TELKOM
NIKA
, Vol.14, No
.1, March 2
0
1
6
, pp. 228~2
3
7
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v14i1.2404
228
Re
cei
v
ed Au
gust 11, 20
15
; Revi
sed
No
vem
ber 2
2
, 2015; Accepte
d
De
cem
ber
11, 2015
A Cellular Automata Modeling for Visualizing and
Predicting Spreading Patterns of Dengue Fever
Puspa Eosin
a
*
1
, Taufik Dj
atna*
2
, Helda
Khusun
3
1
Departme
n
t of Computer Sci
ence, Bog
o
r A
g
ricult
ure Un
iv
ersit
y
, Ind
ones
i
a
2
Departme
n
t of Agro-in
dustria
l
T
e
chnol
og
y,
B
ogor Agr
i
cultur
e Univ
ersit
y
, In
don
esia
3
SEAMEO-T
R
O
PMED Regi
o
nal C
enter for Commun
i
t
y
N
u
trition, Univ
ersi
t
y
of Indon
esi
a
*Co
rre
sp
ondi
ng autho
r, email:
p
u
s
pa
_eo
s@
ap
p
s
.i
pb
.ac.i
d
1
, taufikdjat
na@i
pb.ac.i
d
2
,
hkhus
un@s
e
a
m
eo-recfo
n
.org
3
A
b
st
r
a
ct
A Cellu
lar Aut
o
mata (CA) mode
l is used f
o
r vis
ual
i
z
i
n
g
and pr
edicti
n
g
spread
ing p
a
t
t
ern of the
dise
ase. T
h
e
ma
in
pro
b
le
m
of this
mod
e
l
i
s
how
to
fi
nd
a functi
on
that
repr
esents
an
up
date
rul
e
t
hat
chan
ges th
e s
t
ate of a cel
l
in ti
me ste
p
s
affected
by
ne
igh
borh
o
o
d
. T
h
is res
earch
a
i
ms to
dev
elo
p
visual
i
z
a
t
i
on
a
nd pr
edicti
on
mo
de
l of the
sprea
d
in
g p
a
tterns of D
e
ngu
e H
e
morrh
agic F
e
v
e
r. T
h
e
contrib
u
tion
of our study is to intr
od
uce a n
e
w
approach i
n
defin
ing a
prob
abil
i
stic functio
n
that represe
n
t
s
CA trans
m
i
ssi
on rul
e
by
e
m
ployi
ng V
on N
e
u
m
a
nn n
e
i
g
h
borh
ood
an
d the Hi
dd
en Mar
k
ov Mod
e
l (H
MM).
T
h
is study
o
n
ly
cons
ider
ed
a
n
infectiv
e state
w
h
ich d
e
d
i
cate
d p
a
rticul
ar
attentio
n to
the
s
patia
l d
i
strib
u
ti
on
of infecte
d
ar
e
a
s. T
he i
n
fecte
d
d
a
ta w
e
re
de
vide
d i
n
to
fo
ur
categor
ies
an
d
cha
nge
the
de
finitio
n
of
a ce
ll
as
an ar
ea. T
he
eval
uatio
n w
a
s
cond
ucted
by
compari
ng th
e results
of the
pro
pose
d
mode
l to that of
one
yield
ed by
a Suscepti
b
le-Inf
ected-R
e
cover
ed
(SIR)
mod
e
l. T
he eva
l
ua
tion resu
lt sho
w
ed that the C
A
mo
de
l w
a
s capab
le of g
ener
ating
patterns
that simila
r to
the patterns
g
ener
ated by SI
R mode
ls w
i
th a
similar
i
ties val
u
e of 0.95.
Ke
y
w
ords
: Ce
llul
a
r Auto
mata
, Dengu
e F
e
ve
r, HMM, Neigh
borh
ood, SIR
Copy
right
©
2016 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Modelin
g is
a simplifi
c
ati
on of a
real
probl
em, ai
ming to
stud
y and un
derstand th
e
phen
omen
a i
n
the re
al world. In epidemi
o
logy, system
modelin
g ap
proa
ch i
s
co
mmonly u
s
ed
for
viewing th
e e
p
idemi
c
p
r
o
c
ess [1]. Mo
st of the mo
del
s for epid
e
mi
cs sim
u
lation
s a
r
e
ba
sed
on
Ordin
a
ry
Differential
Equ
a
tions (ODE
) or stati
s
tica
l model
[2-4
]. Moreove
r
,
visuali
z
atio
n
is
requi
re
d as t
he first
step i
n
epide
miolo
g
ical a
nal
ysi
s
to understan
d the sp
atial cha
r
a
c
teri
stics of
a data
s
et [2]. The visu
alization is
nee
ded
for ident
ifyin
g
the epi
demi
o
logy of di
se
ase
pattern i
n
a
given geo
gra
phical area,
predi
cting th
e sp
rea
d
i
ng
pattern of di
sease in the
next perio
d, and
cre
a
ting a
w
a
r
ene
ss to the target sta
k
ehold
e
rs
ba
sed on the predictio
n re
sul
t
s, hence h
e
l
p
clini
c
al man
a
gement of di
sea
s
e [2]. Unfortunately,
ODE or
stati
s
tical m
odel
s are un
able
to
elabo
rate
sp
atial pattern
s and inte
ra
ct
ions
su
ch
as in visuali
z
in
g and
predi
cting sp
rea
d
in
g
dise
ase [3].
To ove
r
come
these limitat
ions,
re
se
archer
s
used
Cellular Autom
a
ta (CA) mo
dels for
involving time
and
sp
ace in
epide
mic
pro
c
e
ss
analy
s
is [5]. Some st
udie
s
have
b
een
con
d
u
c
te
d
su
ch a
s
deve
l
oping a mat
hematical mo
del of di
sea
s
e spread a
n
d
its simulatio
n
using
Cellu
lar
Automata (CA) [6], analyzing som
e
sce
nario
s of
dise
ase
sp
read [
7
], applying the CA ap
pro
a
ch
to the Su
sce
p
tible-Infe
ctive-Recovered
(SIR)
mod
e
l
of disea
s
e
sp
read
by
con
s
i
derin
g bi
rth a
nd
death facto
r
s and the ch
a
nge
s of rule
s for each
stat
e in the dyna
mic CA [8], and analy
z
ing
the
compl
e
x spati
o
tempo
r
al pat
terns
o
b
serve
d
in transmission of vecto
r
infectiou
s
disease [9].
