Intern
ati
o
n
a
l
Jo
urn
a
l
o
f
P
u
b
lic Hea
l
th Science (IJ
P
HS)
V
o
l.4
,
No
.1
, Mar
c
h20
15
, pp
.
7
~
16
I
S
SN
: 225
2-8
8
0
6
7
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPHS
Malaria Disease Distribution
in Sudan Using Time Series
ARIMA Model
Mohammed I.
Mus
a
Economic
and S
o
cial Research
B
u
reau, Ministr
y
of Sc
ien
c
e and
C
o
mmunication,
P.O. Box 1166
,
Khartoum, Sudan
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Mar 17, 2014
Rev
i
sed
No
v
20
, 20
14
Accepte
d
Ja
n 26, 2015
Malaria is widely
spread
and
distri
buted
in
the tropical and
subtropical
regions of
the world. Sudan
is
a sub-
Saharan
African
countr
y
th
at
is hig
h
l
y
affected b
y
malaria with 7
.
5 million
cases and 35
,000 deaths
ever
y
y
e
ar
. The
auto-regr
essive
integr
ated moving av
erag
e (A
RIM
A
) m
odel was
us
ed to
predic
t the spre
a
d
of m
a
laria
in t
h
e
Sudan. Th
e
ARIMA
model used malaria
cases from 2006 to 2011 as a
training set,
and data from 2012 as a testing set,
and cre
a
ted
the
best m
odel fitt
e
d
to forec
a
st the
m
a
laria
cases i
n
Sudan for
y
e
ars 2013 and 2014. The ARIMAX
model was carried out to
examine th
e
relationship between malar
i
a
cases and
climate factors with diagnostics of
previous
m
a
lari
a cas
es
us
ing th
e leas
t B
a
yes
i
an
Inform
ation Criteri
a (BIC)
values.
The res
u
lts indic
a
ted
t
h
at th
er
e were four different
models, the
ARIM
A
m
odel of the
averag
e
for the ov
eral
l
s
t
ates
is
(1
,0,1)(
0,1,1)
. Th
e
ARIM
AX
m
ode
l s
howed that t
h
ere is
a s
i
gnif
i
cant va
ria
tion b
e
tween t
h
e
s
t
ates
in
S
udan
.
Keyword:
AR
IM
A
m
odel
A
R
I
M
AX
BIC
Malaria cases
Tim
e
series
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
M
oham
m
ed
I. M
u
sa,
Econom
ic and
Social Researc
h
B
u
rea
u
,
M
i
ni
st
ry
of
Sci
e
nce a
n
d
Tec
h
nol
ogy
,
P.O. Box
11
66, Kh
ar
tou
m
, Sud
a
n.
Em
a
il: meag
e20
08@yaho
o.com
1.
INTRODUCTION
Th
e
Nation
a
l Malaria Co
n
t
ro
l Prog
ramm
e
(200
4)
d
ecl
ared that m
a
laria is endem
i
c in Sudan; t
h
e
wh
ol
e p
o
pul
at
i
on i
s
at
v
a
ry
i
n
g de
g
r
ees o
f
r
i
sk. F
o
u
r
m
a
i
n
epi
d
em
i
o
l
ogi
c
a
l
m
a
l
a
ri
a areas i
n
Su
da
n c
a
n be
id
en
tified
as fo
llo
ws,
h
i
gh
tran
sm
issio
n
related
to
i
rri
gat
i
on i
n
l
a
r
g
e i
r
ri
gat
i
o
n sc
hem
e
s, seas
onal
m
a
l
a
ri
a
related
to rai
n
fall in
th
e cen
t
ral p
a
rts
of Sudan
,
m
a
n
-
m
a
d
e
u
r
b
a
n
m
a
laria an
d d
e
sert-fri
ng
e m
a
laria related
to
N
ile f
l
ood
[1
].
Tem
p
erature and rai
n
fall are
the
m
o
st im
p
o
rta
n
t in
the transm
ission cycle of
m
a
laria [2]
.
Rainfall
increases
the
relative hum
i
dity, and,
h
e
n
ce,
th
e lon
g
e
v
ity
o
f
th
e adu
lt mo
squ
ito [3
],
wh
ereas tem
p
eratu
r
e is
m
o
re critical to m
a
laria transmission
th
roug
h
its effect on
th
e
d
u
ration an
d
surv
i
v
al o
f
the m
o
sq
u
ito
[4
].
Rain
fall prov
ides a su
itab
l
e
hab
itat for t
h
e life cycle of t
h
e
m
o
sq
u
ito
,
bu
t
ex
cessiv
e
rai
n
fall lead
s to
flush
ou
t
th
e m
o
sq
u
ito
l
a
rv
a. A tem
p
eratu
r
e
rang
e
o
f
2
0
°-25
°C in
creases th
e long
evity o
f
m
o
sq
u
itos; h
o
wev
e
r, ex
t
r
em
e
te
m
p
eratu
r
e
will in
crease mo
rtality [5
]. Th
e clim
a
t
e v
a
riab
ility p
l
ays
an
im
p
o
r
tan
t
ro
le in
starting
m
a
laria
ep
id
em
ics in
the East African
h
i
gh
land
s
[6
].
