Original article Biomath 2 (2013), 1212101, 1–6

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Volume ░, Number ░, 20░░ 

BIOMATH

 ISSN 1314-684X

Editor–in–Chief: Roumen Anguelov  

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BIOMATH
h t t p : / / w w w . b i o m a t h f o r u m . o r g / b i o m a t h / i n d e x . p h p / b i o m a t h / Biomath Forum

Impact of Perfect Drug Adherence on
Immunopathogenic Mechanism

for Dynamical System of Psoriasis

Priti Kumar Roy∗ and Abhirup Datta∗
∗ Centre for Mathematical Biology and Ecology

Department of Mathematics
Jadavpur University, Kolkata 700032, India

Emails: pritiju@gmail.com, abhirupdattajumath@gmail.com

Received: 15 July 2012, accepted: 10 December 2012, published: 04 January 2013

Abstract—Psoriasis is a frequent autoimmune chronic
skin disease differentiated by T-Cells agreeable hyperpro-
liferation of epidermal Keratinocytes. The feature of T-
Cells held up Psoriatic scratches is the epidermal pen-
etration of basically oligoclonal CD8+ T-Cells and also
of CD4+ T-Cells in the dermis. Psoriatic lesions are
sharply distinguished, red and enlarged scratches together
with whitish silver scales. In this research article, we
propose a mathematical depiction for Psoriasis, involving
a set of differential equations, regarding T-Cells, Dendritic
Cells, CD8+ T-Cells and epidermal Keratinocytes. Here,
we specially introduce the interaction between Dendritic
Cells and CD8+ T-Cells to monitor the impact of this
interaction upon the system dynamics. We also analyze
the mathematical model both in presence and absence of
effectiveness of two drugs. We study the system analyti-
cally and numerically to comprehend the significance of
effectiveness of the drugs, integrated in the model system.
Here, we reduce the Keratinocyte population to restrict
Psoriasis by applying the combination of two drugs and
able to enlighten the perspective of the disease dynamics
for Psoriasis.

Keywords-T-Cells; Dendritic Cells; CD8+ T-Cells; Ker-
atinocytes; MHC; pMHC; T-Cells Receptor; Dermis; Epi-
dermis; Lymphocytes; Monocytes; Neutrophils; Cytokines;
Drug Efficacy

I. INTRODUCTION

In spite of precise fundamental and experimental
studies for more than a few decades, many queries

continue relating to Psoriasis. Inflammatory tissues re-
spond along with enormous influxes of T-Cells and
Dendritic Cells (Nickoloff, 2000). A “Perfect Cytokine
Storm” is produced through this multicellular scheme
that synchronizes the cellular attack and links mutually
with connection of both soluble intermediaries and cel-
lular ingredients (Uyemura et. al., 1993, Nickoloff and
Nestle, 2004) [1]. Psoriasis has been measured as a
dermatological chaos, in which T-Cells and epidermal
Keratinocytes perform a relevant pathogenic function.
DCs play an essential role in pathogenesis of Psoriasis by
attending antigens throughout principal major histo com-
patibility (MHC) complex II molecules [2]. Psoriasis is
observed as a widespread inflammatory skin chaos with
an inherited contact. It is illustrious through epidermal
hyperplasia by means of cellular diffusion of Lympho-
cytes, Monocytes and Neutrophils [3]. Local production
of T-Cells is observed as a significant immunological
constituent of Psoriatic lesions. The enormous numbers
of Dendritic Cells below the hyperplastic epidermis,
are surrounded by T-Cells within the Psoriatic plaques
[4]. Roy and Bhadra [5] have clarified that, suppression
made on Dendritic Cells will reduce the expansion of
Keratinocytes and will give better effect than suppression
made on T-Cells. For suppression made on T-Cells, the
pathogenesis continues due to auxiliary basis in presence
of DCs, as the suppression on DCs presents a superior
result. In our very recent work, we have formed a set

Citation: P. Roy, A. Datta, Impact of Perfect Drug Adherence on Immunopathogenic Mechanism for
Dynamical System of Psoriasis, Biomath 2 (2013), 1212101, http://dx.doi.org/10.11145/j.biomath.2012.12.101

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P. Roy et al., Impact of Perfect Drug Adherence on Immunopathogenic Mechanism...

