Indonesi
an
Journa
l
of El
ect
ri
cal Engineer
ing
an
d
Comp
ut
er
Scie
nce
Vo
l.
23
,
No.
1
,
Ju
ly
2021
, p
p.
3
7
0
~
3
7
7
IS
S
N: 25
02
-
4752, DO
I: 10
.11
591/ijeecs
.v
23
.i
1
.
pp
3
7
0
-
3
7
7
370
Journ
al h
om
e
page
:
http:
//
ij
eecs.i
aesc
or
e.c
om
Modelin
g virus
sp
read on a n
etwork u
sing NetL
ogo for
optimu
m netw
ork man
agem
ent
Catherine
R.
Alim
boy
ong
Dep
a
rtm
ent o
f C
om
pu
te
r
Stu
di
es, Suriga
o De
l Su
r
Stat
e
Un
i
ver
sit
y, T
a
nda
g
Ci
ty
, Phil
ipp
i
nes
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Oct
1,
2018
Re
vised Dec
10, 2
018
Accepte
d
Ja
n 2
5,
2019
The
in
fecti
ons
i
n
computer
n
etw
orks
are
compl
ex
.
I
ts
sprea
d
is
ana
logous
to
a
cont
ag
ious
disea
se
which
can
ca
use
destruction
withi
n
a
f
ew
sec
onds
.
Viruses
in
a
computer
or
comp
ute
r
net
works
c
an
sprea
d
rap
idly
b
y
v
ari
ous
m
ea
ns
such
as
ac
ce
ss
to
onli
n
e
social
net
working
site
s
li
ke
twitter
,
Face
book
,
and
o
peni
ng
of
email
attac
hm
en
ts.
Thus,
i
nfe
ct
i
ons
ca
n
go
from
bei
ng
li
ttl
e
dange
rous
to
si
gnifi
c
ant
l
y
h
ar
m
ful
for
a
netw
ork.
Thi
s
pap
er
proposed
a
sim
ula
ti
on
m
odel
tha
t
ca
n
pre
d
ict
the
propa
gat
ion of vi
rus i
ncl
udin
g
the
tre
nd
and
the
ave
r
ag
e
infect
ion
rate
usi
ng
NetL
og
o
software
.
Ob
serve
d
and
sim
ula
te
d
da
ta
sets
were
valid
at
ed
using
chi
-
s
quar
e
t
ests.
R
es
ult
s
of
the
expe
riment
h
ave
demons
tra
te
d
a
cc
ura
te
per
form
anc
e
of
th
e
prop
osed
m
odel
.
The
m
odel
coul
d
be
ver
y
he
lpful
for
net
work
administra
tors
in
m
itigat
ing
th
e
virus
propa
gat
io
n
and
obstruct
the
sprea
d
of
computer
virus
othe
r
tha
n
th
e
usual
pre
v
ent
io
n
sche
m
e
par
ticula
r
l
y
th
e
use
of
antivirus
s
oftwa
re
and
inc
lusion
of
fi
re
wall
se
cur
ity
.
Ke
yw
or
d
s
:
Com
pu
te
r
vi
rus
NetLo
go
Netw
ork
sec
uri
ty
SI
R
This
is an
open
acc
ess arti
cl
e
un
der
the
CC
B
Y
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
Ca
therine R
. A
lim
bo
yong
Dep
a
rtm
ent o
f C
om
pu
te
r
Stu
di
es
Su
ri
ga
o Del S
ur Stat
e
Un
i
ver
s
it
y
Rosari
o,
Ta
nda
g
Ci
ty
, Sur
iga
o del S
ur,
Ph
il
ip
pin
es
Em
a
il
:
cralim
b
oyong@s
ds
s
u.edu.p
h
1.
INTROD
U
CTION
Ma
lware
-
i
nf
est
ed
com
pu
te
r
s
yst
e
m
s
and
network
s
a
re
a
com
m
on
ph
en
om
eno
n
in
t
he
age
of
bi
g
data.
Ma
lwa
re
is
a
broa
d
te
r
m
that
enco
m
passes
c
om
pu
te
r
vir
us
es
,
w
orm
s,
ro
ot
kits,
tro
j
a
n
hor
ses
,
a
dw
a
re
,
sp
ywa
re,
an
d
oth
e
r
ty
pes
of
unwa
nted
soft
war
e
that
ai
m
to
degrad
e
sys
tem
per
f
or
m
an
ce
[
1]
,
[2]
.
Re
centl
y,
m
al
war
e is being
dev
el
op
e
d m
or
e and
m
or
e to af
fect com
pu
te
r
net
works and
s
pr
ea
d
ove
r
netw
orks
to da
m
age
the co
m
pu
te
r
a
s
m
uch
as poss
ible
[3]
. T
her
e
f
or
e
,
a
m
a
lware
-
infe
ste
d
c
om
pu
te
r
im
plies t
h
at
the en
ti
re n
e
twork
m
ay
b
e aff
ect
e
d
in
a s
hort ti
m
e,
exte
nd
i
ng
do
wn
ti
m
e
[4]
.
Ea
ch
m
inu
te
of downti
m
e
m
eans lo
ss
of
inc
ome
and
syst
e
m
per
fo
r
m
ance.
In
m
os
t
ci
rcu
m
sta
nce
s
,
this
co
uld
r
esult
in
sever
e
crises
li
ke
co
ncens
ab
ou
t
se
cur
it
y
.
Ther
e
f
or
e,
it
is
ver
y
i
m
po
rtan
t
to
un
de
rstan
d
how
m
a
lware
sp
rea
ds
an
d
aff
ect
s
the
net
w
orks
[
5]
,
[6]
.
I
n
the
era
of
i
nfor
m
ation
a
nd
c
ommun
ic
at
io
n
te
c
hnol
og
y
(I
CT
)
s
yst
e
m
s,
ever
yo
ne
thi
nks
as
t
o
how
li
fe
is
going
t
o
be
ca
rr
ie
d
out
as
ICT
a
nd
c
om
m
un
ic
at
ion
de
vices
play
a
c
ru
ci
al
r
ole
i
n
t
he
diff
e
re
nt
fie
lds
of
our
dail
y
li
f
e
par
ti
cula
rly
in
this
tim
e
of
pa
nd
em
ic
crisi
s.