Acco
r
d
i
n
g t
o
[7]
c
hl
or
o
qui
ne
i
s
no l
o
n
g
e
r
effect
i
v
e i
n
S
uda
n as t
h
e t
r
eatm
e
nt
of
P .f
al
ci
pa
r
u
m
malaria. There
f
ore, a cha
n
ge
in
m
a
laria tre
a
t
m
en
t to
Aresu
n
ate + Su
lfad
ox
in
e/Py
rim
e
th
amin
e (AS+SP) is
reco
mm
en
d
e
d
for first-lin
e treat
m
e
n
t
o
f
m
a
laria, wh
ile Arte
m
e
th
er + Lu
mefan
t
rin
e
is reco
mmen
d
e
d
as th
e
secon
d
-lin
e treat
m
e
n
t
. Th
e th
ird-lin
e is Qu
in
i
n
e as
well as the drug of choice
for se
ve
re malaria.
Su
lfado
x
i
n
e
/Pyri
m
eth
a
m
i
n
e
i
s
reco
mmen
d
e
d
for
In
term
itte
n
t
Prev
en
tiv
e
Treatm
e
n
t
(IPT) in preg
n
a
n
c
y [7
].
C
ont
r
o
l
M
a
l
a
ri
a i
s
poo
r i
n
m
o
st
of t
h
e Af
ri
can co
unt
ri
es and t
r
eat
m
e
nt
cons
um
es l
a
rge am
ount
s
of
h
ealth
bu
dg
ets in
th
es
e countries. Since malaria poses a threat to
nat
i
v
e po
pul
at
i
o
ns as wel
l
as fore
i
gne
rs.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:2252
-88
06
IJP
H
S
V
o
l
.
4,
No
. 1,
M
a
rc
h 20
1
5
:
7 – 1
6
8
M
a
l
a
ri
a, t
h
eref
ore
,
not
o
n
l
y
affect
s t
h
e heal
t
h
st
at
us of
Af
ri
ca'
s popul
at
i
o
n
,
but
al
so has a
ffect
s t
h
e eco
n
o
m
y
.
M
a
l
a
ri
a di
sease rem
a
i
n
s an im
port
a
nt
p
u
b
l
i
c
heal
t
h
pro
b
l
e
m
i
n
Sub
-
Saha
ran
Af
ri
ca;
hence, t
o
d
e
vel
o
p
su
itab
l
e too
l
s fo
r t
h
e con
t
ro
l
o
f
m
a
laria requ
ires a
b
e
tte
r
un
d
e
rstand
ing
of how m
a
laria
is d
i
stribu
ted
with
in
an a
r
ea [8].
The aim
of thi
s
study is t
o
forecast m
a
laria
cas
es for
2013 and 2014, a
n
d
exam
ine the relationshi
p
betwee
n m
a
lar
i
a cases and c
l
im
a
tic factors
per stat
e
i
n
Su
dan usi
n
g Aut
o
-R
e
g
res
s
i
v
e
I
n
t
e
g
r
at
ed M
ovi
n
g
Ave
r
a
g
e AR
I
M
A m
odel
s
an
d t
h
e
AR
IM
A
X
m
odel
[
9
]
–
[
11]
.
The
p
r
ese
n
t
st
u
d
y
use
d
m
a
l
a
ri
a cases f
r
om
20
06
to 2011 as
a training set, whe
r
eas t
h
e
data from
2012 is
u
s
ed
as a testing
set, and
creates
th
e
b
e
st m
o
d
e
l fit t
o
forecast the
m
a
laria cases in
Suda
n
for yea
r
s
2013 a
n
d 2014.
2.
R
E
SEARC
H M
ETHOD
2.
1. Stu
d
y
Are
a
Thi
s
st
udy
i
n
c
l
udes
al
l
t
h
e s
t
at
es of
Su
da
n
,
nam
e
l
y
, Kha
r
t
o
um
, Kassal
a
, Al
Gazi
ra
h,
N
o
rt
h
e
r
n
,
Si
nna
r, R
i
ve
r
Ni
l
e
, R
e
d Sea
,
Whi
t
e
Ni
l
e
,
Ga
dare
f, B
l
ue
Ni
l
e
, N
o
rt
h Da
rf
u
r
,
West
Da
rf
ur
,
So
ut
h
Dar
f
u
r
,
So
ut
h
Go
rd
o
f
an a
nd
No
rt
h G
o
rd
of
a
n
, as sh
o
w
n i
n
Fi
gu
re 1. T
h
e
s
e st
at
es vary
geo
g
r
ap
hi
cal
l
y
i
n
t
e
r
m
s of cl
im
at
e,
ran
g
i
n
g f
r
om
desert
i
n
t
h
e
No
rt
h
,
sem
i
-de
s
ert
and sa
van
n
ah i
n
t
h
e ce
n
t
re and s
out
h [
12]
. Tem
p
erat
ures are
o
f
ten
h
i
g
h
from March
un
til Jun
e
; fro
m
Ju
ly u
n
til Octob
e
r it is
m
ild
an
d rain
y, an
d co
l
d
fro
m
Nov
e
mb
er t
o
Feb
r
ua
ry
wi
t
h
l
o
w t
e
m
p
erat
ur
e. M
a
l
a
ri
a t
r
an
sm
i
ssi
on i
s
hi
g
h
i
n
t
h
e m
i
ddl
e of aut
u
m
n
and
begi
ns t
o
dec
r
ease
with
co
n
tinu
e
d lo
w tem
p
eratu
r
es in wi
n
t
er
[13
]
.