Basically, CA is one of the dynamic sy
stem
approa
ches that impl
ements di
scretization
of time an
d
space [3, 5, 1
0
]. CA con
s
ists of
ce
lls,
ca
lled cellula
r
space, a lo
cal
con
n
e
c
tion of
to
other
cell
s, a
nd bou
nda
ry
con
d
ition
s
[3]. Each
cell, repre
s
e
n
ting
a stat
e, can
cha
nge at ev
ery
time-ste
p u
s
i
ng lo
cal
tran
smissio
n
rule
s
whi
c
h
wo
u
l
d ge
nerate
a ne
w
state
ba
sed
on
the
previou
s
stat
e of the cell and its neigh
b
o
rho
od.
The
r
efore, the co
nce
p
t of neighborhoo
ds i
s
very
importa
nt. The effects
o
f
neighbo
rho
od structu
r
e
s
on di
sea
s
es spreadin
g
by using
the
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
A Cellula
r Autom
a
ta Modeli
ng for Visu
ali
z
ing a
nd Pre
d
icting Sp
rea
d
ing… (P
usp
a
Eosina
)
229
su
sceptible
-in
f
ected (SI) epidemi
c
s
CA-model
wa
s sho
w
n in
[5]. Moreo
v
er, the rul
e
of
neigh
borhoo
d
in determini
n
g
the model i
n
tera
ction
s
was de
scrib
ed
in [11].
The ot
her im
portant
aspe
ct that dete
r
mi
nes t
he
accu
racy of
CA m
o
del i
s
the
tran
smition
rule
f.
Thi
s
rule
wa
s a
b
le
to be
rep
r
e
s
ented
as a
d
e
termini
s
tic o
r
p
r
ob
abili
stic functio
n
[9
-1
0].
Many methods
to find func
tion
f
as rul
e
of the CA model have
been introdu
ced
su
ch a
s
usin
g
Markov Ch
ai
n [12], the differential eq
uation
s
of the cla
ssi
cal
model [13], and the G
e
n
e
tic
Algorithm [1
4
]. This
re
sea
r
ch
u
s
ed
the
Hid
den
Markov Mo
del
(HMM) to fin
d
a
pro
babili
stic
function that
rep
r
e
s
ente
d
the CA tran
smissi
on
rule, which has n
o
t been used
by resea
r
ch
ers
yet. HMM is
a pro
babili
sti
c
mod
e
l that
is suitable f
o
r solving th
e pro
b
lem
re
lated to the
data
seq
uential
-
te
mporal [15]. To sh
ow the
effectiv
ene
ss of the prop
o
s
ed m
odel, this ap
proa
ch
was
impleme
n
ted
on the De
ngu
e Fever case.
The re
ason f
o
r u
s
ing the
Den
gue F
e
ve
r ca
se i
s
be
cause it cou
n
ts as
one of t
he dea
dly
and infe
ctiou
s
pa
nde
mic
d
i
sea
s
e
s
in In
done
sia.
T
h
is dise
ase, also call
ed
Den
gue
Hemo
rrh
agi
c
Fever (DHF),
is cau
s
ed by
the Dengu
e virus an
d is transmitted by
the
Aedes ae
gypti
mo
squit
o
as a vecto
r
. Several stu
d
ies related
to the monitoring of DHF in Indon
esia have b
een
con
d
u
c
ted, such a
s
the
st
udie
s
that ai
med to
see th
e trend
of de
ngue o
u
tbrea
k
in the future
[16
-
17]. The Time Serie
s
method for sho
w
i
ng the trend
of dengue o
u
t
brea
k wa
s u
s
ed in [16]. The
study predi
cted the num
b
e
r of den
gue
fever pat
ient
s for the n
e
xt four years based on
DHF
patient data i
n
the provin
ce of North Su
matra fr
om
2
005 to 20
09. The Autoregressive Integrated
Moving Ave
r
age
(ARIMA
) wa
s compa
r
ed to
the
Win
t
er a
pproa
ch
to predi
ct the
num
ber of
DHF
ca
se
s in the
next six mon
t
hs [17]. This res
earch
used DHF cases data f
r
om
Surabaya from
Jan
uary 200
5
- June
20
10
and appli
ed four
mo
del
s of
the
Wi
nter
method and
three
m
odel
s
of
the ARIMA method.
This p
ape
r e
x
plained h
o
w to develop a
spreadin
g
p
a
ttern mod
e
l of DHF o
n
CA model
that was u
s
e
d
for visuali
z
i
ng and p
r
edi
cting spre
adi
ng pattern of
DHF. Thi
s
study espe
cial
ly
focu
sed o
n
d
e
termini
ng a
prob
abili
stic f
uncti
o
n
usi
n
g
HMM. The
dataset from
a limited area
su
ch as
We
st Bogor in the perio
d of 2013 wa
s
u
s
e
d
and define
d
the state criteria. More
o
v
er,
this
study onl
y con
s
ide
r
e
d
an inve
ctive
state
whic
h d
edicated p
a
rti
c
ula
r
attentio
n to the
spati
a
l
distrib
u
tion of
infected a
r
e
a
s. The eval
uation
was
condu
cted by
comp
ari
ng th
e re
sults of the
prop
osed mo
del to that of the one yield
e
d
by
the SIR method, as a
cla
ssi
cal a
pproach.
2. Rese
arch
Metho
d
To achieve the re
se
arch
obje
c
tive, se
vera
l sta
g
e
s
were don
e, includi
ng: collectin
g
datasets, d
e
fining the
mod
e
l CA,
con
s
tructing th
e d
a
t
a, predi
cting
the spread
o
f
disea
s
e
u
s
i
ng
an obtain
ed
model, and e
v
aluating the
model.
