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A note on the effects of replenishment of depleted cells on HIV infection dynamics: A graph-theoretic approach

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  • Mukwembi, Simon

Abstract

We study the effects of the rate of replacement of dead cells by either healthy cells or by infected cells on HIV infection dynamics through a graph-theoretic approach. Our framework takes into account a reasonable amount of the immune action to any pathogen and the local cell interactions that occur in the lymph nodes. Our results, in an extremal case where dead cells are highly likely to be replaced by healthy cells, show that all cells become healthy in a finite number of steps of given order and infection stops propagating. Further, for this extremal case, we give an algebraic formula for the number of infected cells at any given time in the HIV progression. We also find a sufficient condition, determined by dead cell replacement rate, which guarantees that an infected patient is continually positive, and give bounds on the number of infected, healthy and dead cells at any given time. We apply our theoretical results to a recently proposed model of the HIV infection dynamics.

Suggested Citation

  • Mukwembi, Simon, 2008. "A note on the effects of replenishment of depleted cells on HIV infection dynamics: A graph-theoretic approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1200-1204.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:5:p:1200-1204
    DOI: 10.1016/j.physa.2007.10.038
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    References listed on IDEAS

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    1. Benyoussef, A & HafidAllah, N.El & ElKenz, A & Ez-Zahraouy, H & Loulidi, M, 2003. "Dynamics of HIV infection on 2D cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 322(C), pages 506-520.
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    Cited by:

    1. Nyabadza, F. & Mukwembi, S. & Rodrigues, B.G., 2011. "A graph theoretical perspective of a drug abuse epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(10), pages 1723-1732.

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    Keywords

    Graph; Lymph node; HIV;
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