Du
e
to
the f
act
that
the
at
ta
ck
of
vir
us
on
net
works
is
har
m
fu
l
and
that
it
can
da
m
age
hard
ware
or
s
oft
war
e
,
the
resea
rch
on
netw
ork
vi
ru
s
has
bec
ome
vital
[7]
.
T
hi
s
stud
y
at
tem
pts
to
generate
a
m
od
el
of
how
v
ir
us
s
pr
ea
ds
o
n
a
net
wo
rk
us
i
ng
a
N
et
Lo
go
softw
are
v.5
.3.1.
in o
r
der
to
i
m
pr
ove the
str
at
egies of c
on
t
ro
ll
in
g
the
in
fe
sta
ti
on
am
on
g
netw
orks.
Ma
lware
at
ta
c
ks
o
n
c
om
pu
te
r
netw
orks
a
re b
ecom
ing
m
ore
com
m
on
,
a
nd r
esearc
hers
a
re w
orki
ng
to
bette
r
trai
n
ne
twork
m
anag
e
rs
to
av
oid
hu
ge
ly
cat
ast
ro
phic
threats
.
D
ub
ey
et
al
.
[8]
aff
irm
ed
that
e
m
a
il
Worm
s
no
t
on
l
y
decr
ease
eff
i
ci
ency,
resu
lt
in
g
in
a
loss
of
ti
m
e
and
resource
s,
bu
t
they
al
so
ha
ve
an
ef
fe
ct
on
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
Mo
deling vi
ru
s
sp
re
ad
on a ne
tw
or
k usi
ng N
et
Lo
go f
or
opti
mum
…
(
Cat
he
rine R.
Ali
m
boyong
)
371
intangi
ble
asse
ts
su
ch
as
a
co
m
pan
y'
s
rep
uta
ti
on
an
d
cust
om
er
loya
lt
y
[9]
.
Infecti
ons
ca
n
thus
pro
gr
e
s
s
fro
m
bein
g
relat
ivel
y
har
m
le
ss
to
be
ing
e
xtrem
el
y
har
m
fu
l
to
a
ne
twork
[
10
]
.
S
ever
al
st
ud
ie
s
hav
e
re
ported
at
ta
cks
from
i
ntern
et
s
ources
s
uch
as
incidents
of
di
stribu
te
d
de
nial
of
ser
vice
(
DDoS),
at
ta
ck
s
by
la
rg
e
dist
rib
uted
orga
nizat
ion
s
li
ke
Ya
hoo,
A
m
azon
,
CN
N.
c
om
and
oth
e
r
webpa
ges
i
n
2000
.
Acc
ordi
ng
to
A
r
bor
Ne
tworks'
2010
s
urvey,
t
her
e
was
a
sta
r
tl
ing
10
2
per
ce
nt
inc
rease
i
n
DDoS
at
ta
cks
i
n
2010
c
om
par
ed
to
20
09
[6
]
,
[
11]
,
[12]
.
At
prese
nt,
the
re
a
re
num
ero
us
m
ech
anism
s
d
evelo
ped
go
vernin
g
the
s
pread
of
m
a
lware
a
rou
nd
the
netw
orks
s
uc
h
as
m
at
he
m
atical
m
od
el
s
c
apab
le
of
acc
ur
at
el
y
f
or
ese
ei
ng
t
he
propagati
on
of
e
pi
dem
i
c
m
al
ic
iou
s
so
ft
war
e
.
T
he
S
I
R
m
od
el
of
Ma
j
i
et
al
.
[4]
;
Up
a
dhya
y
et
al
.
[
7]
wh
e
re
a
fixe
d
popul
a
ti
on
of
necessa
ry asp
e
ct
s w
as take
n
i
nto
acc
ount
.
T
hese
feature
s
a
re suscepti
ble
(
S)
, i
nf
ect
e
d
(
I),
and r
em
ov
e
d
(
R).
In
epidem
iolog
y,
this
m
et
ho
d
w
as
us
ed
to
e
valuate
the
nu
m
ber
of
s
us
ce
ptib
le
,
sic
k,
an
d
re
cov
e
re
d
pe
op
l
e
in
a
popula
ti
on
[13]
.
Deep
e
ned
by
the
stud
y
of
Zha
ng
et
al
.
[
14]
,
si
m
ulati
ng
of
in
fecti
ous
di
seases
is
a
te
c
hn
i
qu
e
that
has
bee
n
us
e
d
to
resea
r
ch
the
proce
ss
es
as
to
how
infecti
ons
are
t
ran
sm
it
te
d
,
fo
r
ecast
an
ou
t
break’s
po
te
ntial
p
at
h
, a
nd tes
t
ap
proa
ches
for
m
anagi
ng
a
n
outb
rea
k
, acc
ordi
ng to
the a
uthors.
Conver
sel
y
,
c
om
pu
te
rs
with
instal
le
d
so
ft
war
e
ar
e
not
ind
e
finite
ly
viru
s
resist
ant
,
bu
t
they
are
check
e
d
f
or
th
e
viru
s
on
a
re
gu
la
r
basis,
a
nd
the
softwa
re
rem
ov
es
it
if
t
he
de
vice
is
found
to
be
in
fec
te
d
.
A
dev
ic
e
m
ay
be
infecte
d
by
th
e
sam
e
viru
s
s
ever
al
ti
m
es
and
sta
y
in
fected
un
ti
l
the
a
ntiviru
s
s
of
tw
are
r
uns
ano
t
her
sca
n
[6
]
,
[
15]
.
Alte
r
nativel
y,
w
he
n
vir
us
es
m
utate,
the
con
ta
ct
process
al
so
r
oughly
descr
i
be
s
the
sp
rea
d
of
epi
dem
ic
s
in
the
pr
e
sence
of
regularly
up
da
te
d
antivi
ru
s
s
of
t
war
e,
w
hic
h
c
onfer
s
pe
r
m
anen
t
i
m
m
un
it
y.