2.1. Data
se
t
In coll
ectin
g
the
data
s
e
t
s, some
st
eps
were d
one
as follo
ws: i
dentification of
geog
rap
h
ical study area, c
ondu
cting fiel
d study for d
a
ta colle
ction
,
decidin
g sa
mple u
s
ed in
this
resea
r
ch, determini
ng the sou
r
ce of the data. T
he dat
aset were
col
l
ected fro
m
Dinas Ke
seh
a
tan
Kota Bogo
r
(DKK-Bog
o
r)
an inte
rview tech
niqu
e. Th
e intervie
w
was
co
ndu
cted
with th
e DK
K-
Bogor
Data
Officer o
n
Ju
ly 16, 2014.
Table 1
sh
o
w
ed th
e data
s
et that cont
ains th
e De
n
gue
Fever cases t
hat occurre
d
in We
st Bogor in 2013.
2.2. Defining
of CA Mo
del
A Cellula
r Au
tomata (CA) i
s
a di
screte
model
con
s
i
s
ting of point
s or ide
n
tical
cells that
each in
one
certain
state
at the time. A
state value th
a
t
is allo
we
d t
o
a
cell i
s
the
value of
set
of
states
whi
c
h have been d
e
fined. The State of a cell
cha
nge
s accordin
g to a local tran
sition
rul
e
at the next time in time-s
tep [3, 18]. Those
c
e
ll
s a
r
e arra
nge
d u
n
iformly in
ce
llular
sp
ace t
hat
can
be on
e-d
i
mensi
onal, t
w
o-dime
nsio
nal or th
re
e
-
d
i
mensi
onal. T
he state
con
d
ition of one
cel
l
at the next
time,
t+
1
, d
epen
ds
on t
he state
s
of the othe
r
cell
s surrou
n
d
ing, called
its
neigh
borhoo
d
,
at the time,
t
. Mathematically the CA model is
define
d
as a 4
-
u
p
le
t (C, S, V,
f
). C
rep
r
e
s
ent
s a
cellula
r
spa
c
e. S re
pre
s
ents a
set of
possible
sta
t
e values fo
r each cell i
n
the
cellul
a
r spa
c
e. V is a set of neighbo
rhood
s aroun
d a focus
ce
ll. Function
f
defines a lo
cal
transitio
n fun
c
tion th
at re
p
r
esents an
u
pdate
rule
for ea
ch
state
chang
e of e
a
ch cell [6]. Th
ere
are fou
r
st
e
p
s for
defini
ng the CA
model, such
as: definin
g a cell
ula
r
spa
c
e, defi
n
ing
neigh
borhoo
d
used i
n
a
cellular spa
c
e,
definin
g the
criteria
of th
e po
ssible
st
ate value
s
, a
nd
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 1, March 2
016 : 228 – 2
3
7
230
finding som
e
prob
abili
stic
f
unctio
n
s
f
tha
t
rep
r
e
s
ent th
e CA
rul
e
. Fu
nction
f
is req
u
ired
to
obtai
n
a spreadi
ng p
a
ttern of Den
gue Feve
r.
Table 1. Nu
m
ber of De
ngu
e Ca
se
s in West Bogo
r in 2013
Id of cell
Region
Number of
DHF
cases per period
1 2 3 4
5 6 7 8 9 10
11 12
1.
Situ
Gede
1 0 0 0
0 1 0 0 0
0
0
0
2.
Bubulak
2 1 4 0
1 0 3 0 0
0
0
0
3.
Curug
7 2 2 3
3 0 1 0 1
0
3
3
4.
Curug
Meka
r
1 0 3 0
1 0 0 0 0
0
2
0
5.
Balumbang
Ja
y
a
0 0 0 0
1 0 0 0 0
0
0
3
6.
Sindang
Barang
2 2 4 0
1 2 6 0 2
2
0
0
7.
Semplak
2 0 1 0
1 0 0 0 1
0
3
1
8.
Cilendek
Timur
5 2 0 0
1 1 4 0 0
0
1
0
9.
Margaja
y
a
1 0 0 2
0 1 0 0 0
0
0
0
10.
Menteng
2 1 2 1
0 2 6 0 0
1
2
0
11.
Cilendek
Barat
1 4 3 0
2 1 4 0 4
0
2
0
12.
Pasir
Jay
a
1 0 0 1
1 0 0 0 0
0
0
0
13.
Gunung
Batu
7 3 1 2
0 1 4 0 1
0
1
1
14.
Loji
0 1 1 0
1 0 0 0 0
0
6
0
15.
Pasir
Muly
a
1 1 0 0
0 0 2 0 0
0
0
0
16.
Pasir
Kuda
2 3 1 1
0 0 1 0 1
0
2
1
Source: Din
a
s
Kese
hatan
Kota Bogor
This re
se
arch defin
ed
16
cell
s in t
w
o
-
dime
nsi
onal
cell
ula
r
spa
c
e
(Fig
ure 1
)
, which
rep
r
e
s
ent 16
regio
n
s i
n
West Bogo
r (T
able 1
)
.
Each
cell represe
n
ts a region
according to
id
o
f
cell
li
sted i
n
Table
1. Fo
r i
n
stan
ce, th
e first
cell i
n
Fig
u
re
1 rep
r
e
s
e
n
ts a
re
gion
of Situ Ged
e
(a
regio
n
with id
1 in Table 1
)
. Each cell de
fines un
unifo
rmed obj
ect
s
and de
scri
be
s the num
be
r of
deng
ue
ca
se
s that o
c
curred in th
e re
g
i
on. The
nu
mber
of cell i
n
the
cellula
r spa
c
e
s
actu
ally
doe
s not always have to b
e
the sam
e
a
s
the num
ber of the obse
r
ved re
gion
s. For in
stan
ce, T
h
e
20 o
r
2
5
cellu
lar
spa
c
e
s
fo
r the 1
6
o
b
served re
gion
s could be defin
ed
by
addi
ng the
definitio
n of
boun
dary reg
i
ons
(the re
g
i
ons
whi
c
h a
r
e not in
clud
ed into the 16 ob
serve
d
region
s) [3]. In
addition, in t
h
is
study a
s
sume
d null
boun
dary
co
ndition
s for t
he propo
se
d
model. Th
e
4
-
neigh
borhoo
d
s
fro
m
Von
Neuman
n
wa
s
use
d
, a
colle
ction of five
cel
l
s in
whi
c
h
th
e middl
e
cell i
s
a focu
s of attention a
s
sh
o
w
n in Figu
re
2 [6].