Fig
u
r
e
1
.
Cho
r
o
p
l
eth m
a
p
o
f
malar
i
a r
a
te in
Sud
a
n fo
r 2006
-20
11
2.
2.
Mal
a
ri
a D
a
t
a
The m
ont
hl
y
m
a
l
a
ri
a cases
were
obt
ai
ne
d
fr
om
t
h
e Nat
i
o
nal
M
a
l
a
ri
a C
ont
r
o
l
Pro
g
r
am
m
e
(NM
C
P),
whi
c
h
was
est
a
bl
i
s
he
d
by
t
h
e Fe
deral
M
i
n
i
st
ry
of
Heal
t
h
(FM
H
)
,
S
u
da
n,
f
r
om
y
ears 20
0
6
t
o
20
1
2
.
The
malaria cases from
several levels of health centres,
a
n
d
hos
pi
t
a
l
s
are r
e
po
rt
ed t
o
t
h
e
NM
C
P
eve
r
y
m
ont
h.
These health centres
and hospitals
pr
o
v
i
d
e m
a
l
a
ri
a di
agn
o
si
s ei
t
h
er
by
dem
onst
r
at
i
on
o
f
ase
x
ual
f
o
rm
s
(t
ro
p
hoz
oi
t
e
st
age)
o
f
t
h
e
par
a
si
t
e
i
n
t
h
e t
h
i
c
k o
r
t
h
i
n
peri
phe
ral
bl
oo
d
fi
lm
or by
ra
pi
d
di
ag
no
st
i
c
t
e
st
(R
DT
)
in the
presenc
e
of fe
ve
r [7].
M
a
l
a
ri
a di
st
ri
but
i
o
n va
ri
es
great
l
y
bet
w
e
e
n t
h
e st
at
es [1
2]
. Fi
g
u
re
1 sh
ow
s t
h
e m
a
l
a
ri
a rat
e
d
i
stribu
tio
n, wh
ich
is repo
rted
as h
i
gh
in
th
e Cen
t
ral a
nd
Eastern states in the study
are
a
. The data refl
ects the
ag
greg
ated
malaria cases at th
e states
le
v
e
l, wh
ich
v
a
ries in
q
u
a
lity an
d
m
a
y
h
a
v
e
li
m
i
ted
v
a
lu
e in
Le
g
e
nd
Mal
a
ria
Ra
t
e
20 -
2
3
24 -
3
5
36 -
7
5
76 -
1
0
3
104
-
1
5
1
01
5
0
75
K
i
l
o
m
e
t
e
r
s
¬
N
o
rt
h
e
rn
N.
D
a
r
f
u
r
Re
d
S
e
a
N.
G
o
r
d
of
a
n
S.
D
a
r
f
u
r
N
ile
R
i
v
e
r
S
.
G
o
rdof
a
n
Ge
d
a
r
e
f
S
i
nnar
K
a
ssa
l
a
W, D
a
r
f
u
r
Bul
e
Ni
l
e
Khartoum
Wh
ite
N
i
le
Al
Gaz
i
r
a
h
18
.
6
813
71
25
.
6
8
137
1
25
.
6
8
137
1
32
.
681
371
32
.
681
371
39
.
681
371
39
.
681
371
10
.
9
9023
4
10
.
9
9023
4
17
.
9
9023
4
17
.
9
9023
4
24
.
9
90
234
24
.
9
90
234
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PH
S I
S
SN
:
225
2-8
8
0
6
Mal
a
ri
a Di
sea
s
e
Di
st
ri
b
u
t
i
o
n
i
n
Su
d
a
n
U
s
i
n
g
Ti
me Seri
es ARIMA
Mo
del
(
M
oh
am
me
d I. Mus
a
)
9
un
de
rst
a
n
d
i
n
g t
h
e act
ual
m
a
lari
a bu
rde
n
;
h
o
we
ve
r, i
t
m
a
y be usef
ul
f
o
r
un
de
rst
a
n
d
i
n
g t
r
en
ds i
n
t
h
e r
e
l
a
t
i
v
e
burden of m
a
la
ria in t
h
e public
health sector.
