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2 The Computational Model
Here we illustrate the basic concepts of DTHI. The first subsection introduces
shortly the context of the problem, including the models of ODE/ PDE. The
second section presents the CArules and corresponding description for mimicked
biological concepts in the HI model as well as the correctness for one of rules.
The third section defines our DTHI model.
2.1 The Problem of Modelling Drug Therapy
With continuous progress of medical and biological research, three kinds of ther-
apy have been gradually developed. The long-term survival with combined drug
therapy is considered to be longer than with mono-therapy. The appearance of
resistance virus against HAART is apparently much longer than with combined
drug therapy. Up to now, the extension of long-term survival with HAART is
not yet known. Mathematical ODE/PDE models have di
A
culties to simulate the
four phases (acute, chronic, drug treatment responds and AIDS) in one model
but have also di
A
culties to unify three therapies into one model. Because these
models could not describe two kinds of time scales (weeks in primary response
and years in the clinical latency and AIDS) which might be related to two kinds
of interactions: one local and fast, and the other long-ranged and slow [13].
2.2 The HI Model
Here we first review the rules and biological descriptions of HIV infection model
(HI) with Moore neighbourhood and periodic boundary from reference [13].
[Rule 1] Update of a healthy cell.
(a) If it has at least one infected-A1 neighbour, it becomes an infected-A1
cell.
-
The spread of the HIV infection by contact before the immune system
had developed its specific response against the virus.
(b) If it has no infected-A1 neighbour but does have at least
R
(2
<R<
8)
infected-A2 neighbours, it becomes infected-A1.
-
Before dying, infected-A2 cells may contaminate a healthy cell if their
concentration is above some threshold.
(c) Otherwise it stays healthy.
[Rule 2] An infected-A1 cell becomes an infected-A2 cell after
τ
time steps.
-
An infected cell is the one against which the immune response has devel-
oped a response hence its ability to spread the infection is reduced. The
τ
represents the time required for the immune systems to develop a spe-
cific response to kill an infected cell. Atime delay is requested for each
cell because each new infected cell carry a different lineage (strain) of
the virus. This is the way to incorporate the mutation rate of the virus
in this model. On the average, one mutation is produced in one gen-
eration due to the error occurrence during HIV transcription. Assume
that mutation in each trial is varied in this model due to the stochastic
characteristics.