Figure 1. An Example of a Cellula
r Spa
c
e
C
o
ns
tr
uc
tio
n
Figure 2. Von Neuma
n
n
-
Neighb
orh
ood
s
The
rem
a
inin
g cells a
r
e
cells th
at affect the
stat
e
ch
ange
of a
cel
l
in
sub
s
e
que
nt pe
riod
s. T
h
e
resea
r
ch that related to the state ch
ang
es of a
cell in
a two-dim
e
n
s
ion
a
l has p
e
rforme
d in [19].
In this resea
r
ch, th
e con
c
ept of
state
cha
nge
wa
s use
d
for
se
lecting
attrib
utes. Th
e st
ate
cha
nge
s wa
s calculated b
a
se
d on the cha
nge of
sh
ape of the ge
ometry
whi
c
h
represe
n
ted
the
affecting
re
su
lt of two di
m
ensi
onal
rul
e
s
whi
c
h i
s
a
p
p
lied to th
e p
a
ir of th
e attri
butes [19]. T
h
e
prop
osed mo
del define
d
st
ate ch
ange
s
based on
dat
a
co
ntent on
locatio
n
. First, the catego
ri
es
values we
re defined
i
n
fo
ur catego
rie
s
and setting colo
r
for ea
ch
cate
gory. Next,
the
sta
t
e
cha
nge
s
were se
en a
s
a
cell col
o
r
cha
n
ge in the
ce
ll
ular
spa
c
e. In
HMM, the
state ch
ang
es
are
descri
bed
a
s
the state
tra
n
s
ition
diag
ra
m. The fo
ur
colors a
nd it
s
crite
r
ia
of stat
es
are
sho
w
n
in
Table
2. Th
e
next step
wa
s h
o
w to d
e
te
rmine
a F
u
n
c
tion
f
that rep
r
esented
the
CA Rule
ba
sed
on the define
d
para
m
eters.
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30
A Cellula
r Autom
a
ta Modeli
ng for Visu
ali
z
ing a
nd Pre
d
icting Sp
rea
d
ing… (P
usp
a
Eosina
)
231
In detail, the
prop
osed me
thod was
describ
ed a
s
foll
ows. Firstly, from the
data
s
et that
con
s
i
s
t of 16
regio
n
s, thi
s
study defin
e
d
t
he two
-
di
mensi
onal
sp
ace
and p
u
t each re
gion i
n
to
one
cell a
nd
set an i
ndex f
o
r e
a
ch cell, then it defin
ed
an a
rray va
ri
able to
rep
r
e
s
ent the
16
cells
in whi
c
h ea
ch cell ha
s an
index. Next, the numbe
r of data ca
se
s for ea
ch re
gion (n
umb
e
r of
infected
) we
re put into an array varia
b
l
e
in which the data in on
e perio
d we
re store
d
into
an
array variabl
e, runni
ng a
s
time-step.
Finally, with
a set of stat
es
crite
r
ia (T
able 2
)
, the data
ca
se
s with th
e data state
s
were re
pla
c
e
d
.
Table 2. State Definition of
Infected Are
a
State
State Definition
State Colour
S
1
:
all peoples have been recovere
d,
or no one
was infected
S
2
:
1-2 peoples
w
e
re infected
S
3
:
3-5 peoples
w
e
re
infected
S
4
:
> five peoples were infected
The main problem of this rese
arch is h
o
w
to find the func
tion that
rep
r
e
s
ent
s a prop
er
CA’s
rule. Many methods
t
o
find func
tion
f
as
rule
of
CA mod
e
l ha
ve been
co
nd
ucted, a
n
d thi
s
resea
r
ch u
s
e
d
HMM, a
me
thod that
ha
s
not be
en
us
e
d
by
re
sea
r
ch
ers yet. By ig
norin
g
b
o
th t
he
death
and
th
e bi
rth fa
ctors, and
by a
s
su
ming th
at
the
prob
ability of
an infe
cted
cell was affect
ed
by su
rroundi
ng
cells, th
e
HMM
app
roa
c
h
wa
s
suita
b
le to b
e
u
s
e
d
to dete
rmin
e a p
r
o
babili
sti
c
function
f
.
The
CA characteri
stic wa
s r
epresente
d
as a M
a
rkov pro
c
e
s
s [20]. Since th
e data
set
was able to
be classified
as a time
series datase
t, it was
proper to use
a probabilisti
c functi
on
that can be f
ound u
s
in
g HMM. HMM
is a proba
bilis
tic mo
del th
at is suitabl
e
for solving t
he
probl
em
relat
ed to the
dat
a seque
ntial-temporal
[12]
. Mathemati
c
ally, the HM
M is
written
as
(,
,
)
TE
, where
λ
is the HMM m
o
del,
T
is a matrix of Tr
ansition Probabilities,
E
is a Matri
x
of
Emission Proba
bilities, and
π
is
a
Pri
o
r
M
a
trix [15
]. In the CA
model th
at h
a
s
bee
n defi
ned,
the cha
nge of
a cell state to anothe
r sta
t
e can be
de
scrib
ed by a State Tran
sitio
n
Diag
ram. T
h
e
State Tra
n
siti
on
Diag
ram
e
x
press HM
M
model
a
s
T
.
The
state
ch
ange
p
r
oba
bil
i
ties of
a
ce
rtain
area
affe
cted
by its n
e
igh
b
o
rho
o
d
s
a
r
e
called
as
emi
s
sion
proba
bili
ties
that express HMM mo
del
as
E
.