In
t
his
case
,
antiv
irus
s
of
twa
re
s
top
s
a
de
vice
from
being
inf
ect
ed
with
the
sa
m
e
viru
s,
but
not
with
al
l
m
utated
va
riants
[
16]
.
Seve
ral
stu
dies
ha
ve
bee
n
co
nducte
d
and
m
any
m
at
h
e
m
at
ic
al
m
od
el
s
an
d
strat
egies
ha
ve
bee
n
pr
opos
e
d
to
at
le
ast
obstr
uct
the
s
pread
the
vir
us
on
net
works,
SI
R
m
od
el
[
4]
,
SI
R
S
m
od
el
[13]
,
S
EIR
m
od
el
[
17]
,
SE
IQ
R
m
od
el
[
18]
,
SIPS
m
od
el
[19]
,
S
AI
R
m
od
el
[20
]
,
[
21]
,
SLB
RS
[
22
]
,
SI
IRS
m
od
el
[
23
]
,
d
el
ay
ed
m
od
el
[
24
]
on v
i
ru
s
propa
gatio
n.
In
this
w
ork,
a
new
m
od
el
descr
ibin
g
the
spread
of
vir
us
es
on
a
netw
ork
is
intro
duce
d
as
there
ar
e
sti
ll
so
m
e
def
ic
ie
ncies
an
d
is
su
es
i
n
m
od
el
secur
it
y
a
naly
sis
an
d
c
on
t
ro
l
strat
egies
[7]
.
An
at
te
m
pt
has
be
e
n
m
ade
w
hich
is
ve
ry
use
f
ul
on
the
pa
rt
of
netw
ork
adm
inist
rator
s
in
conveyi
ng
how
syst
em
s
cou
ld
be
config
ur
e
d
t
o
pr
e
ve
nt
or,
at
t
he
ver
y
le
ast
,
s
low
t
he
s
pr
ea
d
of
m
al
war
e
to
the
gr
eat
est
e
xtent
po
s
sible
.
Using
the
m
od
el
,
it
present
t
hr
ee
sta
te
s
of
a
node
in
a
net
work
(a
)
s
us
ce
ptible
(
b)
infecte
d
a
nd
(c)
resist
a
nt
a
nd
how
they
rank
in
te
rm
s
of
m
a
lware
pro
pag
at
io
n
vulner
abili
ty
.
This
stud
y
would
be
extr
e
m
el
y
ben
efic
ia
l
to
orga
nizat
ion
s
in
m
aking
network
i
nfrastr
uc
ture
de
sig
n
decisi
ons
an
d
can
assist
the
m
in
dev
el
opin
g
or
form
ulat
ing
po
li
ci
es
fo
r
opt
i
m
u
m
netwo
r
k
con
fi
gurati
o
n.
The
fo
ll
owin
g
is
how
the
rest
of
the
a
rt
ic
le
is
orga
nized:
T
he
m
od
el
def
i
ni
ti
on
an
d
f
orm
ula
ti
on
are
giv
e
n
in
Sect
ion
2,
the
res
ults
an
d
discu
ssion
is
pr
ese
nted
in Se
ct
ion
3,
a
nd t
he
conclusi
on is presente
d
in
S
ect
ion
4
.
2.
MO
DEL DEF
INITIO
N A
N
D
F
ORM
ULA
TION
This
stu
dy
util
iz
es
the
sim
ula
ti
on
m
et
ho
d
of
researc
h.
This
te
chn
i
qu
e
is
use
d
to
sim
ulate
the
sprea
d
of
c
om
pu
te
r
viru
s
on
netw
orks.
T
he
m
ai
n
f
ocus
of
this
st
ud
y
is
to
ge
nerat
e
a
m
od
el
by
visu
al
iz
in
g
how
th
e
syst
e
m
si
m
ula
t
es
the
infe
sta
ti
on
of
vir
us
on n
et
w
orks
in r
el
at
ion
to
t
he
pa
r
a
m
et
ers
po
i
nted
out
in
this pa
per.
It
is
deem
ed
nec
essary
to
unde
r
sta
nd
t
he
m
echan
ism
on
how
these
vi
ru
se
s
s
pr
ea
d
s
o
that
a
possible
c
on
tr
ol
can
be
de
sig
ned
;
i
n
this
e
nd,
sec
ur
it
y
an
d
safet
y
of
file
s
a
nd
i
m
po
rtant
do
c
um
ents
can
b
e
ens
ur
e
d.
C
hi
-
sq
ua
re
te
sts wer
e
u
se
d t
o
e
xam
ine if an
y si
gnific
a
nt d
if
fer
e
nces e
xi
ste
d
bet
ween t
he obse
r
ved an
d
sim
ulate
d
dat
a
2.1.
Model
d
efinition
This
pa
per
e
nd
eavors
t
o
m
odel
how
a
vir
us
spread
s
ac
ro
s
s
net
works
us
i
ng
the
Vir
us
on
Netw
orks
from
the
m
od
e
ls
li
br
ary
NetL
ogo
v.5.3.
1
(
ve
rsion
2016)
[
25]
.
U
ri
W
il
e
nsky
di
rected
t
he
creati
on
of
an
agen
t
-
base
d
softwa
re
pac
kag
e
cal
le
d
NetL
ogo
at
North
wester
n
Un
i
ver
sit
y'
s
Ce
nter
for
Co
nnect
ed
Le
ar
ning
a
nd
com
pu
te
r
-
base
d
m
od
el
ing
(
CC
L)
.
It
is
the
m
os
t
no
ta
ble
case
of
a
m
ulti
-
agen
t
s
i
m
ulator
that
include
s
StarLo
go, w
hich W
il
e
nsky a
nd Mi
tc
hel Res
nick desi
gn
e
d at
the MIT
Media La
b
[
26]
.
NetLo
go
sho
ws
w
hat
can
act
ually
ta
ke
place
wh
e
n
turtle
popula
ti
on
s
are
giv
en
se
ries
of
requirem
ents
t
o
f
ollow.