2.
3. Me
teor
ol
o
g
i
c
al
Da
t
a
A clim
a
tic reco
rd
fro
m
2
0
0
6
to
2
012
was ob
tain
ed fro
m
th
e Su
d
a
n Meteo
r
o
l
og
ical Au
t
h
ority
(SM
A
). M
ont
hly
rep
o
rte
d
c
l
im
atic variabl
e
s incl
ude ave
r
age m
i
nim
u
m and m
a
xim
u
m te
m
p
erature
,
and
rainfall. T
h
e clim
ate
data are
collected and recorde
d
at
the
weathe
r stations in each
state. The
m
e
teorol
ogical
u
n
it m
a
in
tain
s th
e reco
rd
s of
all th
e state climatic v
a
riab
les at th
e cen
t
ral l
e
v
e
l.
2.
4. A
R
IM
A Mo
del
G
e
n
e
r
a
lly, Auto
-
R
egr
e
ssi
v
e
I
n
teg
r
ated
M
o
v
i
ng
Av
er
ag
e
(
A
RI
M
A
)
m
o
d
e
ls w
e
r
e
popu
lar
i
zed
b
y
Geo
r
ge B
ox a
nd
Gwi
l
y
m
Jenki
ns i
n
t
h
e 1
9
7
0
s;
t
r
adi
t
i
o
n
a
l
l
y
know
n as
B
ox-
Jen
k
i
n
s
anal
y
s
i
s
[1
4]
. M
a
ny
pre
v
i
o
us st
u
d
i
e
s used t
h
e
AR
I
M
A m
odel
i
n
the st
u
d
y
of t
i
m
e seri
es of m
a
lari
a i
n
di
ffe
re
n
t
part
s of t
h
e
w
o
rl
d
whe
r
e t
h
ere
wa
s hi
gh m
a
laria
transm
ission.
Th
e pr
esen
t stu
d
y
adop
ted
t
h
e no
n-
seasonal A
u
to
-re
gre
s
si
ve Int
e
grat
e
d
M
ovi
n
g
A
v
e
r
age AR
IM
A
(p
,d
,q
) a
n
d
sea
s
on
al AR
IM
A
(P,
D
,
Q
)
s
m
ode
l
m
e
nt
i
one
d
by
[
11]
,
w
h
ere:
p is t
h
e a
u
toregressive
term
and P is the
seas
onal aut
o
re
gress
i
ve term
.
d is t
h
e
non-se
asonal differe
n
ce. D is the
sea
s
onal differe
n
c
e
.
q is t
h
e m
oving a
v
era
g
e
para
meters. Q is
the seasonal m
o
ving a
v
e
r
age
pa
ram
e
ters.
s re
prese
n
ts t
h
e lengt
h
of the
seasonal pe
riod.
A station
a
ry time series is on
e
who
s
e
statistical
prope
r
ties, s
u
ch as m
ean,
va
riance, do not cha
n
ge
o
v
e
r ti
m
e
. In
ord
e
r to
ob
tain
co
nsisten
t
an
d
reliab
l
e re
su
lts, th
e n
on-station
a
ry d
a
ta n
e
eds to
b
e
tran
sform
e
d
in
to
station
a
ry
d
a
ta. Th
e
presen
t stud
y
was m
a
k
i
ng
a ti
m
e
series statio
n
a
ry
in
m
ean
b
y
fi
rst rem
o
v
i
n
g
a tren
d
b
y
d
i
f
f
e
r
e
n
tiatio
n, an
d, second
,
r
e
m
o
v
i
ng
a
season
al p
a
ttern
by consi
d
eri
n
g the
seasona
l
AR a
n
d MA
m
odels
com
b
ined
with a seas
onal
differenci
n
g.
The forecasting AR
IMA m
odels we
re esta
blishe
d fo
r eac
h state as well as the overall
states. The
dat
a
f
r
om
2
0
0
6
t
o
2
0
1
1
we
r
e
use
d
as
a t
r
a
i
ni
ng
set
whe
r
eas dat
a
fr
om
20
1
2
were
use
d
as
a t
e
st
i
n
g s
e
t
.
Th
e
Mean Absol
u
t
e
Percenta
ge E
r
rors
(M
AP
E)
was com
put
ed
.
The best
m
odel
with
th
e least MAPE was
used
to
forecast the
malaria cases
for the y
ears 2013
a
n
d 2014.
Be
fore
c
o
nductin
g the
tim
e series a seas
onal
ARIM
A
m
o
d
e
l o
f
t
h
e av
erag
e
ov
erall
trend
of
th
e
malaria d
a
ta, see Figu
re 2,
sh
ows v
a
riab
ility an
d
d
ecreases ov
er
t
i
m
e
peri
odi
cal
l
y
.
Fi
gu
re 2.