Figure 3. State Tran
sition
Diag
ram – Ergodi
c
HMM
Table 3. Tran
sition Pro
babi
lities Matrix
Period n-1
Period n
S
1
S
2
S
3
S
4
Σ
S
1
P(S
1
|S
1
)P
(
S
1
|S
2
) P(
S
1
|S
3
) P(
S
1
|S
4
)
1
S
2
P(S
2
|S
1
)P
(
S
2
|S
2
) P(
S
2
|S
3
) P(
S
2
|S
4
)
1
S
3
P(S
3
|S
1
)P
(
S
3
|S
2
) P(
S
3
|S
3
) P(
S
3
|S
4
)
1
S
4
P(S
4
|S
1
)P
(
S
4
|S
2
) P(
S
4
|S
3
) P(
S
4
|S
4
)
1
Table 4. Emission Probabilities Matrix
Main O
b
ject (
C
)
Obs
e
rv
ed Obj
e
c
t
(V
i
)
S
1
S
2
S
3
S
4
S
1
P(C=S
1
|X
i
=S
1
)P
(
C
=
S
1
|X
i
=S
2
)P
(
C
=
S
1
|X
i
=S
3
)P
(
C
=
S
1
|X
i
=S
4
)
S
2
P(C=S
2
|X
i
=S
1
)P
(
C
=
S
2
|X
i
=S
2
)P
(
C
=
S
2
|X
i
=S
3
)P
(
C
=
S
2
|X
i
=S
4
)
S
3
P(C=S
3
|X
i
=S
1
)P
(
C
=
S
3
|X
i
=S
2
)P
(
C
=
S
3
|X
i
=S
3
)P
(
C
=
S
3
|X
i
=S
4
)
S
4
P(C=S
4
|X
i
=S
1
)P
(
C
=
S
4
|X
i
=S
2
)P
(
C
=
S
4
|X
i
=S
3
)P
(
C
=
S
4
|X
i
=S
4
)
Σ
1 1 1 1
Based
on the
states
crite
r
i
a
(Fig
ure
3),
Ergodi
c
Hidd
en Ma
rkov Model
s (Ergodi
c
-HMM
)
wa
s appli
ed to get a pro
b
a
b
ilistic fun
c
tio
n
[21, 22]. Each a
rro
w in th
e state diag
ra
m rep
r
e
s
ent
s a
prob
ability value of an obje
c
t to chang
e the value
of a state from on
e perio
d to the next one. The
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93-6
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016 : 228 – 2
3
7
232
values were
store
d
i
n
T
as
shown in T
able
3. The
Emi
ssi
on P
r
obabilities
were stored in
E
as
sho
w
n in Ta
ble 4. This
study assume
d that the
initial state of a cell at the begin
n
ing of
the
period
had the
sam
e
probability of
possi
ble states
values.
Thus
, the pri
o
r probabilities were
ignored.
The probabilit
y of an object
(
C
i
) to chan
g
e
its state
wa
s ca
lculated
usin
g Bayes t
heorem
as
follows
:
(
|
C)
.
(
C)
(C
|
)
()
ii
i
ii
i
PX
P
PX
PX
(1)
In general, it
wa
s written a
s
:
12
1
2
1
11
(
,
,
...,
|
,
,
...,
)
(
|
)
.
(
|
)
nn
n
n
ii
ii
ii
PC
C
C
X
X
X
P
X
C
P
C
C
(
2
)
The Transition Probabilit
y value was cal
c
ulated by the formula:
(|)
ij
i
S
PS
i
S
j
S
(
3
)
Moreover, the Emissi
on Proba
bilities value was calcul
ated by the formul
a:
0
(|
S
)
j
Vi
ij
Vi
S
PV
V
S
(
4
)
2.3. Data
Co
nstru
c
tion f
o
r Spreading
Patte
rn
Data attri
bute
s
u
s
ed i
n
thi
s
research
are:
“nam
e of
a re
gion
” an
d
“num
be
r of
Den
gue
ca
se
s”. Th
e
cellular
sp
ace
is defin
ed a
s
a two
-
dime
nsional
spa
c
e i
n
whi
c
h
ea
ch
cell
rep
r
e
s
en
ts
a regio
n
with
some
Den
g
u
e
cases in
ea
ch
pe
riod.
Th
e total
regi
on
in
We
st Bo
g
o
r i
s
16
re
gio
n
s.
Thus, 16
cell
s we
re defin
ed. Each cell
cont
aine
d some un-unifo
rmed obj
ect
s
that describ
ed
some
Den
g
u
e
ca
se
s that occurre
d
in a region fo
r th
e certai
n peri
od. Each cell wa
s defined
as a
one-dime
nsio
nal variabl
e
/1
,
2
,
.
.
,
1
6
i
XX
i
. Variabl
e
X
i
re
pre
s
ente
d
a region a
s
sho
w
n in
Figure
.
1. Cell neig
hbo
rhood
s
we
re
define
d
a
s
a
on
e-di
mensi
onal
array varia
b
le
|
0
,
1
,2
,
3
,4
,
5
j
VV
j
.
The Neig
h
borh
ood fra
m
e moved i
n
the cellul
a
r sp
ace with
th
e
equatio
n:
0
i
VX
;
14
i
VX
;
21
i
VX
;
34
i
VX
;
44
i
VX
(
5
)
The Neigh
b
o
r
hoo
d fram
e as indi
cate
d
in Figure 2
moved to ea
ch cell in the
cellula
r
spa
c
e. When
ever moving,
the initial condition
st
ates of ea
ch
cell we
re che
c
ked. Next, the
maximum
pro
bability value
of the fo
cu
s
cell to
ch
ange
s of
the
state
value fo
r the
next pe
riod
was
cal
c
ulate
d
.
States value
wa
s
re
pre
s
ente
d
by
an a
r
ray, with the
a
r
ray vari
able
of
12
3
4
,,
,
SS
S
S
S
. To build a
simulatio
n
model, Excel sprea
d
sheet
s wa
s use
d
as a tool to
find a prob
a
b
ilistic fun
c
tio
n
, and used
Scipy modul
e in Python 3.4 as tool for evaluatin
g
the
prop
osed mo
del.
