Cellular Automata Model of Drug Therapy for HIV Infection - Cellular Automata - page 292

biologically more relevant response functions into the model. This future work
requires in depth investigation of the parameter space of P resp .
The results from Fig. 3 with respect to the amount of CD4 T counts are
not completely supported by clinical data. The number of CD4 T cells should
completely go down at least to a level that is undetectable. We will investigate
the influence of P resp on the steady state in our model. The chosen value of
P HIV in this paper ( P HIV = 0.05) is too large with respect to data known
for clinic. Amore realistic value would be 1 infected cell per 10 2 to 10 3 cells,
resulting in P HIV = 0.005. This effect will also be investigated. Clinical data
indicate a increased sensitivity of T-cells over time, probably due to activation
of the immune system. This will be modelled by making P infec a function of the
number of infected cells. Finally, it is known that in the early stages of infection,
virus replication is confined to monocytic white blood cells. Only in later stages,
CD4Tcellswillbecomethenewtargetcells.Thistrophysmeffectwillbestudied
in the future.
Acknowledgement. The authors would like to thank the anonymous referees
for many valuable comments and suggestions that have improved the quality of
this paper. We also like to thanks suggestions of Roeland Merks.
References
1. M.A. Fischl, D.D. Richman, Hansen. N., A.C. Collier, J.T. Carey, M.F. Para, W.D.
Hardy, R. Dolin, W.G. Powderly, J.D. Allan, and et al. The safety and e * cacy of
azt in the treatment of subjects with mildly symptomatic HIV type 1. Annals Int.
Med. , pages 727-737, 1990.
2. U. Hershberg, Y. Louzoun, H. Atlan, and S. Solomon. HIV time hierarchy: Winning
the war while, loosingall the battles. Physica. , pages 178-190, 2001.
3. D. E. Kirschner and G. F. Webb. A mathematical model of combined drugtherapy
of HIV infection. J. Theoret. Med. , pages 25-34, 1997.
4. D. E. Kirschner and G. F. Webb. Understandingdrugresistance for mono-therapy
treatment of HIV infection. Bull. Math. Biol. , pages 763-185, 1997.
5. A. Mielke and R. B. Pandey. A computer simulation study of cell population in a
fuzzy interaction model for mutatingHIV. Physica A , 251:430-438, 1998.
6. A. S. Perelson. Modellingthe interaction of the immune system with HIV. In:
C. Caastillo-Chavez (ed): Mathematical and Statistical Approaches to AIDS Epi-
dermiology. Lecture Notes in Biomathematics, Springer-Verlag , 83:350-370, 1989.
7. N. Stilianakis, C.A.B. Boucher, M.D. De Jong, R. Van Leeuwen, R. Schuurman, and
R.J. De Boer. Clinical data sets of HIV-1 reverse transcriptase-resistant mutants
explained by a mathematical model. J. of Virol. , pages 161-168, 1997.
8. T. Toffoli and N. Margolus. Cellular Automata Machines . Cambridge, Mas-
sachusetts: The MIT Press, 1987.
9. S. Vella, M. Giuliano, L.G. Dally, M.G. Agresti, C. Tomino, M. Floridia, A. Chiesi,
V. Fragola, M. Moroni, M. Piazza, and et al. Long-term follow-up of zidovudine
therapy in asymptomatic HIV infection: results of a multicenter cohort study. J.
AIDS. , pages 31-38, 1994.
10. D. Verotta and F. Schaedeli. Non-linear dynamics models characterisinglong- term
virological data from aids clinical trials. Math. Biosci. , pages 1-21, 2002.