of differential equations to exhibit a course of stable
connection to the growth of epidermal Keratinocytes
through negative feedback control, that is comparable
to the favorable drug management. We also integrate a
time delay in our model to furnish the time from creation
of T-Cells and DCs to the enhancement of epidermal
Keratinocytes [6]. In our present research article, we
introduce CD8+ T-Cells population which interacts with
DCs in the dynamical system. This interaction leads to
generate Keratinocytes, which in turn supports to expand
the Keratinocytes growth. Cyclosporin and FK506 are
applied as drugs, that perform to restrict Psoriasis [7].
To confine this growth, we apply drug at the interaction
between CD8+ T-Cells and DCs. Another method to
create Keratinocytes is the interaction between T-Cells
and Keratinocytes itself. Here, we also set the drug in
that interaction to control the growth of Keratinocytes,
whose surplus production directs to create Psoriasis. In
this article, we study the effectiveness of two drugs on
the cell biological scheme to build a comparative analysis
for the drugs to restrain the disease.

II. THE BASIC ASSUMPTIONS AND FORMULATION
OF THE MATHEMATICAL MODEL

We consider the mathematical model of Psoriasis to
describe the dynamical cell biological system. Let us
assume l(t), m(t), c(t) and k(t) to represent the densities
of T-Cells, Dendritic Cells, CD8+ T-Cells and epidermal
Keratinocytes correspondingly at a specific time t to
attain a set of differential equations.

In the region proximity, the accumulation of T-Cells
is considered at a constant rate a and the accumulation
of Dendritic Cells is taken at a constant rate b at
the appropriate regime. It is assumed that, the rate of
activation of T-Cells by DCs is δ and β is the rate of
activation of DCs by T-Cells. Expansion of Keratinocytes
density is taken to be proportional to the production
of T-Cells and DCs densities with a rate η. The rate
of activation of Keratinocytes by T-Cells due to T-
Cells mediated Cytokines is referred as γ1 and γ2 is
the rate at which growth of Keratinocytes takes place.
The per capita removal rate of T-Cells is denoted by
µ and µ′ is the per capita removal rate of Dendritic
Cells throughout normal procedure. The premature Den-
dritic Cells turn into mature in the course of some cell
biological procedures and move into the lymph node.
In that lymph node, the mature DCs interrelate with
CD8+ T-Cells at a rate qn, where q is the average
peptide specific T-Cells Receptor (TCR) and n is the
average number of the related pMHC complexes per DCs

and this contact gives a negative effect to DCs as well
as positive effect to CD8+ T-Cells. The CD8+ T-Cell
proliferation is stimulated by similar antigen presenting
DCs at a rate r. We assume here also that, α is the
rate of interaction between DCs and CD8+ T-Cells. It
gives negative impact to CD8+ T-Cell population. In
addition, Keratinocytes are produced through interaction
between DCs and CD8+ T-Cells at a rate α1. Again,
we assume ξ and λ as the per capita removal rate of
CD8+ T-Cells and epidermal Keratinocytes respectively.
All the parameters, described above, are always positive.
Here, we assimilate the combination of two drug efficacy
parameters u1 and u2, placed between the interaction of
T-Cells and epidermal Keratinocytes and Dendritic Cells
and CD8+ T-Cells respectively to restrain the growth of
epidermal Keratinocytes, whose excess production is one
of the main reasons to form Psoriasis.

Accumulating collectively the above assumptions, we
can formulate the mathematical model given below:

dl

dt
= a − δlm − γ1lk(1 − u1) − µl,

dm

dt
= b − βlm − qnmc − µ′m,

dc

dt
= rqnmc − αmc(1 − u2) − ξc, (1)

dk

dt
= ηlm + γ2lk(1 − u1) + α1mc(1 − u2) − λk,

where l(0) > 0, m(0) > 0, c(0) > 0 and k(0) > 0 at
a specific time period t.

The communication is organized as follows: We com-
prise the general outlook and discuss about the effective-
ness of drugs on the cell biological system of Psoriasis
in section I. In section II, we represent the mathematical
model of Psoriasis including basic assumptions. Section
III describes theoretical analysis of the model system
(1). This section is also integrated with two equilibrium
points of the system dynamics. Theoretical explanation
of the model parameters, centering on its stability and
associated features are discussed in the same section. In
section IV, we include results from numerical simulation
of the system and finally section V ends with the
conclusion of the model dynamics.

III. LOCAL STABILITY ANALYSIS FOR THE SYSTEM

The RHS of the equation (1) is a smooth function
of l(t), m(t), c(t) and k(t) and also the parameters,
as long as these quantities are non-negative. For that
reason, local existence and uniqueness properties hold
in the positive octant.