2.4. Predict the Disea
se
Spread Patte
r
ns using a
Proposed M
odel
In orde
r to predict the spre
ading patte
rn
of
Dengue F
e
ver, the CA model was a
pplied to
a ne
w data
s
e
t. To initialize
the sim
u
latio
n
, the John v
on Neuma
n
n
-
Ran
dom
Nu
mber
Gen
e
ra
tor
based on th
e
CA rule
wa
s
use
d
, that is
equivalent
to
a two-dimen
s
ional spa
c
e f
o
r ge
nerating
the
j
th
cell in the i
th
-ro
w by takin
g
cell
s from the pr
evio
us
row [23] as foll
ows:
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TELKOM
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ISSN:
1693-6
930
A Cellula
r Autom
a
ta Modeli
ng for Visu
ali
z
ing a
nd Pre
d
icting Sp
rea
d
ing… (P
usp
a
Eosina
)
233
(
)
(
1
)(
1
)
(
1
)(
1
)
(
1
)
11
1
mo
d
4
ii
i
i
i
i
j
jjjj
j
xx
x
x
x
x
(6)
Whe
r
e
mod
4 indi
cate
s th
e num
be
r of
states that
()
i
j
x
might de
scri
b
e
the
j
th
cell i
n
the i
th
-r
ow
whi
c
h can ta
ke on th
e val
ue 0,1,2, and
3. The valu
e
s
of the cells in the first ro
w, whi
c
h
ran
g
e
from 0 to 3, were rand
omly assign
ed by
Simple Linea
r Cong
rue
n
tial
Generators.
2.5. Verification and Validation
Evaluation of
the p
r
op
ose
d
mod
e
ls wa
s
con
d
u
c
ted
by doing
verif
i
cation
and
validation.
Model ve
rification aim
s
to
ensure th
at the CA
mod
e
l h
a
s b
een im
pl
emented
co
rrectly. More
over,
the purpo
se
of validation i
s
to dete
r
min
e
wh
ether th
e theory a
n
d
assumptio
n
s unde
rlying t
he
prep
aration o
f
this model
a
r
e corre
c
t [24
]. The
SIR-m
odel (S
uscept
ible-Infe
c
ted
-
Re
covered
)
is a
simple
mathe
m
atical m
ode
l based
on
O
D
E that
h
a
s been proven to
be
a
n
a
cceptable mod
e
l
in
the epidemi
c
fields [25]. Th
e SIR model
wa
s rep
r
e
s
e
n
t
ed as sho
w
n
:
(
7
)
(
8
)
(
9
)
Whe
r
e
S
= n
u
mbe
r
of susceptibl
e
,
I
= numbe
r of inf
e
ctiou
s
, an
d
R
= numb
e
r of
recovered.
Ca
se
β
rep
r
e
s
ent
s the t
r
a
n
smi
ssi
on
probability of th
e disea
s
e
an
d
γ
re
pre
s
e
n
ts
the pe
riod of
infection.
Verificatio
n
of the model wa
s con
d
u
c
ted by
comp
a
r
ing the tend
ency of gra
p
h
s yielded
by the prop
osed mod
e
l, an
d the trend
graph
s yiel
ded
by the SIR model. Sequ
en
tially, validation
of the m
odel
wa
s
pe
rforming
by me
asu
r
ing
the
proximity of
the si
mulatio
n
results
of
the
prop
osed mo
del and th
ose
of the SIR-m
odel u
s
ing
a correl
ation co
efficient mea
s
ure to comp
ute
s
i
milarity [26]:
1
()
(
)
(,
)
(1
)
n
ii
i
XY
XX
Y
Y
Co
r
r
X
Y
n
(
1
0
)
Whe
r
e
i
X
and
X
are de
cla
r
e
d
time-serie
s
data and t
h
e
averag
e gen
erated
by the prop
osed
model, re
sp
e
c
tively,
i
Y
and
Y
are de
cla
r
ed
time-serie
s d
a
ta and the a
v
erage g
ene
rated by the
SIR model, resp
ectively.
X
and
Y
rep
r
e
s
en
ted stan
dard
deviation of variabl
e
X
and
variab
l
e
Y
. The simila
rity value lies betwe
en 0.5 - 1. The clo
s
er it gets to 1, the two time-serie
s data ca
n
be sai
d
to be simila
r [27].
3. Results a
nd Analy
s
is
3.1. Probabilistic Functions Obtained
as Rule on
CA Model
The spreadi
n
g
pattern
an
d
pre
d
ictio
n
model we
re rep
r
e
s
ente
d
by
the
prob
abilisti
c
function th
at rep
r
e
s
ent
s the CA rule.
The p
r
ob
ab
ili
stic fun
c
tion
obtaine
d in this research
is
descri
bed a
s
follows:
4
4
1
00
0
i1
1
(|
S
)
.
(
S
|
)
max
nn
n
ji
i
j
fP
V
V
P
V
V
(
1
1
)
dS
SI
dt
dI
SI
I
dt
dR
I
dt
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
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930
TELKOM
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Vol. 14, No. 1, March 2
016 : 228 – 2
3
7
234
Whe
r
e
0
n
V
represe
n
ts state
value of cell
V
0
in n-th
period, an
d
1
0
(|
)
nn
oi
PV
S
V
is the
probability of
V
0
that is at
S
i
in the next perio
d. This
function all
o
ws us to
cho
o
se the maximu
m
value of the probability of the
st
ate
change. It means
that the
chan
ge
of a state in
the cell
of V
0
in the next p
e
riod
dep
end
s on th
e max
i
mum prob
a
b
ility value obtained from e
quation
(12
-
1
5
).
These probabilities consist of
four possi
bility values that
are defined as follows.
4
1
01
1
2
3
4
01
01
0
1
(S
|
,
,
,
)
(
|
S
)
.
(S
|
)
nn
n
n
i
i
PV
V
V
V
V
P
V
V
P
V
V
(12
)
4
1
02
1
2
3
4
02
0
2
0
1
(S
|
,
,
,
)
(
|
S
)
.
(S
|
)
nn
n
n
i
i
PV
V
V
V
V
P
V
V
P
V
V
(13
)
4
1
03
1
2
3
4
03
03
0
1
(S
|
,
,
,
)
(
|
S
)
.
(S
|
)
nn
n
n
i
i
PV
V
V
V
V
P
V
V
P
V
V
(14
)
4
1
04
1
2
3
4
04
0
4
0
1
(S
|
,
,
,
)
(
|
S
)
.