Give
n
it
s
us
er
-
f
riend
ly
pro
gra
m
m
ing
interfa
ce,
NetLo
go
can
ha
ndle
co
m
plex
s
i
m
ulati
on
as
well
as
t
he
abili
ty
fo
r
ad
van
ce
d
pro
gra
m
m
ers
to
ad
d
their
own
Ja
va
e
xtensi
on
s
.
As
a
conseq
ue
nce,
NetLo
go
is
uti
li
zed
by
di
verse
gro
up
of
pe
op
le
,
ra
ng
i
ng
f
ro
m
el
e
m
entary
school
stu
de
nts
to
academ
ic
s
in
the
s
ocial
,
el
ec
tro
nic,
a
nd
ha
r
d
fiel
ds
of
sci
ence
.
O
n
the
NetLo
go
we
bsi
te
,
a
dow
nlo
a
d
are
a,
tem
plate
pag
es
,
sam
ple
dow
nl
oad
a
ble
e
xten
sion
s
,
us
er
gu
i
des,
a
F
A
Q,
a
nd
li
nks
to
vari
ou
s
res
ources
are
al
l
avail
able
[
26]
.
Since
the
re
a
re
obser
vatio
ns
wh
ic
h
in
dicat
e
that
com
pu
te
r
eve
n
if
i
ns
ta
ll
ed
with
a
ntivir
us
s
of
t
war
e
are
sti
ll
found
to
be
infecte
d
after
bein
g
sca
nn
e
d
[6]
.
The
sam
e
viru
s
can
infect
m
ulti
ple
m
achines.
se
ver
al
tim
es,
and
it
r
e
m
ai
ns
inf
ect
ed
each ti
m
e
un
ti
l
the a
ntivir
us
pro
gr
am
r
uns a
nothe
r
sca
n
[
1
]
, [
6
]
.
Since c
ompu
te
r
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
23
, N
o.
1
,
Ju
ly
2021
:
3
7
0
-
3
7
7
372
vir
us
es
a
nd
e
pid
em
ic
diseases
ha
ve
sim
il
a
r
pro
pa
gation
char
act
e
risti
cs,
so
m
e
research
ers
ha
ve
pr
opose
d
m
a
t
h
e
m
a
t
i
c
a
l
m
o
d
e
l
s
t
o
r
e
p
r
e
s
e
n
t
t
h
e
s
p
r
e
a
d
o
f
c
o
m
p
u
t
e
r
w
o
r
m
s
o
v
e
r
n
e
t
w
o
r
k
s
i
n
r
e
c
e
n
t
d
e
c
a
d
e
[6
], [
27
], [
2
8
]
.
By
lookin
g
at
t
he pr
opagati
on
, th
e
resea
rch
e
r
conside
rs
t
his
m
od
el
w
hich
re
li
es o
n t
he f
ollow
in
g
a
ssu
m
ption
s:
−
Ma
j
ori
ty
are us
ing
c
om
pu
te
rs t
o
chec
k
em
ai
l
s,
s
o
c
han
ce
s
of
virus in
festat
ion are
expect
e
d.
−
People
us
e
a
nd
i
nteract
with
net
work
s
th
r
ough
onli
ne
so
c
ia
l
netw
orkin
g
sit
es
li
ke
t
witt
er,
f
aceb
ook
.
in
wh
ic
h
the
av
e
r
age
of n
et
work u
sa
ge
ca
n be
draw
n
-
t
his leads
to
the
s
pr
ea
d o
f virus.
−
On
a
ny
giv
e
n
instance,
a
n
e
m
ai
l
or
file
con
ta
ini
ng
vir
us
is
acce
ssed
,
it
beco
m
es
a
ct
ive;
therefor
e,
a
com
pu
te
r or
no
de becom
es act
ive
-
re
sist
ance
can
be
m
easure
d or d
rawn.
−
Com
pu
te
rs
without
sca
nnin
g
or
protect
io
n
t
hro
ugh
a
ntivir
us
s
of
t
war
e
s
uffe
r
m
axi
m
u
m
dam
age
or
s
hut
dow
n becau
se
of the att
ack
.
Figure
1
sho
ws
the
su
sce
ptibl
e
-
infecte
d
-
rec
overe
d
(
SI
R
)
m
od
el
.
The
S
-
I
-
R
m
od
el
is
the
m
os
t
widely
us
e
d
m
et
ho
d
f
or
a
naly
zi
ng
c
om
pu
te
r
vi
ru
s
infecti
ons
(Ma
j
i
et
al
.,
2020
).
Each
nod
e
i
n
a
netw
ork
m
ay
ei
ther
be
in
one
of
th
ree
sta
te
s.
T
hat
is,
the
node
ca
n
be
s
us
ce
ptible,
in
fected,
or
r
ecov
e
re
d.
T
he
m
od
el
si
m
ulates
the
sp
rea
d
of
vir
us
on
net
wor
ks
.
The
var
ia
bles
are
util
iz
ed
a
nd
processe
d
in
a
Net
L
ogo
s
of
t
war
e
t
o
outl
ine
th
e
aver
a
ge
o
f
inf
ect
ed
nodes.
T
he
m
od
el
and
the
program
c
od
e
a
dopted
f
r
om
W
il
ensk
y
[
25
]
are
sho
wn
in
the
fo
ll
owin
g
sect
ion
belo
w.
I
nd
i
vidual
m
ov
em
ent
is
on
e
-
way
S
→
I
→
R
a
nd
t
he
rate
wh
ic
h
con
t
ro
l
how
quic
kly
m
e
m
ber
s
pro
gress
int
o
the
Infecte
d
(I)
a
nd
Re
co
ver
e
d
(R)
gro
up
s
are
the
m
od
el
'
s
two
f
unda
m
ental
par
am
et
ers,
na
m
el
y
a)
infecti
on
rate
and
b)
recovery
rate.
A
com
po
sit
e
at
tribu
te
,
cl
ass
ifie
d
as
the
co
ntact
nu
m
ber
,
is freq
uen
tl
y u
sed
.
Figure
1
.