The
a
v
e
rag
e
ma
la
ria
cases dist
ribut
ion
f
o
r ov
era
ll sta
t
es f
r
om 200
6-
201
2
The
Aut
o
co
rre
l
a
t
i
on F
unct
i
o
n (
A
C
F
) and
Partial Au
t
o
correlatio
n Fu
n
c
t
i
o
n
(PACF)
of th
e ov
erall
st
at
es sho
w
i
n
Fi
gu
re 3 t
h
e
(
A
C
F
) i
s
t
h
e pl
ot
of l
a
gs
fo
r t
h
e fi
rst
1
2
m
ont
hs
of t
h
e se
ri
es, t
o
sh
ow
(A
C
F
) an
d
(PAC
F).
M
a
ny
l
a
gs
per
f
o
rat
e
t
h
e bl
ue l
i
n
es
,
i
ndi
cat
i
n
g t
h
at
t
h
e l
a
g
(
s)
i
s
si
gni
fi
cant
l
y
di
f
f
e
rent
fr
om
zero a
n
d
th
e series is no
t wh
ite no
ise. Fu
rt
h
e
rm
o
r
e,
slo
w
ly d
i
es of (ACF) evide
n
ce that th
e dat
a
no
n-st
at
i
o
nar
y
and
strongly seas
onal, it is
neede
d
to be
di
ffe
renced.
12000
14000
16000
18000
20000
22000
24000
26000
28000
Jan-06
Mei-06
Sept-06
Jan-07
Mei-07
Sept-07
Jan-08
Mei-08
Sept-08
Jan-09
Mei-09
Sept-09
Jan-10
Mei-10
Sept-10
Jan-11
Mei-11
Sept-11
Jan-12
Mei-12
Sept-12
Malaria Cases
Time
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:2252
-88
06
IJP
H
S
V
o
l
.
4,
No
. 1,
M
a
rc
h 20
1
5
:
7 – 1
6
10
Fi
gu
re 3.
The
Pl
ot
s of AC
F a
n
d
P
A
C
F
fu
nct
i
on wi
t
h
out
di
f
f
ere
n
ci
n
g
After acc
ounting for the seasonal diffe
re
nces, th
e d
a
ta b
eco
m
e
sta
t
i
o
n
a
ry, wh
ich
satisfies th
e
no
rm
al
it
y
cond
i
t
i
on an
d
h
o
m
ogenei
t
y
o
f
vari
ance
of
t
h
e
resi
dual
s
, Fi
gu
re
4
.
Fi
gu
re
4.
The
s
easo
n
al
di
ffere
n
ce
of m
a
laria
cases ave
r
a
g
e
ove
rall states 2006-2012
The a
u
t
o
c
o
r
r
e
l
at
i
on f
unct
i
o
ns (
A
C
F
) an
d
part
i
a
l
aut
o
c
o
r
r
el
at
i
on
fu
n
c
t
i
ons (
P
AC
F)
, sh
ow
n i
n
Figure
5, we
re use
d
t
o
defi
ne a
suitable
m
odel.
The
forecasting m
o
dels were
de
ve
lope
d
for eac
h state
separately as
well as the a
v
era
g
e
for
ove
rall s
t
ates Figure
5.
Fi
gu
re 5.
The
Pl
ot
s of AC
F a
n
d
P
A
C
F
fu
nct
i
on wi
t
h
seaso
n
al
di
ffe
renci
n
g
‐
6000
‐
4000
‐
2000
0
2000
4000
Jan
‐
06
Jun
‐
06
Nov
‐
06
Apr
‐
07
Sept
‐
07
Feb
‐
08
Jul
‐
08
Dis
‐
08
Mei
‐
09
Okt
‐
09
Mac
‐
10
Ogos
‐
10
Jan
‐
11
Jun
‐
11
Nov
‐
11
Apr
‐
12
Sept
‐
12
Value Seasonal
Difference
Time
0
1
2
3
4
5
6
7
8
9
10
11
12
Lag
1.0000
-0.0091
-0.0603
0.1581
0.1151
-0.0059
0.0628
0.0663
-0.0533
-0.0227
-0.0522
0.0655
0.0950
Au
t
o
C
o
r
r
-.8-.6
-.4-.2
0
.
2
.
4
.
6
.
8
.
0.0052
0.2387
1.8693
2.7495
2.7518
3.0236
3.3317
3.5350
3.5725
3.7753
4.1010
4.8008
Ljung-Box Q
.
0.9426
0.8875
0.6000
0.6006
0.7382
0.8059
0.8527
0.8965
0.9372
0.9569
0.9669
0.9643
p-Value
0
1
2
3
4
5
6
7
8
9
10
11
12
Lag
1.0000
-0.0091
-0.0604
0.1575
0.1163
0.0156
0.0533
0.0341
-0.0625
-0.0402
-0.0933
0.0667
0.1150
Partial
-.8-.6
-.4-.2
0
.
2
.
4
.
6
.
