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3.2
Introduction of Drug Therapy into the DTHI Model
In the previous sections we introduced new rules to model the response of the
system to drug therapy. In figure 4 four different time scales (weeks and years)
can be observed. The data shown were averaged over 500 simulations. The first
acute phase indicates the fast proliferation of the original HIV strains before the
actual immune system response. This phase ends when specific immune response
occurs for these strains. The next phase, the chronic phase that takes years, is
the phase where the viral load increases slowly and CD4 counts decrease slowly.
When CD4 T counts drop to a certain level (normal 200 to 500 counts per ml),
the drug therapy is started. In this phase, virus replication is blocked and CD4
T counts increase. Once resistant strains against the drugs evolve, the last phase
of the disease occurs disrupting the whole immune system.
CD4+T
1
0.8
0.6
0.4
0.2
weeks
100
200
300
400
500
600
Fig. 4. Four-phase dynamics with two time scales (weeks and years) were obtained,
which were qualitatively comparable with clinical data. The solid, hash and hash-dot
lines represent healthy, infected (A1 and A2) and dead cells respectively. The vertical
hash line indicates the startingpoint of the therapy. The profile indicated that after
primary response, the CD4 T cells decreased gradually in the latency period. Once
the therapy started, CD4 T cell count increased due to the drugtherapy. Finally they
evolved into AIDS state due to the resistance against drug.
Our simulation results indicate that the extension of long-term survival is
dependent on the drug effectiveness ( N ) and the response function ( P resp ). The
high quality of the drug (modelled by small N ) e A ciently prevents the virus from
replication, and thus few resistant new viruses are generated. As a consequence,
a relatively prolonged long-term survival is obtained such as shown for N =0
in Fig. 5. We can also simulate HAART treatment by selecting a suitable P resp
response function in our model such as P resp 2 and P resp 3 in Fig. 6.
In our simulation model, we get insights into local behaviour and spatial
structures. Two typical spatial structures wave-like (left structure) and solid-like
structures (right structure) are shown in Fig. 7a. The solid-like structures spread
in all directions and wave-like structures generate a propagating front wave with
width τ +1.” After the therapy started, original spatial structures disappeared
 
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