SI
R
m
od
el
[4]
2.2.
P
ar
amete
rs
T
he
pro
pa
gation
of
a
vir
us
i
s
determ
ined
by
al
l
of
the
pa
ram
et
ers
set
.
The
f
ollow
i
ng
crit
eria
are
consi
der
e
d
when
determ
inin
g
how
c
om
pu
te
r
vir
us
s
pr
ea
ds
on
netw
ork
s
:
(a)
init
ia
l
nu
m
ber
of
node
s;
(b)
aver
a
ge
e
-
m
ai
l
check
/
file
down
l
oad
;
(c
)
a
ve
rag
e
netw
ork
us
a
ge/acc
ess;
and
(d)
f
reque
nc
y
of
vi
ru
s
sca
nn
i
ng.
Du
e
to
t
he
c
omplexit
y o
f
the
m
ai
l netwo
r
k
a
nd the
uncertai
nty of the
be
ha
vior of em
ai
l user
s,
t
his
pap
e
r
r
el
ie
s
m
ai
nly
on
sim
ulati
on
rathe
r
t
han
m
at
he
m
a
tical
analy
sis.
It
is
in
this
way
,
a
reali
sti
c
scen
ario
for
the
spr
ead
of
the v
i
ru
s
is
pr
e
sented
.
The
par
am
et
ers
show
n
in
Ta
ble
1
a
re
ta
ke
n
from
W
il
ens
ky
(2016)
'
s
Vir
us
on
a
Net
wor
k
m
od
el
[26]
in
the
m
od
el
s
li
br
ary.
I
n
ord
er
to
determ
ine
the
beh
a
vior
of
sprea
d
of
vir
us
es
on
net
works,
the
f
ollow
i
ng
par
am
et
ers
are
def
i
ned.
−
In
it
ia
l n
um
ber
of no
des
-
num
ber
of
node
s at t
he
sta
rt
of s
im
ulati
on
.
−
Av
e
ra
g
e
of
em
ai
l check/fil
e
dow
nlo
a
d
-
the a
ver
a
ge n
um
ber
of em
ai
l check/fil
e d
ow
nlo
a
d i
n
each
no
de.
−
Av
e
ra
ge of net
work usa
ge
-
the
av
e
rag
e
num
ber
of
netw
ork
usage i
n
eac
h node.
−
Fr
e
qu
e
ncy
of
vi
ru
s c
hec
k
-
t
he nu
m
ber
of inst
ances a
v
ir
us s
can is
perf
or
m
ed fo
r
eac
h
in
f
ect
ed
no
de.
Table
1.
C
onsist
ency o
f para
m
et
ers
to b
e
de
fine
d
f
or c
om
pu
te
rs
i
n
a
netw
ork
Para
m
eters
on
VI
R
US
Para
m
eters
of
Vir
u
s o
n
netwo
rks
Initial
-
n
o
d
es
Initial
-
n
o
d
es
Av
erage of
inf
ectio
u
s n
o
d
es
Av
erage of
inf
ectio
u
s n
o
d
es
Av
erage of
i
m
m
u
n
e no
d
es
Av
erage of
i
m
m
u
n
e no
d
es
Av
erage of
Vir
u
s
Ch
eck Frequ
en
n
cy
(0.0
0
ti
m
es/
y
ear
)
Av
erage of
Vir
u
s
Ch
eck Frequ
en
n
cy
(
0
.00
ti
m
es/
y
ear
)
2.3.
Sce
na
ri
os fr
om the
m
odel
Table
2
s
hows
the
param
et
er
s
an
d
valu
es
th
at
are
us
e
d
t
o
determ
ine
the
act
ion
of
virus
pro
pa
gatio
n
in
a
network
a
t
the
sta
rt
of
t
he
si
m
ulati
on
.
By
loo
king
at
Figure
2,
on
e
i
s
able
to
visu
a
li
ze
ho
w
the
s
yst
e
m
si
m
ulate
s
the
beh
a
vior
of
vi
ru
s
propagati
on
on
netw
orks
in
relat
ion
to
the
aver
a
ge
of
em
ai
l
check
/fil
e
dow
nlo
a
d,
av
e
rag
e
of
netw
ork
us
a
ge,
a
nd
fr
e
que
ncy
of
vir
us
chec
k
(
scan
ning).
T
he
sim
ulatio
n
sc
enar
i
o
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
Mo
deling vi
ru
s
sp
re
ad
on a ne
tw
or
k usi
ng N
et
Lo
go f
or
opti
mum
…
(
Cat
he
rine R.
Ali
m
boyong
)
373
pr
ese
nted
in
F
igure
2
is
su
ffi
ci
ently
accurate
to
per
m
it
n
et
work
adm
inist
rator
s
dev
el
op
an
d
form
ula
te
a
com
pr
ehe
ns
ive
poli
cy
to
re
du
ce if
no
t i
m
pedes the s
pread
of
vir
us.
Table
2
.
Param
et
ers
of
vir
us
on
netw
orks
act
ual d
at
a
Para
m
eters
of
viru
s o
n
netwo
rks
Valu
e
Initial Nu
m
b
e
r
o
f
no
d
es
85
Av
erage of
e
m
ail
c
h
eck/
f
ile do
wn
lo
a
d
65
Av
erage of
netwo
r
k
us
ag
e/access
70
Frequ
en
cy
of
viru
s ch
eck (scan
n
in
g
)
50%
Av
erage
Nu
m
b
e
r
o
f
inf
ected n
o
d
es
16
Figure
2
.
Sce
na
rios from
the m
od
el
(
NetL
ogo
s
of
t
war
e
)
2.4.
Mathem
at
ic
al
a
na
l
ys
is
In
this
m
od
el
,
a
chi
-
squa
re
goodness
of
fit
te
st
decides
wh
et
her
or
no
t
a
sam
pl
e
of
data
is
represe
ntati
ve
of
the
popula
ti
on
.
T
he
good
ness
of
fit
te
s
t
is
us
ed
to
m
ake
su
re
whet
her
sam
ple
data
is
represe
ntati
ve
of
the
ge
ner
al
popula
ti
on
(i.e
.
a
popula
ti
on
with
a
norm
al
distrib
ution
or
on
e
with
a
W
e
ibu
ll
distrib
ution).
