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3 Results
3.1
DTHI Model Simulations
To repeat the HI model, we use the same parameters as reference [13], using a
Moore neighbourhood, periodic boundary conditions on a lattice of 700 sites,
initial infected A1 cells (with
P
HIV
= 0.05),
τ
= 4 and
R
= 4. Because the
delay parameter
τ
may vary from 2 to 6 weeks, and the number of infected-A2
neighbours vary from 3 to 7 due to some of threshold. In Fig. 3, we show the
densities of healthy, infected (A1 and A2) and dead cells using the modified Rule
3 with the other rules the same as in the HI paper. The results are averaged over
500 simulations. The variance which do not show in this paper is consistent with
Fig. 2 in reference [13]. The reason to do this modification of the Rule 3 comes
from two facts. Analytically, infected A2 cells will be only present transiently in
the lattice during execution of a set of rules if we don't modify Rule 3. Infected
A1 cells, however do have an opportunity to be present because of its related
τ
time steps. Moreover, there is hardly opportunity for Rule 1b to contribute. As
a consequence the evolution speed with which the cells enter the AIDS phase
is too fast, without correction and Rule 1b has no chance to be activated. Our
simulations show that the density of the dead cells in Fig. 3 are shifted one
time step with respected to the results shown in reference [13]. This results in a
required conservation of densities of healthy, infected and dead cells, normalized
to unity in each time step.
CD4+T
CD4+T
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
weeks
years
2
4
6
8 10 12
2
4
6
8
10
12
Fig. 3.
Three-phase dynamics with two time scales (weeks and years) were obtained
which were primary response (within 12 weeks), clinical latency (within 10 years) and
AIDS (steady state after 10 years). The solid, hash and hash-dot lines represent healthy,
infected (A1 and A2) and dead cells respectively. The density of dead cells shifted one
time step, compared with the result of HI model. The evolution speed of cells with
corrected rule was consistent with the result of HI model, but was slower than the
result without correction.