8
Resid
u
a
ls
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PH
S I
S
SN
:
225
2-8
8
0
6
Mal
a
ri
a Di
sea
s
e
Di
st
ri
b
u
t
i
o
n
i
n
Su
d
a
n
U
s
i
n
g
Ti
me Seri
es ARIMA
Mo
del
(
M
oh
am
me
d I. Mus
a
)
11
The best ARI
M
A
m
odels fo
r
m
a
laria data
series we
re investigated and com
p
ared with
actual cases
and pre
d
icted c
a
ses according
to the
Mea
n
Absol
u
te Pe
rcent
a
ge E
r
rors
(M
APE
)
as
shown in (E
q. 5.1).
100%
n
y
y
/
y
…
………….
5
.
1
Whe
r
e,
y
is th
e actu
a
l v
a
lu
e an
d
y
is th
e forecast v
a
lu
e. The b
e
st fittin
g
m
o
d
e
l with
th
e lo
west
MAPE
was
us
ed to pre
d
ict the m
a
laria cases for t
h
e year 2012.
Th
e AR
IMA
m
o
d
e
ls were used
to
fit th
e time series
m
a
la
ria data for eac
h state from
ye
ars 2006 t
o
2
011
an
d m
a
k
e
pr
ed
iction
s
fo
r
year
2
012
.
A
co
m
p
ar
iso
n
o
f
t
h
e
nu
m
b
er
o
f
actu
a
l an
d pr
ed
icted m
a
lar
i
a cases
f
o
r
2
012
w
a
s
car
r
i
ed
o
u
t
. The r
e
su
lt is show
n in Figu
re
6 for the
all states. T
h
e
best
ARIMA m
odels
we
re
selected
fo
r d
i
fferen
t tim
e seri
es d
a
ta
d
e
p
e
ndin
g
on
th
e lower MAPE.
Fi
gu
re
6.
Act
u
al
m
a
l
a
ri
a cases fr
om
20
0
6
t
o
20
1
2
a
n
d
p
r
e
d
i
c
t
e
d cases
fr
o
m
2012
f
o
r
ave
r
age
o
v
eral
l
st
a
t
es
2.
5. A
R
IM
A
X
M
o
del
The ARIM
AX
m
odel is one type of AR
IMA with pr
edict
o
r va
riables. T
h
e pre
s
ent study adopts the
ARIMAX m
e
t
h
od
to
pred
ict th
e
m
a
laria cas
es u
s
ing
cli
m
atic factors and the num
b
er
of
malaria cases in the
pre
v
i
o
us m
ont
h acc
or
di
n
g
t
o
B
a
y
e
si
an I
n
f
o
r
m
at
i
on C
r
i
t
e
ri
a (B
IC
) wi
t
h
t
h
e f
o
rm
ul
a
L
s
log
N
/2
, w
h
ere
L is m
a
x
i
m
u
m lik
elih
oo
d, s i
s
nu
m
b
er
of
par
a
m
e
ter
s
an
d
N
is
n
u
m
b
e
r
of
ob
ser
v
ation
s
[
1
5
]
fo
r
go
odness of
fit, wh
ere th
e
sm
a
llest
BIC v
a
lu
es
with
a p
-
v
a
lu
e le
ss t
h
an
(0.05
)
m
easu
r
ed
th
e
b
e
st fittin
g
m
o
d
e
l. Th
e
cl
im
at
e fact
ors
i
n
cl
ude t
h
e a
v
era
g
e m
ont
hl
y
t
e
m
p
erat
ure of m
a
xim
u
m
and m
i
nim
u
m
and a
v
era
g
e m
ont
hl
y
rain
fall lag
g
e
d at a p
e
riod
o
f
on
e m
o
n
t
h
.
Th
e
ARIM
A and
ARIMAX m
o
d
e
l
fittin
g
were carried ou
t
u
s
ing
JMP,
v
e
rsi
o
n 9 (SAS
In
stitu
te In
c., Cary,
NC
, USA,
2
010
).
3.
R
E
SU
LTS AN
D ANA
LY
SIS
3.1. Over
all Mal
a
ria Incidence
The t
r
en
d
of
ove
ral
l
ave
r
a
g
e m
ont
hl
y
m
a
l
a
ri
a cases i
n
Su
dan
wa
s
no
n-st
at
i
o
nary
a
n
d
g
r
a
dual
l
y
decrease
d
f
r
o
m
200
6 t
o
20
1
2
, as can be se
en i
n
Fi
gu
re 2
.
The peak
peri
od
of m
a
l
a
ri
a
was o
b
ser
v
e
d
i
n
Jul
y
t
o
October whe
n
the avera
g
e ca
ses signi
fica
ntly increased,
while
the lowest
points appea
r
ed from
Decem
ber to
Februa
ry for each year. The
distributions
of
m
a
laria fluctuated greatly in
the study are
a
, with the high rates
conce
n
trate
d
in the middle of the study are
a
, and the lo
w
e
st
rat
e
s conce
n
t
r
at
ed i
n
t
h
e
west
and
no
rt
h
of t
h
e
st
udy
a
r
ea, see Fi
gu
re 1.