I
n
oth
e
r
wor
ds,
it
inf
orm
s
yo
u
w
heth
er
t
he
data
i
n
yo
ur
sam
ple
is
in
dicat
ive
of
th
e
data
con
ta
ine
d
i
n
t
he
en
ti
re
popula
ti
on
[29].
E
qua
ti
on
1
s
hows
th
e chi
-
s
quare
fo
rm
ula u
sed
i
n
t
his a
naly
sis.
2
=
∑
(
O
i
−
E
i
)
2
E
i
(1)
w
here:
O
i
= t
he ob
se
r
ve
d fr
e
qu
e
ncy
(the obse
r
ved co
un
ts
in
t
he
cel
ls)
E
i
= the
expect
ed fre
qu
e
ncy
if
NO r
el
at
io
nsh
ip ex
ist
e
d betw
een th
e
v
a
riabl
es
2.4.
Sim
ulat
i
on
In
this
sect
io
n,
the
resu
lt
s
of
si
m
ulati
on
s
a
re
pr
e
sente
d
in
order
to
be
tt
er
under
sta
nd
how
vir
us
sp
rea
d.
Table
3
a
nd
Fig
ur
e
3
pr
e
sents
t
he
a
ct
ual
data
c
ollec
te
d
f
ro
m
the
univer
sit
y’s
ne
twork
a
dm
inist
rator.
Data
set
of
i
nfect
ed
nodes
f
ro
m
Janu
a
ry
t
o
Decem
ber
wer
e
colle
ct
ed
from
the
re
port
pr
e
sente
d
by
the
netw
ork
a
dm
in
ist
rator
wh
e
re
N=85
a
re
the
num
ber
of
avai
l
able
com
pu
te
rs
(no
des)
util
iz
ed
by
t
he
stu
de
nts
in
the
inter
net
la
bo
rat
or
y.
T
he
st
ud
y
c
on
si
der
s
t
en
(
10)
obse
rvat
ion
s
as
ca
n
be
seen
in
Ta
ble
3.
U
sin
g
the
m
ean,
the total
nu
m
ber
of
i
nf
ect
e
d n
od
e
s
ov
e
r
a
12
-
m
on
th sp
a
n
is
15.83.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
23
, N
o.
1
,
Ju
ly
2021
:
3
7
0
-
3
7
7
374
Table
3
.
Actua
l data gat
he
re
d from
8
5 nodes
Para
m
eters
(N=85
)
Tr
ial
1
(Jan
)
Tr
ial
2
(Feb)
Tr
ial
3
(M
a
r)
Tr
ial
4
(Apr)
Tr
ial
5
(M
a
y
)
Tr
ial
6
(Ju
n
e)
Tr
ial
7
(Ju
l)
Tr
ial
8
(Aug
)
Tr
ial
9
(Sept)
Tr
ial
10
(Oct)
Tr
ial
11
(Nov
)
Tr
ial
12
(Dec
)
Av
erage
o
f
in
f
ected
n
o
d
es
Inf
ected
18
16
19
14
12
15
15
18
16
18
15
14
1
5
.83
Figure
3
.
Act
ua
l/
o
bs
er
ve
d dat
a
Fu
rt
her
m
or
e,
the
gr
a
ph
i
n
Figure
3
de
pi
ct
s
the
data
gathe
red
f
ro
m
the
unive
rsity
'
s
netwo
r
k
adm
inist
rator
,
sp
eci
fical
ly
in
Suriga
o
del
Su
r
Stat
e
U
ni
ver
sit
y,
Ta
nd
a
g
Ci
ty
,
Ph
il
ip
pin
es
.
T
he
str
eng
t
h
of
vir
us
tra
ns
m
iss
ion
is best
desc
ribe
d
by
the p
l
ot
in
the g
ra
ph,
wh
ic
h
is
cal
cu
la
te
d
by
the p
r
ob
a
bili
ty
of
op
enin
g
of
em
ail
at
ta
chm
ents
an
d
network
us
e.
It
al
so
de
pends
on
the
am
ou
nt
of
tim
e
and
f
re
quency
at
wh
ic
h
vir
us
es
are
scan
ne
d.
Th
e
res
ult
is
affi
rm
ing
to
the
cl
aim
of
M.
Zhang
et
al
.
[18]
that
la
rg
e
-
s
cal
e
and
ra
pid
virus
dissem
inati
on
occurs
durin
g
the
m
os
t
fr
eq
ue
nt
acce
ss
to
e
m
ai
ls.
As
Up
a
dh
ya
y
et
al
.
[5]
pu
ts
it
,
if
su
s
cepti
ble
com
pu
te
rs
c
ome
into
c
onta
ct
with in
fected
c
om
pu
te
rs,
t
he vir
us
ca
n
s
pr
ea
d
s
wiftly
3.
RESU
LT
S
A
ND
D
IS
C
USS
ION
S
Com
pu
te
r
vi
rus
has
bec
om
e
on
e
of
t
he
m
ajo
r
threats
to
t
he
secu
rity
of
the
netw
ork.
It
has
rap
i
dly
evo
l
ved
ac
ro
s
s
the
i
ntern
et
,
causin
g
m
i
ll
ion
s
or
eve
n
bill
ion
s
of
data
los
s
[29]
.
At
pr
es
ent,
acce
ss
to
on
li
ne
so
ci
al
netw
ork
ing
sit
es
(such
as
twit
te
r,
faceboo
k
.
)
that
even
t
ually
at
tra
ct
e
d
pe
op
le
of
al
l
ages
fr
om
arou
nd
the
gl
ob
e
is
t
he
pr
im
ary
veh
i
cl
e
for
tra
ns
m
i
tt
ing
com
pu
te
r
vir
us
es
[4]
.