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0 20 40 60 80 100
0

200

400

600

800

1000

Time ( Day
−1
 )

C
e
l
l
 
P
o
p
u
l
a
t
i
o
n
 
(
 
m
m
−
3
 
)

 

 

(a)

λ=0.4

0 20 40 60 80 100
0

200

400

600

800

1000

Time ( Day
−1
 )

 

 

l(t)

m(t)

c(t)

k(t)

(b)

λ=0.6

0 20 40 60 80 100
0

200

400

600

800

Time ( Day
−1
 )

 

 

(c)

λ=0.8

Fig. 1. Behaviors of different cell biological masses of the system (1) with u1=0.5 and u2=0.7 for λ = 0.4 (Panel a), λ = 0.6 (Panel b)
and λ = 0.8 (Panel c), keeping other parameters at their standard values as in Table 1.

A. Equilibria of the Model System

The model equation (1) has two equilibrium points,
i.e., Ẽ(l̃, m̃, 0, k̃) and E∗(l∗,m∗,c∗,k∗). Now, m̃= b

βl̃+µ′
,

k̃= a−δl̃m̃−µl̃
γ1l̃(1−u1)

and l̃ is the positive root of the equation

Al̃3 − Bl̃2 + Cl̃ + D = 0, (2)

where

A = βδγ1γ2m̃(1 − u1) + βγ1γ2µ(1 − u1) > 0,
B = aβγ1γ2(1 − u1) + bηγ21 (1 − u1) + δγ1m̃(βλ−

γ2µ
′) + γ1µ(βλ − γ2µ′) + γ1γ2µ′u1(δm̃ + µ) > 0,

C = aγ1(βλ − γ2µ′) + γ1µ′(aγ2u1 − δλm̃ − µλ) > 0,
D = aγ1µ′λ > 0.

This cubic equation (2) has positive real root if the
coefficients of l̃3, −l̃2 and l̃ are positive. Now, consid-
ering Descartes’ rule of sign, we may conclude that the
equation Al̃3 −Bl̃2 + Cl̃ + D = 0 has two positive real
roots (multiplicities of roots are adequate) [8] if and only
if the following conditions are hold:

(i) βλ > γ2µ
′ and (ii) aγ2u1 > λ(δm̃ + µ).

From the second equation of system (1), we include
m̃ is always positive by our necessary assumptions.
From the first equation of system (1), we state that
k̃ is realistic if a > l̃(δm̃ + µ). As a result, if (i)
and (ii) are persuaded, then we may bring to an end
that, the equation (2) has two positive real roots and
henceforth positive equilibrium point Ẽ(l̃, m̃, 0, k̃) of
the system (1) exists. Finally, for the interior equilibrium
point E∗(l∗,m∗,c∗,k∗), l∗, m∗, c∗ and k∗ are the non-
trivial solutions of the model equation (1).

Remark 1. The system (1) exists if the two conditions
are hold, (a) the product of the rate of activation of
DCs by T-Cells and the per capita removal rate of
Keratinocytes should be greater than the product of the
rate of growth of Keratinocytes due to T-Cells mediated
Cytokines and the per capita removal rate of DCs and (b)

the rate of accumulation of T-Cells itself and the product
of the rate of accumulation of T-Cells, the rate of growth
of Keratinocytes due to T-Cells mediated Cytokines and
the first drug efficacy parameter must be greater than a
pre-assigned positive quantity.

The characteristic equation of the matrix related to
the equilibrium point Ẽ(l̃, m̃, 0, k̃) in presence of
effectiveness of both drugs (u1 = u2 = 1) is illustrated
by,

(−λ − φ)(rqnm̃ − ξ − φ)[φ2 − (trace V )φ
+det V ] = 0,

where trace V = −(βl̃ + δm̃ + µ + µ′) < 0 and
det V = βµl̃ + δµ′m̃ + µµ′ > 0.

Now, φ1 (=−λ) is always negative, φ2=rqnm̃−ξ and
the roots of the equation φ2 − (trace V )φ + det V = 0
are negative since trace V < 0 and det V > 0.
Hence the equilibrium point Ẽ(l̃, m̃, 0, k̃) in presence
of effectiveness of both drugs is stable only if m̃ < ξ

rqn
.

Remark 2. The CD8+ T-Cells free equilibrium point
in presence of effectiveness of both drugs is stable if
DC population is less than some pre-determined positive
value.