3.2.
Malaria T
i
me Series
The
best-fit models
of m
a
laria cases
for
different
st
ates and a
v
era
g
e
overall states by
us
ing seas
onal
AR
IM
A m
e
t
hods
fr
om
y
ears 20
0
6
-
2
0
1
1
t
o
pre
d
i
c
t
y
ear 2
0
1
2
a
r
e sh
o
w
n i
n
Tabl
e
1
.
These m
odel
s
were
selected based on the least MAPE and a com
p
arison
of
act
ual
and pr
edi
c
t
e
d m
a
l
a
ri
a cases i
n
201
2. Th
e
resul
t
s
o
f
t
h
e s
easo
n
al
AR
IM
A m
odel
s
sho
w
t
h
at
fo
u
r
Gr
ou
ps
have
di
ff
erent
m
odel
s
. The best
-fi
t
m
odel
f
o
r
gr
o
up
I i
n
cl
u
d
e
K
h
art
oum
, A
l
Gazi
ra
h a
nd
No
rt
he
rn
st
at
es were
(
0
,
1
,
1
)
(
0
,1,
1
)
12
, whe
r
e t
h
e MAPE
were 6.81,
7.69 a
n
d 12.28, respectively;
this gr
oup has the
forecast
equa
tion
(5.2). T
h
e best
-fit m
odel for
Group II were
5000
10000
15000
20000
25000
30000
Jan
‐
06
Mei
‐
06
Sept
‐
06
Jan
‐
07
Mei
‐
07
Sept
‐
07
Jan
‐
08
Mei
‐
08
Sept
‐
08
Jan
‐
09
Mei
‐
09
Sept
‐
09
Jan
‐
10
Mei
‐
10
Sept
‐
10
Jan
‐
11
Mei
‐
11
Sept
‐
11
Jan
‐
12
Mei
‐
12
Sept
‐
12
Malaria Cases
Time
Actual
Cases
Predicted
C
ases
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:2252
-88
06
IJP
H
S
V
o
l
.
4,
No
. 1,
M
a
rc
h 20
1
5
:
7 – 1
6
12
K
a
ssala,
Sinn
ar
, Blu
e
N
ile and
N
G
o
r
dof
an
states w
e
r
e
(1
,1
,1
)(
0,1,1)
12
, t
h
e M
A
PE
wer
e
5.
1
4
,
8.
2
3
,
5.
97
an
d
6.
25
, res
p
ect
i
v
el
y
,
equat
i
o
n (
5
.
3
) f
o
r fo
reca
st
i
ng t
h
i
s
G
r
o
u
p
. T
h
e AR
IM
A (
1
,
0
,
0
)
(
0
,
1
,
1
)
12
m
odel fo
r G
r
o
u
p
II
I
wi
t
h
M
A
P
E
w
e
re 1
0
.
9
3 an
d
8.
00
, f
o
r t
h
e st
at
es of t
h
e
Re
d Sea and Ge
da
ref, re
spectively
,
with e
quation (5.4).
While the average overall states, as
well as N. Dar
f
u
r
,
W.
Darf
ur
, S. Da
rf
ur
, S. G
o
r
d
o
f
an
,
W
h
ite Nile an
d
Ni
l
e
R
i
ver
,
rep
r
esent
e
d
i
n
Gr
ou
p I
V
ha
d
M
A
PE
4
.
1
7
,
15
.0
2, 13
.1
7, 8
.
4
4
,
20.20
,
8.07
an
d 7
.
4
1
, r
e
sp
ectiv
ely,
th
e b
e
st-fit ARIMA m
o
d
e
l were (1
,0
,1
)(0,1,1)
12
, the forecast
i
ng e
quation model fo
r this group in the e
quation
(5
.5
).
The
forecasting e
quation m
o
del
for Group
I:
(0,1,1)(
0,1,1)
12
1
2
1
1
3
Ɵ
1
Θ
1
2
ƟΘ
1
3
…
5.2
The
forecasting e
quation m
o
del
for Group
II:
(1,1,1)(
0,1,1)
12
1
2
1
1
3
Ɵ
1
Θ
1
2
ƟΘ
1
3
...
5
.
3
The
forecasting e
quation m
o
del fo
r Group
III:
(1,0,0)(
0,1,0)
12
μ
1
2
1
1
3
…
5.4
The
forecasting e
quation m
o
del
for Group
IV:
(1,0,1)(0
,1,1)
12
μ
1
2
1
1
3
Ɵ
1
Θ
1
2
ƟΘ
1
3
…
5
.
5
Whe
r
e
de
notes the
AR(1) coefficient,
Ɵ
is MA(1) coe
fficient and
Θ
is SMA(1) c
o
efficient.
Table
1.