C
om
pu
te
r
vi
ru
se
s,
on
th
e
ot
her
ha
nd,
are
ty
pical
ly
delivered
t
o
a
c
om
pu
te
r
as
an
at
ta
chm
ent
to
a
n
em
ail
m
essa
ge,
w
hic
h
w
he
n
act
ivate
d
by
the
us
e
r
sen
ds
ex
te
nde
d cop
ie
s of the
vi
ru
s to
ot
her
re
ci
pients.
Ba
sed
o
n
the act
ual dat
a sets, the r
esearche
r
at
tem
pts to
est
ablish
a
sim
ulati
on
e
nviro
nm
ent
wh
ic
h
i
nclu
des
85
no
des.
T
he
n
te
n
(
10)
sim
ulati
on
runs
wer
e
perform
ed
giv
e
n
the
init
ia
l data coll
ect
ed
.
Table
4
an
d
Figure
4
pres
ents
the
si
m
ulati
on
of
te
n
obser
vatio
ns
or
tria
ls.
Hen
ce,
the
aver
a
ge
nu
m
ber
of
inf
ect
ed
no
des
w
hich
is
15.
03
ov
e
r
a
pe
rio
d
of
12
m
on
ths
,
cl
os
el
y
ex
hib
it
s
an
d
has
al
m
os
t
the
sam
e
value
fro
m
the
ave
rag
e
of
i
nf
ect
e
d
nodes
of
the
act
ua
l
data
w
hich
is
15.
83.
T
he
r
esult
is
evi
dent
after
te
n
(10
)
si
m
ulati
on
r
uns
has
been
perform
ed.
T
his
i
m
pli
es
that
the
sim
ula
ti
on
m
od
el
cou
ld
r
efle
ct
the
beh
a
vior
of
how
a
vir
us
spread
over
a
ne
twork
.
Sim
i
lar
ly
,
it
can
hel
p
pre
dict
the
pro
pag
at
io
n
of
vir
us
includi
ng the
tr
end whic
h hel
ps net
work adm
inist
rator
s
pre
ve
nt and c
ontr
ol the vir
us
s
pr
ea
d
.
T
a
bl
e
4.
S
i
m
ul
a
t
e
d
da
t
a
Para
m
eters
(N=8
5
)
Tr
ial
1
(Jan
)
Tr
ial
2
(Feb)
Tr
ial
3
(M
a
r)
Tr
ial
4
(Apr)
Tr
ial
5
(M
a
y
)
Tr
ial
6
(Ju
n
e)
Tr
ial
7
(Ju
l)
Tr
ial
8
(Aug
)
Tr
ial
9
(Sept)
Tr
ial
10
(Oct)
Tr
ial
11
(Nov
)
Tr
ial
12
(Dec
)
Av
erage
o
f
in
f
ected
n
o
d
es
Inf
ected
1
6
.47
1
6
.67
1
2
.94
1
4
.12
1
2
.96
1
1
.76
1
9
.05
1
6
.47
1
5
.29
1
4
.12
1
7
.65
1
2
.94
1
5
.03
Figure
5
de
picts
the
sim
ulatio
n
res
ult
of
both
scena
rios.
The
fig
ur
e
re
ve
al
ed
that
t
he
act
ual
an
d
si
m
ulate
d
data
is
ver
y
cl
os
e.
Th
us
,
it
i
m
plies
that
the
m
od
el
after
bein
g
va
li
dated,
is
suf
fici
ently
accur
at
e
and
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
Mo
deling vi
ru
s
sp
re
ad
on a ne
tw
or
k usi
ng N
et
Lo
go f
or
opti
mum
…
(
Cat
he
rine R.
Ali
m
boyong
)
3
75
consi
ste
nt.
I
n
t
erm
s
of
i
m
plem
entat
ion
,
howe
ve
r,
t
her
e
is
li
ttle
that
network
adm
inist
rator
s
ca
n
do
to
con
t
ro
l
the
sp
rea
d
of
a
viru
s
in
the worl
d
at
la
rg
e.
T
he
res
ult
sh
ow co
nsi
ste
ncy
with
the
stud
y
of
Tan
g
et
al
.
[7]
,
as
he
pu
ts
it
that
i
n
the
process
of
vir
us
pr
e
ven
ti
on
a
nd
c
ontr
ol,
we
m
us
t
no
t
only
i
m
pr
ove
pe
op
le
'
s
unde
rst
and
i
ng
of
virus
trans
m
issi
on
m
echa
nism
s
,
bu
t
al
so
evaluate
the
s
ecur
it
y
of
a
c
om
plex
env
iro
nm
ent
us
ing
t
he
safety
entr
op
y
of n
et
work ne
tw
orks
and thei
r
e
vo
l
ving
patte
rn
s
.
Figure
4
.
Sim
ulate
d
data
Figure
5
.
Sim
ulati
on
of
both s
cenari
os
(sim
ul
at
ed
an
d o
bs
er
ved)
Con
se
quently
,
w
hilst
t
he
e
f
forts
of
netw
ork
adm
inist
rator
s
are
usual
ly
fo
c
us
e
d
on
m
ini
m
iz
ing
dam
age
on
ce
the
in
fecti
on
e
nters
t
he
com
pu
te
r
syst
em
f
or
w
hich
t
hey
ha
ve
res
ponsi
bili
ty
.
Th
is
fin
ding
s
su
ggest
t
hat
it
is
vital
ly
i
m
po
rtant
to
im
po
se
no
t
only
to
ne
twork
a
dm
inistr
at
ors
but
al
so
to
the
inte
rn
et
us
er
s
with
ne
tw
ork
secur
it
y
awa
re
ness
trai
nings
and
t
o
be
able
to
ta
ke
pro
pe
r
m
easur
es
to
reno
vate
the
s
yst
e
m
,
m
aking
it
strongly
-
protect
ed
[
4]
,
[30
]
.
F
ur
t
her
m
or
e,
the
r
esult
cl
early
s
hows
that
the
sp
rea
d
of
vir
us
can
be
pr
e
dicte
d
us
in
g
the
pro
posed
m
od
el
.
T
hus,
t
he
m
od
el
en
ha
nces
a
nd
ce
rtai
nly
expan
ds
th
e
process
of
sc
ann
i
ng
the
c
om
pu
te
rs
as
a
way
of
a
ddressi
ng
the
is
su
e
of
netw
ork
secu
rity
.