The characteristic equation of the matrix related to
the equilibrium point Ẽ(l̃, m̃, 0, k̃) in absence of
effectiveness of both drugs (u1 = u2 = 0) is furnished
by,

(rqnm̃ − αm̃ − ξ − ψ)(ψ3 + A1ψ2 + A2ψ + A3) = 0.

Here, ψ1=rqnm̃ − αm̃ − ξ and from Routh-Hurwitz
criterion, A1 > 0 if β > γ2, A3 > 0 if ηγ1 > δγ2,
βλ > γ2µ

′ and k̃
l̃
>

γ2µ
γ1λ

and A1A2 − A3 > 0 if β >
γ2. Thus the equilibrium point Ẽ(l̃, m̃, 0, k̃) in absence
of effectiveness of both drugs is stable if m̃ < ξ

rqn−α ,

β >max[γ2,
γ2µ

′

λ
] and γ2

γ1
<min[ η

δ
, λk̃

µl̃
], provided rqn >

α.

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0

200

400

600

800

1000

Time ( Day
−1
 )

C
e
l
l
 
P
o
p
u
l
a
t
i
o
n
 
(
 
m
m
−
3
 
 
)

 

 

u
1
=u

2
=0.5

(a)

0 20 40 60 80 100
0

200

400

600

800

1000

Time ( Day
−1
 )

 

 

l(t)

m(t)

c(t)

k(t)

u
1
=0.9, u

2
=0.5

(b)

0 20 40 60 80 100
0

200

400

600

800

1000

Time ( Day
−1
 )

 

 

(c)

u
1
=0.5, u

2
=0.9

Fig. 2. Behaviors of different cell biological masses of the system (1) for different values of two drug efficacy parameters u1 and u2,
keeping other parameters at their standard values as in Table 1.

Remark 3. The CD8+ T-Cells free equilibrium point
in absence of effectiveness of both drugs is stable if (1)
DC population is less than some pre-assigned positive
quantity, (2) the rate of activation of DCs by T-Cells
should be always greater than the maximum of [γ2,

γ2µ
′

λ
]

and (3) the ratio of γ2 and γ1 should be always less than
the minimum of [ η

δ
, λk̃

µl̃
].

Also we study another two cases, i.e., first drug (u1)
is present and second drug (u2) is absent and vice-versa
in the system dynamics. The characteristic equation of
the matrix related to the equilibrium point Ẽ(l̃, m̃, 0,
k̃) in presence of effectiveness of first drug (u1 = 1)
and absence of effectiveness of second drug (u2 = 0) is
illustrated by,

(−λ − ϕ)(rqnm̃ − αm̃ − ξ − ϕ)[ϕ2 − (trace W)ϕ
+det W ] = 0,

where trace W = −(βl̃ + δm̃ + µ + µ′) < 0 and
det W = βµl̃ + δµ′m̃ + µµ′ > 0.

Now, ϕ1 (=−λ) is always negative, ϕ2=rqnm̃−αm̃−ξ
and the roots of the equation ϕ2−(trace W)ϕ+det W =
0 are negative since trace W < 0 and det W > 0.
Hence the equilibrium point Ẽ(l̃, m̃, 0, k̃) in presence
of effectiveness of first drug (u1 = 1) and absence of
effectiveness of second drug (u2 = 0) is stable only if
m̃ <

ξ
rqn−α , provided rqn > α.

Remark 4. The CD8+ T-Cells free equilibrium point
in presence of effectiveness of first drug and absence
of effectiveness of second drug is stable if DC popu-
lation is less than some pre-determined positive value,
provided the product of the rate at which CD8+ T-Cell
proliferation is stimulated by antigen presenting DCs,
average peptide specific T-Cells Receptor (TCR) and
average number of the related pMHC complexes per DCs
is greater than the rate of interaction between DCs and
CD8+ T-Cells.

The characteristic equation of the matrix related to
the equilibrium point Ẽ(l̃, m̃, 0, k̃) in absence of
effectiveness of first drug (u1 = 0) and presence of
effectiveness of second drug (u2 = 1) is demonstrated
by,

(rqnm̃ − ξ − χ)(χ3 + B1χ2 + B2χ + B3) = 0.

Here, χ1=rqnm̃ − ξ and from Routh-Hurwitz criterion,
we obtain β > γ2, ηγ1 > δγ2, βλ > γ2µ

′ and k̃
l̃
>

γ2µ
γ1λ

. Thus the equilibrium point Ẽ(l̃, m̃, 0, k̃) in absence
of effectiveness of first drug (u1 = 0) and presence of
effectiveness of second drug (u2 = 1) is stable if m̃ <

ξ
rqn

, β >max[γ2,
γ2µ

′

λ
] and γ2

γ1
<min[ η

δ
, λk̃

µl̃
].

