria in Delay Differential Equations Systems with Delay Dependent Parameters. SIAM J. Math. Anal. 5, 1144–1165 (2002)

    Article  Google Scholar 

  3. Jiandong, M., Wei, W.: Nonlinear Numerical Method for Stiff Systems. In: International Conference on Computer Application and System Modeling, pp. 437–439. IEEE Press, New York (2010)

    Google Scholar 

  4. Blower, S.M., Gerberding, J.L.: Understanding, Predicting and Controlling the Emergence of Drug-resistant Tuberculosis: A Theoretical Framework. J. Mol. Med. 76, 624–636 (1998)

    Article  Google Scholar 

  5. Feng, Z., Huang, Castillo-Chavez, W.C.: On the Role of Variable Latent Periods in Mathematical Models for Tuberculosis. J. Dynam. Differential Equations. 13, 425–452 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  6. Feng, Z., Thieme, H.R.: Endemic Models with Arbitrarily Distributed Periods of Infection II: Fast Disease Dynamics and Permanent Recovery. SIAM J. Appl. Math. 61, 983–1012 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  7. Feng, Z., Iannelli, M.: A Two-Strain Tuberculosis Model with Age of Infection. SIAM J. Appl. Math. 62, 1634–1656 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Milner, F.A., Pugliese, A.: Periodic solutions: a robust numerical method for an SIR model of epidemics. J. Math. Biol. 39, 471–492 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  9. da Cruz, A.R., Cardoso, R.T.N., Takahashi, R.H.C.: Multiobjective Dynamic Optimization of Vaccination Campaigns Using Convex Quadratic Approximation Local Search. In: Takahashi, R.H.C., Deb, K., Wanner, E.F., Greco, S. (eds.) EMO 2011. LNCS, vol. 6576, pp. 404–417. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  10. Xueyong, Z., Jingan, C.: Analysis of Stability and Bifurcation for An SEIV Epidemic Model with Vaccination and Nonlinear Incidence Rate. Nonlinear Dyn. 63, 639–653 (2011)

    Article  Google Scholar 

  11. Xiaobing, Z., Haifeng, H.: The Differential Susceptibility SIR Epidemic Model with Time Delay and Pulse Vaccination. J. App. Math. Comp. 34, 287–298 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wei, W. (2012). Numerical Simulation Method for the SIV Epidemic Model with Impulsive Vaccination and Infection-Age. In: Liu, C., Wang, L., Yang, A. (eds) Information Computing and Applications. ICICA 2012. Communications in Computer and Information Science, vol 308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34041-3_75

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-34041-3_75

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34040-6

  • Online ISBN: 978-3-642-34041-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics