Digital Signal Processing Reference
In-Depth Information
Fig. 8.11. Schematic models for
the immune response system.
(a) Detailed model;
(b) simplified model.
s
−
+
+
1
s
−
1
b
exp(−
t
s
)
+
+
g
(
t
)
number of
antigens
m
b
(
t
)
number of
antibodies
s
+
g
s
+
l
−
h
(a)
+
mb
exp(−
t
s
) −
s
(
s
+
g
)
+
g
(
t
)
number of
antigens
b
(
t
)
number of
antibodies
M
(
s
) =
(
s
−
a
)(
s
+
l
)(
s
+
g
)
−
h
(b)
the human immune system shown in Fig. 8.11. We have assumed a hypothetical
case with the values of the proportionality constants given by
α
=
0
.
1
,β=
0
.
5
,γ=
0
.
1
,=
0
.
5
,τ=
0
.
2
,λ=
0
.
1
,
σ
=
0.1,
and
η =
0
.
5
.
The proportionality constants
α
,
γ
,
σ
, and
λ
related to the antigens are deliber-
ately kept smaller than the proportionality constants
β
,
η
, and
related to the
antibodies for quick recovery from the infection. The input signal
g
(
t
) modeling
the number of antigens entering the human body is approximated by a pulse
and is shown in Fig. 8.13(a). The duration of the pulse is 0.5 s, implying that
the antigens keep entering the human body at a constant level for the first 0.5 s.
The outputs
a
(
t
),
p
(
t
), and
b
(
t
) are monitored by the simulated scope available
in simulink. The output of the scope is shown in Fig. 8.13(b), where we observe
Fig. 8.12. Simulink model for
Simulation 1 modeling the
immune response system of
humans.
a
(
t
)
1
s
− 0.1
0.5
a
(
t
)
a
(
t
)
1
s
+ 0.1
b
(
t
)
+
+
_
germs
_
0.5
scope
b
(
t
)
s
+ 0.1
p
(
t
)
error
lymphocyte
delay
gain1
antigen
generation
antigen
generation
input germs
0.1
gain2
gain3
0.5
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