Remark 5. If (1) DC population is less than some
pre-assigned positive quantity, (2) the rate of activation
of DCs by T-Cells should be always greater than the
maximum of [γ2,

γ2µ
′

λ
] and (3) the ratio of γ2 and γ1

should be always less than the minimum of [ η
δ
, λk̃

µl̃
], then

the CD8+ T-Cells free equilibrium point in absence of
effectiveness of first drug and presence of effectiveness
of second drug is stable.

Now, we analyze the roots of the characteristic equa-
tion of the matrix related to the interior equilibrium point
in presence of effectiveness of both drugs and study
it’s stability analysis. We discard the cases where (a)
effectiveness of both drugs are absent and (b) one is
present and other is absent and vice-versa, as they are
not realistic for the interior equilibrium in true sense.
The characteristic equation is furnished by,

(−λ − τ)(τ3 + C1τ2 + C2τ + C3) = 0.

Here, τ1 (=−λ) is always negative and from Routh-
Hurwitz criterion, we have δ > rqn and m∗ < ξ

rqn
.

Hence the interior equilibrium point E∗(l∗, m∗, c∗, k∗)
in presence of effectiveness of both drugs (u1 = u2 = 1)
is stable if rqn <min[δ, ξ

m∗
].

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0

200

400

600

800

1000

Time ( Day
−1
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C
e
l
l
 
P
o
p
u
l
a
t
i
o
n
 
(
 
m
m
−
3
 
)

 

 

u
1
=u

2
=0

(a)

0 20 40 60 80 100
0

200

400

600

800

1000

Time ( Day
−1
 )

 

 

l(t)

m(t)

c(t)

k(t)

(b)

u
1
=1, u

2
=0

0 20 40 60 80 100
0

200

400

600

800

1000

Time ( Day
−1
 )

 

 

(c)

u
1
=0, u

2
=1

Fig. 3. Behaviors of different cell biological masses of the system (1) for perfect absence and presence of two drug efficacy parameters
u1 and u2, keeping other parameters at their standard values as in Table 1.

Remark 6. The interior equilibrium point in presence
of effectiveness of both drugs is stable if the product of
the rate at which CD8+ T-Cell proliferation is stimulated
by antigen presenting DCs, average peptide specific T-
Cells Receptor (TCR) and average number of the related
pMHC complexes per DCs should be less than the
minimum of [δ, ξ

m∗
].

IV. NUMERICAL SIMULATION OF THE SYSTEM

In the previous section, we have initiated analytical
techniques for qualitative study of the system with effec-
tiveness of two drugs. In this part, we perform numerical
simulation of the model system (1). We approximate the
parameters in the course of our analytical outcomes and
conditions. Numerical values of the model parameters,
used in our numerical simulation, have been specified in
Table 1.

Table 1. Parameters used in the model equation (1)
Para- Default Values Assigned
meter
a 9 mm−3 Day−1 [6]
b 14 mm−3 Day−1 [6]
δ 0.01 mm3 Day−1 [6]
β 0.065 mm3 Day−1 [6]
η 1.5 mm3 Day−1 [6]
γ1 0.0002 mm

3 Day−1 [6]
γ2 0.0001 mm

3 Day−1 (estimated)
r 0.9 Day−1 (estimated)
q 0.001 Day−1 (estimated)
n 7 (estimated)
α 0.0007 mm3 Day−1 (estimated)
α1 0.0005 mm

3 Day−1 (estimated)
µ 0.07 Day−1 (estimated)
µ′ 0.002 Day−1 [6]
ξ 0.08 Day−1 (estimated)
λ 0.4 Day−1 [6]

We are trying to monitor the cell behavioral patterns
of different cells, involved in the system dynamics for

variation in the values of the parameters. Firstly, we set
u1 = 0.5 and u2 = 0.7 and assume the value of the
decay rate of Keratinocytes (λ) as 0.4 Day−1, then we
notice that, Keratinocytes initially increase around 900
cells/mm3, decline slightly just below 800 cells/mm3