T
he
i
ncr
easi
ng
nu
m
ber
of
i
nf
ect
e
d
node
s
con
ti
nues to chal
le
ng
e the n
et
work
a
dm
inist
r
at
or
to upgra
de
the so
ftwa
re perio
dical
ly
an
d
to incr
ease security
awar
e
ness
.
At
m
ulti
ple
te
st
runs,
t
he
sim
u
la
ti
on
m
od
el
can
predict
the
pro
pag
at
io
n
of
virus
inclu
ding
the
tren
d,
w
hich
is
of
big
help
for netw
ork
ad
m
i
nistrato
rs
in
ob
ta
ining
opti
m
u
m
n
et
wo
r
k
m
a
nag
em
en
t.
4.
CONCL
US
I
O
N
The
sim
ulati
o
n
sho
wed
that
sp
rea
d
of
vir
us
on
net
wor
ks
can
be
m
ini
m
iz
ed
and
pre
dicte
d.
T
o
si
m
ulate
viru
s
sp
rea
d,
W
il
e
nsky'
s
Viru
s
on
a
Network
m
od
el
was
us
e
d
in
a
com
pu
te
r
netw
ork
an
d
da
ta
set
s
wer
e
validat
ed
us
in
g
chi
s
qu
are
te
st
.
Re
su
lt
s
of
t
he
ex
pe
rim
ent
hav
e
de
m
on
strat
ed
acc
ur
at
e
perform
a
nce
of
the
pro
pose
d
m
od
el
.
The
st
ud
y
s
uggests
t
hat
scan
ning
c
an
be
pe
rfo
rm
ed
we
ekly
or
perha
ps
re
gula
rly
at
a
sp
eci
fied
ti
m
e
fr
am
e.
More
ov
e
r,
the
sim
ulati
on
e
xp
e
ri
m
ent
m
ade
in
this
stud
y
si
gn
i
f
ic
antly
i
m
pro
ves
0
5
10
15
20
25
0
2
4
6
8
10
12
14
Av
e Num
ber
o
f
Infecte
d
No
des
M
o
nth(
s)
Sim
u
lated
Act
u
al/
Ob
se
rved
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
23
, N
o.
1
,
Ju
ly
2021
:
3
7
0
-
3
7
7
376
epidem
ic
erad
i
cat
ion
as
c
ompare
d
t
o
em
plo
yi
ng
a
l
on
e
s
trat
egy
li
ke
t
he
cu
rr
e
nt
vir
us
preve
ntio
n
sc
hem
e
util
iz
ing
a
ntiviru
s
softwa
re a
nd
firew
al
l sec
uri
ty
.
ACKN
OWLE
DGE
MENTS
The
aut
hor
ex
pr
ess
es
grat
it
ud
e
to
the
eva
luators
for
th
ei
r
insigh
t
fu
l
com
m
ents
.
Th
is
wo
r
k
is
su
pp
or
te
d by the
Office
of th
e Rese
arc
h
a
nd D
e
velo
pm
ent o
f Su
riga
o del
Su
r
Stat
e Univ
ersit
y, Ma
in C
a
m
pu
s
,
Tan
dag Ci
ty
Su
ri
gao d
el
Sur,
Ph
il
ip
pin
es
.
REFERE
NCE
S
[1]
Z.
Masood,
R
.
Sa
m
ar,
M.
A.
Z.
Raj
a
,
“
Design
of
a
m
at
hemat
ic
a
l
m
odel
for
the
St
uxnet
virus
in
a
net
work
of
cr
it
i
c
a
l
cont
rol
infra
st
ru
ct
ure
,
”
Compute
r and
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uri
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v
ol.
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p
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2019
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doi
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[2]
P.
Shahre
ar
,
A.
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Chakra
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a,
“
Analy
sis
of
Com
pute
r
Virus
Propaga
ti
on
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ase
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o
n
Com
par
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”
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utat
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[3]
A.
Raz
a
et
al
,
“
Mathe
m
at
i
ca
l
an
aly
s
is
and
design
of
the
nonstanda
rd
comput
at
io
nal
m
et
hod
for
an
epi
demic
m
ode
l
of
computer
viru
s
with
del
a
y
Eff
ec
t
:
Applicati
on
of
m
at
hemati
c
al
biol
og
y
in
computer
sci
ence,
”
R
esult
s
in
Ph
ys
ics
,
vol.
21
,
p
.
10375
0,
2021
,
doi
:
10
.
1016/j
.
r
inp.
2020
.
103750.
[4]
G.
Maji
,
S.
Man
dal
,
S.
Sen
,
“
A
s
y
stemat
ic
sur
ve
y
on
infl
uent
i
al
sp
rea
der
s
id
ent
if
icati
on
in
complex
net
works
with
a
foc
us
on
K
-
sh
el
l
bas
ed
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5.
BIOGR
AP
H
Y
O
F
AU
TH
OR
Cath
er
ine
R.
Alimboy
ong
is
a
n
As
socia
te
P
rofe
ss
or
at
Surigao
Del
Sur
Stat
e
Univer
sit
y
,
where
she
teac
h
es
computer
sc
i
enc
e
.
She
obtain
ed
a
n
MIT
degr
ee
in
2018
from
Saint
Pau
l
Univesrity
Phil
i
ppine
s,
Tugue
ga
ro
Cit
y
and
a
d
oct
ora
te
of
IT
i
n
2019
from
Technol
ogi
ca
l
Instit
ute
of
T
echnolog
y
,
Que
zo
n
Cit
y
,
Phili
pp
i
nes
.
Dee
p
learni
ng,
n
e
twork
pro
te
c
ti
on,
data
m
ini
ng
,
and
IT
software
p
roject
m
ana
gement
are som
e
of
her
cur
ren
t
r
ese
ar
ch int
ere
sts.
cra
l
imbo
y
ong@
sds
su.e
du.
ph
Evaluation Warning : The document was created with Spire.PDF for Python.