Skip to main content

Advertisement

SpringerLink
Log in

HIV/AIDS Model with Delay and the Effects of Stochasticity

  • Published:
Journal of Mathematical Modelling and Algorithms

Abstract

We present a deterministic HIV/AIDS model with delay. We then extend the model by adjoining terms capturing stochastic effects. The intensity of the fluctuations in the stochastic system is analytically evaluated using Fourier transform methods. We carry out simulations to assess differences in the dynamical behavior of the deterministic and stochastic models. Simulation results show that they are no significant differences in the behavior of the two models.

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

Access this article

Log in via an institution

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. Anderson, R.M., Gupta, S., May, R.M.: Potential of community-wide chemotherapy or immunotherapy to control the spread of HIV-1. Nature 350(6316), 356–359 (1991)

    Article  Google Scholar 

  2. Horsthemke, W., Lefever, R.: Noise Induced Transitions. Springer, Berlin (1984)

    MATH  Google Scholar 

  3. Hsu Schmitz, S.F.: A mathematical model of HIV transmission in homosexuals with genetic heterogeneity. J. Theor. Med. 2, 285–296 (2000)

    Article  MATH  Google Scholar 

  4. Hsu Schmitz, S.F.: Effects of treatment or/and vaccination on HIV transmission in homosexuals with genetic heterogeneity. Math. Biosci. 167(1), 1–18 (2000)

    Article  MATH  Google Scholar 

  5. Gardiner, C.W.: Handbook of Stochastic Methods. Springer New York (1983)

    MATH  Google Scholar 

  6. Kurtz, T.G.: Solutions of ordinary differential equation as limits of pure jumps Markov process. J. Appl. Probab. 7, 49–58 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  7. Kurtz, T.G.: Limit theorems for sequences of jump Markov processes approximating differential equations. J. Appl. Probab. 8, 344–356 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  8. May, R.M., Anderson, R.M.: Transmission dynamics of HIV infection. Nature 326, 137–142 (1987)

    Article  Google Scholar 

  9. May, R.M.: Stability and Complexity in Model Ecosystems. Princeton University Press, Princeton (1974)

    Google Scholar 

  10. Mukandavire, Z., Garira, W., Chiyaka, C.: Asymptotic properties of an HIV/AIDS model with a time delay. J. Math. Anal. Appl. 330(2), 916–933 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. Nisbet, R.M., Gurney, W.S.C.: Modelling Fluctuating Populations. Wiley-Interscience (1982)

  12. Renshaw, E.: Modelling Biological Population in Space and Time. Cambridge University Press, Cambridge (1995)

    Google Scholar 

  13. Samanta, G.P.: The effect of random fluctuating environment on interacting species with time delay. Int. J. Math. Educ. Sci. Technol. 27, 13–21 (1996)

    Article  MATH  Google Scholar 

  14. Samanta, G.P.: Permanence and extinction of a nonautonomous HIV/AIDS epidemic model with distributed time delay. Nonlinear Anal.: Real World Appl. 12(2), 1163–1177 (2011). doi:10.1016/j.nonrwa.2010.09.010

    Article  MathSciNet  MATH  Google Scholar 

  15. Samanta, G.P.: Analysis of a nonautonomous HIV/AIDS epidemic model with distributed time delay. Math. Model. Anal. 15(3), 327–347 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  16. Samanta, G.P.: Analysis of a nonautonomous HIV/AIDS model. Math. Model. Nat. Phenomena 5(6), 70–95 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  17. Turelli, M.: Stochastic community theory: a partially guided tour. In: Hallam, T.G., Levin, S. (eds.) Mathematical Ecology. Springer, Berlin (1986)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Emerging Pathogens Institute, University of Florida, Gainesville, FL, 32610, USA

    Z. Mukandavire & C. Chiyaka

  2. The Kidderpore Academy, 35 Ramkamal Street, Kolkata, 700 023, India

    P. Das

  3. St. Xavier’s College, 30, Park Street, Kolkata, 700 016, India

    N. H. Gazi

  4. School of Advanced Sciences, Department of Mathematics, VIT University, Vellor, 632 014, Tamil Nadu, India

    K. Das

  5. School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg, South Africa

    T. Shiri

Authors
  1. Z. Mukandavire
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Das
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. Chiyaka
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. N. H. Gazi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. K. Das
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. T. Shiri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Z. Mukandavire.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mukandavire, Z., Das, P., Chiyaka, C. et al. HIV/AIDS Model with Delay and the Effects of Stochasticity. J Math Model Algor 10, 181–191 (2011). https://doi.org/10.1007/s10852-010-9148-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10852-010-9148-7

Keywords

Mathematics Subject Classifications (2000)

Search

Navigation