A Closed loop Replicated Virus Model with Effective Delay

Article Sidebar

PDF
Published: Mar 30, 2018
Keywords:
Steady state, Effective delay, Bifurcation, Free virus, infect

Main Article Content

Kanchana Kumnungkit*
Department of Mathematics and Computer Science, Faculty of Science, King Mongkut’s Institute of Technology LadKrabang, Bangkok, Thailand.

Abstract

 


We investigate some closed loops of a replicated virus model, to analyses a mathematical model for virus replication. A bifurcation analysis is performed to determine the ranges of parameter values that lead to a steady state. A Hopf bifurcation occurs of a critical value of the time delay for some ranges of parameters.


Keywords: Steady state, Effective delay, Bifurcation, Free virus, infect


Corresponding author: E-mail: [email protected]


 

Article Details

Issue
Vol. 6 No. 2a (2006)
Section
Original Research Articles

Copyright Transfer Statement

 The copyright of this article is transferred to Current Applied Science and Technology journal with effect if and when the article is accepted for publication. The copyright transfer covers the exclusive right to reproduce and distribute the article, including reprints, translations, photographic reproductions, electronic form (offline, online) or any other reproductions of similar nature.

 The author warrants that this contribution is original and that he/she has full power to make this grant. The author signs for and accepts responsibility for releasing this material on behalf of any and all co-authors.

Here is the link for download: Copyright transfer form.pdf

 

 

References

[1] Nowak, M.A. and Bangham, C.R.M. 1996 Population Dynamics of Immune Responses to Persistent Viruses. Science 272, 74-79.
[2] Tam, J. 1999 Delay Effect in a Model For Virus, IMA J of Mathematics Applied in Medicine and Biology, 16, 29-37.
[3] Murray, J.D. 2002, Mathematical Biology I:An introduction, Springer.
[4] Nowak, M.A. and May, R.M. 1991 Mathematical Biology of HIV Infections: Antigenic Variation and Diversity Theshold. Math. Biosci. 106, 1-21.
[5] Nowak, M.A. and Mclean, A.R. 1991 A Mathematical Model of Vaccination Against HIV to prevent the Development of AIDS, Proc. R. Soc. Lond B 246, 141-146.
[6] Khan, Q.J.A. and Greenhalgh, D. 1999 Hopf Bifurcation in Epidemic Models With a Time Delay in Vaccination, IMA J of Mathematics Applied in Medicine and Biology, 16, 113-142.
[7] Murray, J.D. 1977 Lectures on Nonlinear-Differential-Equation Models in Biology, Oxford University Press.
[8] Culshaw, R.V. and Ruan, S. 2000. A Delay Differential Equation Model of HIV Infection of CD4+ T-cells. Math. Biosci. 165, 27.
[9] Nelson, P.W., Murray, J.D. and Perelson, A.S., 2000, A Model of HIV-1 Pathogenesis That Includes an Intracellular Delay., Math Biosci. 163, 201.