(S
|
)
nn
n
n
i
i
PV
V
V
V
V
P
V
V
P
V
V
(15
)
\
T
h
e
va
lu
es
of
01
(|
S
)
n
i
PV
V
;
02
(|
S
)
n
i
PV
V
;
03
(|
S
)
n
i
PV
V
;
04
(|
S
)
n
i
PV
V
were
o
b
tained from
the Emission Probabilities Mat
r
ix using the
equation (15-18). Mor
eover, the values of
1
01
0
(S
|
)
nn
PV
V
;
1
02
0
(S
|
)
nn
PV
V
;
1
03
0
(S
|
)
nn
PV
V
;
1
04
0
(S
|
)
nn
PV
V
we
re
o
b
tained
from
T
,
1
00
(|
)
nn
PV
V
wa
s o
b
tain
ed ba
se
d o
n
the form
ula
de
scribe
d i
n
Tabl
e 3
with the results of
probability values as fo
llows (Equation 16):
1
00
0.
6
0
0.
32
0.
06
0.
01
0.
5
4
0.
30
0
.
13
0.
03
0.
5
9
0.
24
0
.
18
0.
0
0
0.
6
0
0.
20
0.
20
0.
0
0
(|
)
nn
PV
V
(
1
6
)
This m
a
trix shows that th
e ch
ang
e fro
m
state S
4
to S
1
has the
highest probability value. The
matrix also shows that the
possibility of
a
cell'
s state cha
nge next
perio
d
from
S
3
to S
4
was v
e
ry
small o
r
n
e
ver o
c
curred.
More
over, if the
conditio
n
of a cell
wa
s in the state
of S
4
, the state
tends to cha
nge to the better con
d
itio
n becau
se
the prob
ability of the cell’s
state to kee
p
its
state
wa
s ve
ry small
or ne
ver o
c
curred.
It mean
s
th
a
t
there
were
alway
s
the
preventive a
c
tions
to stop the sp
readi
ng of De
ngue Feve
r di
sea
s
e
s
in this area.
In this
res
e
arc
h
,
E
is a mat
r
ix for rep
r
e
s
enting the
sta
t
e chan
ge p
r
obabilitie
s of a ce
rtain
area affe
cted
by its neighborho
od. The
r
e were four matrices
E
a
s
seq
uently, from Equatio
n
17
up to Equatio
n 20 as follo
ws.
10
0
.
657
9
0
.
250
0
0
.
0
789
0.
0
132
0.
4423
0.
403
8
0
.
1346
0.
0
192
0.
5833
0
.
250
0
0
.
166
7
0
.
0
000
0
.
000
0
0
.
500
0
0
.
2
500
0.
2
500
(|)
PV
V
(
1
7
)
Equation (17) describ
ed th
e prob
ab
ility of a state ch
ange of cell
V
1
on the next period that is
affected by th
e state
ch
ang
e of cell V
0
. It was
shown t
hat the probability of V
1
’s state cha
ngin
g
to S
4
wa
s very small
or
ne
ver o
c
curred,
while
V
0
was in S
3
. Moreover, this
ma
t
r
i
x
also
sh
ow
e
d
that the chan
ge from the st
ate of area V
1
to S
1
, while V
0
was in S
4
never o
c
curre
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
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ISSN:
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930
A Cellula
r Autom
a
ta Modeli
ng for Visu
ali
z
ing a
nd Pre
d
icting Sp
rea
d
ing… (P
usp
a
Eosina
)
235
20
0.
6
538
0.
269
2
0
.
0769
0.
0000
0.
4
255
0.
42
55
0.
1277
0.
0213
0.
4667
0.
2667
0.
2000
0.
0667
0.
250
0
0
.
500
0
0
.
2500
0.
0000
(|
)
PV
V
(
1
8
)
Equation
(18
)
sho
w
s that
the state
ch
an
ge of V
2
to S
4
, affected by V
0
, would ne
ver occu
r
whi
l
e
the state of V
0
is in the con
d
ition of S
1
or S
4
.
30
0.
6250
0.
2
875
0.
0875
0.
00
00
0.
4222
0.
4667
0
.
0667
0.
04
44
0.
3750
0.
4
375
0.
1
250
0.
0625
0.
3333
0.
3333
0.
0
000
0.
3333
(|)
PV
V
(
1
9
)
Equation
(19
)
describe
s
th
e probab
ility of
a
state ch
ange of
cell V
3
on the ne
xt period th
at is
affected by th
e state
con
d
ition of V
0
. Equ
a
tion (2
0)
de
scrib
e
s t
he p
r
o
bability of a state cha
nge
o
f
cell V
4
on th
e next pe
riod
that is affected by the V
0
state condit
i
on. Fro
m
th
e four m
a
tri
c
es
above, it is concl
ude
d that
the extrem
e
cha
nge
co
ndi
tions
of the n
e
ighb
orh
ood
s to S
4
, affec
t
ed
by the focus
area, a
r
e very rare.
40
0.
6456
0.
2532
0.
0886
0.
0127
0.
446
8
0
.
425
5
0
.
085
1
0
.
0426
0.
3750
0.
3750
0
.
1875
0.
06
25
0.
0000
0.
5000
0.
5000
0.
0000
(|)
PV
V
(
2
0
)
3.2. Prediction Model Re
sult
s Obtained Using
CA Model
An example
of the simulat
i
on re
sults i
s
sho
w
n in Fig
u
re 4. The p
a
ttern obtain
ed usi
n
g
Equation (11
)
. The input
s to this eq
uati
on we
re
th
e Odd
s
Tran
sition Matrix (E
quation 1
6
), t
he
Odd
s
Emi
ssi
ons Matrix
(Equation
17-20), a
nd t
h
e
ran
domi
z
ed
data initiali
zation
that
wa
s
obtaine
d by Equation
(6).
The vi
su
alization of the
obtaine
d patt
e
rn
re
sults in
dicate
d that the
spread of De
ngue di
se
ase
occurred o
n
averag
e in se
ven to eight period
s
.