and finally become stable, displayed in Fig. 1(a). When
the value of λ is 0.6 Day−1, Keratinocytes raise up to
800 cells/mm3, after that decrease below 600 cells/mm3,
at last turn into stable, shown in Fig. 1(b). Finally,
considering the value of λ as 0.8 Day−1, Keratinocytes
increase below 800 cells/mm3, next decrease at about
400 cells/mm3 and lastly develop into stable in nature,
portrayed in Fig. 1(c). Thus we conclude that, due to
increase in the value of decay rate of Keratinocytes,
its population must be decreased. Next, we monitor the
performances of four different cells in the system for
alteration in the values of two drug efficacy parameters
(u1 and u2). At Fig. 2(a), we consider u1 and u2 are
both as 0.5. When the value of u1 is increased by 0.4
at Fig. 2(b) (i.e., u1 = 0.9), then we study that, T-
Cells are increased than the earlier case. Again, when
u1 is decreased to 0.5, the behavior of T-Cells at Fig.
2(c) is rolled back like Fig. 2(a). Besides, we notice
that, Keratinocytes arrive quicker in the direction of the
stable region than for the lower value of effectiveness
of first drug. No specific change is occurred for the
presence and increase of effectiveness of second drug
in the system. At Fig. 3(a), we assume perfect absence
of effectiveness for both the drugs, effectiveness of first
drug is perfectly present and effectiveness of second
drug is absent perfectly, illustrated at Fig. 3(b) and
vice-versa at Fig. 3(c). The increasing and decreasing
natures of T-Cells are repeated as like Fig. 2 for the
perfect absence and presence of effectiveness of two
drugs. There is not at all any significant change in the
behavioral pattern, observed in DC and CD8+ T-Cell

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P. Roy et al., Impact of Perfect Drug Adherence on Immunopathogenic Mechanism...

population for variation in the values of the system
parameters and also for the change (increase or decrease)
in the values of two drug efficacy parameters.

V. CONCLUSION

The effectiveness of first drug has an imperative
effect rather than the second drug upon our proposed
model. In presence of first drug, the system develops
into stable condition very smoothly. There is not at all
any significant difference between absence and presence
of second drug. Thus the second drug has not any
significant impact on the interaction between DCs and
CD8+ T-Cells, which are not influenced for change
in the value of the model parameters. They maintain
the same pattern, which is independent of any model
parameter of the system. It is numerically revealed that,
increase in the value of decay rate of Keratinocytes leads
to the decrease in Keratinocytes and hence increase in
T-Cells is occurred simultaneously. Enhancing in the
value of decay rate of Keratinocytes has no impact on
DCs and CD8+ T-Cells. With the increasing value of
decay rate of Keratinocytes, population of Keratinocyte
is decreased and thus T-Cell population is gradually
increased. Increasing in the value of u1 forwards to the
increase in T-Cells, because increase in the value of u1
reduces Keratinocytes and thus T-Cells are increased.
Keratinocytes reach stable situation more rapidly with
the increase in the value of first drug efficacy parameter.
But unfortunately, the second drug has not any significant
effect on the system, specially on the interaction between
DCs and CD8+ T-Cells and thus the second drug does
not take part to control the Keratinocyte population in
broad sense. We may also predict another important
feature that, decrease in Keratinocytes provides increase
in T-Cells but increase in T-Cells does not essentially
lead to decrease in Keratinocytes or the decrease is not
too prominent to observe. We have used the combination
of two drugs to get enhanced result but from analytical
and numerical points of view, the first drug has the
significant effect compared to the second drug on our
proposed mathematical model for Psoriasis. Hence, to
put the drug in the interaction between DCs and CD8+

T-Cells may not be successful enough to restrict the
expansion of Keratinocytes growth. Thus applying the
drug at the place of interaction between T-Cells and DCs
on Psoriatic patients in a systematic way would be able
to obtain the improved outcome for better cure of the
disease Psoriasis.

ACKNOWLEDGMENT

Research is supported by the Council of Scientific
and Industrial Research, Government of India, Ref. No.
38(1320)/12/EMR-II, dated 3rd April, 2012.

REFERENCES

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Biomath 2 (2013), 1212101, http://dx.doi.org/10.11145/j.biomath.2012.12.101 Page 6 of 6

http://dx.doi.org/10.1038/sj.jidsymp.5650010
http://dx.doi.org/10.1172/JCI117308
http://dx.doi.org/10.1142/S0218339009002934
http://dx.doi.org/10.11145/j.biomath.2012.12.101

	Introduction
	The Basic Assumptions and Formulation of the Mathematical Model
	Local Stability Analysis for the System
	Equilibria of the Model System

	Numerical Simulation of the System
	Conclusion
	References