Figure 4. The
Predictio
n Result
s of Den
gue Spreadi
n
g
Pattern on
The CA Mod
e
l
From several comp
utationa
l
simulation
s, it
wa
s
see
n
that if the dise
ase b
ega
n to spread
simultan
eou
sl
y in cells 11
a
nd 1
6
, the
pa
ndemi
c
woul
d
su
bsi
de i
n
a
longe
r p
e
ri
od.
For exam
ple,
cell
s 11
and
16, re
sp
ectiv
e
ly, represen
ted the a
r
ea
of Cilen
d
e
k
Barat an
d Pa
sir Ku
da. It a
l
so
appe
ars that
cell 15,
rep
r
e
s
entin
g t
he area Pasi
r Muly
a, is the mo
st vulnera
b
le cell to the sp
re
ad
of the disea
s
e. It was sho
w
n with the
color indi
cato
r
in that area.
5
th
Pe
r
i
o
d
6
th
Pe
r
i
o
d
7
th
Pe
r
i
o
d
D
a
ta
I
n
i
t
i
a
li
z
a
ti
o
n
8
th
Pe
r
i
o
d
1
st
Pe
r
i
o
d
2
nd
Pe
r
i
o
d
3
th
Pe
r
i
o
d
4
th
Pe
r
i
o
d
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 1, March 2
016 : 228 – 2
3
7
236
3.3. Ev
aluation
Verificatio
n
was
con
d
u
c
ted
by com
p
a
r
in
g the p
r
edi
cti
on results yie
l
ded by the
p
r
opo
se
d
model (u
sin
g
the CA approach) to
those of the ones yielded by
the SIR mode
l (a classi
c a
n
d
popul
ar
app
roach). Th
e v
e
rificatio
n
results sho
w
ed
that the sl
op
e of the infe
cted a
r
e
a
-p
eriod
grap
h (Figu
r
e
5) that
rep
r
e
s
ente
d
the
CA model
(the
prop
osed m
o
del)
wa
s
simil
a
r to that of t
h
e
SIR model.
Figure 5. The
Tenden
cy of Grap
h Nu
mb
er of Infected
Area in Bogo
r Barat
In addition, validation
wa
s con
d
u
c
ted b
y
calc
ulating
the simila
rity betwe
en the
resulting
predi
ction u
s
i
ng the CA m
odel an
d that of
the one obtained by th
e SIR model
usin
g Equati
on
10. The validation re
sult indicat
ed that the resulting
predi
ction u
s
ing CA ha
d simila
rities to
the
SIR mod
e
l o
f
0.95. Th
us,
ba
sed
on
th
e verification
and
validati
on results, it
wa
s
able
to
be
stated that t
he propo
se
d
approa
ch u
s
ing
CA
ha
d
been im
ple
m
ented
co
rre
ctly, and that
the
assumptio
n
s
unde
rlying thi
s
mod
e
l are
corre
c
t. Thu
s
, the visualization of the sprea
d
ing p
a
ttern
yielded by th
is mod
e
l wa
s abl
e to be
use
d
for
un
derstandi
ng
and p
r
edi
ctin
g the spread
of
Den
gue di
se
ase. Thi
s
p
r
e
d
iction i
s
re
q
u
ired fo
r
helpi
ng prevent the sp
rea
d
of Dengu
e disea
s
e in
pron
e
regi
on
s. However, t
he p
r
o
p
o
s
ed
model
still
ha
s a
limitation
in that it
did
not con
s
ide
r
t
he
behavio
r of people. Thu
s
, this mod
e
l is o
n
ly
valid to a
relatively static so
ciety.
4. Conclusio
n
From
the
re
sults, it was co
nclu
ded
that
a spre
adin
g
p
a
ttern m
odel
of the
Den
g
u
e
Feve
r
based on the
CA app
roa
c
h
wa
s su
cce
ssf
ully develope
d by setting four pa
ram
e
te
rs
sup
porte
d by
HMM a
nd u
s
ing Von
Ne
u
m
ann
neigh
b
o
rho
od. Th
e
prop
osed m
o
del was
able
to pre
d
ict th
e
spread of De
ngue di
sea
s
e
and provid
e
d
us the in
formation of whi
c
h area shou
ld be observ
ed
carefully. Moreover, the
ev
aluation
re
sul
t
sho
w
e
d
that
the
CA mo
d
e
l was ca
pab
le of g
ene
rati
ng
pattern
s simil
a
r to that of the one g
ene
rated by
SIR model
s with a
similarity value of 0.95.
Ackn
o
w
l
e
dg
ements
This research
did not con
s
i
der the be
ha
vior
of people
.
It was re
alized that the sp
read of
the Deng
ue f
e
ver
depe
nd
s on th
e
popul
ation of
A
e
id
es aeg
ypti
mos
q
uito, which is related to the
behavio
r of people. Thu
s
, the system d
y
namic ap
pro
a
ch
could b
e
con
s
ide
r
ed f
o
r mod
e
ling the
spreadi
ng p
a
ttern as
a future wo
rk.
Moreover,
the imp
r
ovin
g
of this research
co
uld
be
con
d
u
c
ted b
y
using othe
r techni
que
s for sub
s
tituting HMM in
orde
r to find a prob
abili
stic
function that repre
s
e
n
ts the
CA.
Referen
ces
[1]
Cuesta H. Prac
tical Data Analy
s
is. Packt
Publishing Ltd, Birmingha
m-Mumbai. 2013:
153-173.
[2]
Pfeiffer D. Spatial Analy
s
is in Epid
emiology
. Ox
ford
Univ
ers
i
t
y
Press. 20
08
.
[3]
White SH, Re
y AMD, Sänche
z GR. Modelin
g Epid
emic Usi
ng Ce
llu
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o
mata.
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pl
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th
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a
t
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cs
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o
mput
ati
ons
. 200
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: 193-20
2.
[4]
Nishi
ura H. M
a
thematic
al a
n
d
Statisti
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ys
es of the
Sprea
d
of De
n
gue.
D
eng
ue Bull
etin
. 20
06
;
30: 51-5
7
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
A Cellula
r Autom
a
ta Modeli
ng for Visu
ali
z
ing a
nd Pre
d
icting Sp
rea
d
ing… (P
usp
a
Eosina
)
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id
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