Actua
l
and pre
d
icted m
a
laria cases
of Suda
n states
Groups
States
Model
Malaria
Cases
MAPE
Actua
l
Predic
ted
I Kh
arto
u
m
(0
,1
,1
)(0
,1
,1
)
12
6182
83
6190
09
6.
81
Al Gazi
rah
(0
,1
,1
)(0
,1
,1
)
12
7140
61
7293
08
7.
69
No
rth
e
rn
(0
,1
,1
)(0
,1
,1
)
12
3098
9
3079
8
12.
28
II
Kassala
(1
,1
,1
)(0
,1
,1
)
12
2096
67
2033
24
5.
14
Sin
n
a
r (1
,1
,1
)(0
,1
,1
)
12
2370
44
2359
91
8.
23
Blu
e
Nile
(1
,1
,1
)(0
,1
,1
)
12
2123
13
2081
07
5.
97
N. Go
rd
o
f
an
(1
,1
,1
)(0
,1
,1
)
12
2789
57
2773
54
6.
25
III
Red
Sea
(1
,0
,0
)(0
,1
,1
)
12
2276
2
2209
7
10.
93
Ged
a
ref
(1
,0
,0
)(0
,1
,1
)
12
1468
68
1490
35
8.
00
IV
N.
Da
rf
u
r
(1
,0
,1
)(0
,1
,1
)
12
7454
6
7101
6
15.
02
W.
Darf
u
r
(1
,0
,1
)(0
,1
,1
)
12
2018
7
1972
3
13.
17
S. Da
rf
u
r
(1
,0
,1
)(0
,1
,1
)
12
6713
8
6826
2
8.
44
S. Go
rd
o
f
an
(1
,0
,1
)(0
,1
,1
)
12
1354
80
1295
84
20.
20
Wh
ite Nil
e
(1
,0
,1
)(0
,1
,1
)
12
1103
89
1136
17
8.
07
Nile Riv
e
r
(1
,0
,1
)(0
,1
,1
)
12
1192
49
1175
23
7.
41
Ov
erall Sta
t
es
(1
,0
,1
)(0
,1
,1
)
12
2096
35
2065
02
4.
17
The
best m
ode
l was
fitted to
forecast the
malaria cas
es in
Sudan for years 2013 a
n
d
2014, as
shown
i
n
Tabl
es
2 a
n
d
3. S
o
rt
i
ng t
h
e st
at
es i
n
de
s
cendi
ng
o
r
de
r
fr
om
t
h
e hi
g
h
e
s
t
rat
e
s o
f
case
s
t
o
t
h
e l
o
we
st
i
s
as
fol
l
o
ws,
Al
G
ezi
rah,
Kha
r
t
o
um
, Nort
h G
o
rd
ofa
n
,
Whi
t
e
Ni
l
e
, Si
nna
r,
B
l
ue Ni
l
e
, Ka
ssal
a
, Gada
ref
,
Sout
h
G
o
r
dof
an,
N
i
l
e
Riv
e
r
,
No
r
t
h
D
a
rf
ur
, Sou
t
h
D
a
rf
ur
, No
r
t
her
n
,
Red
Sea an
d
W
e
st D
a
rfu
r.
A
l
G
azir
a
h
state
r
e
po
r
t
ed
t
h
e
h
i
g
h
e
st fo
r
ecast
n
u
m
b
e
r
o
f
m
a
l
a
r
i
a cases
w
ith 70
8,815
and
70
5,749
,
fo
llo
wed
b
y
Kh
ar
toum
sta
t
e
w
ith
5
9
3
,
12
6
an
d 568
,9
67
cases in
year
s
20
13
an
d
20
14
, r
e
sp
ectiv
ely. Th
e lo
w
e
st cases
w
e
r
e
r
e
p
o
r
t
ed
b
y
the
No
rt
he
rn
, R
e
d
Sea, an
d
W
e
st
Darf
ur st
at
e
s
, wi
t
h
m
a
l
a
ria cases 29
,8
5
8
, 2
0
,
9
59 a
n
d
19,
3
77 i
n
2
0
1
3
,
an
d
2
8
,650
,
18
,9
89
an
d
18
,8
03
in
year
2
014
,
r
e
sp
ectiv
ely.
In
g
e
n
e
r
a
l, th
ere w
a
s a
d
e
cr
ease in
th
e num
b
e
r
o
f
malar
i
a cases in
year 201
4,
wh
ich
w
a
s esti
mated
to
b
e
about 1
5
% co
m
p
ar
ed
to th
e year
20
06
.
3.
2.
M
a
l
a
ri
a
a
nd Pre
d
i
c
tor
Vari
abl
e
s
Th
e AR
IMAX
m
o
d
e
ls were
fitted
to
th
e
malaria d
a
ta from 2
0
0
6
to
201
2. Th
e m
o
d
e
ls u
s
ed
the
pre
v
ious m
a
lar
i
a cases with clim
a
t
e factors,
whic
h in
clude
d
the ave
r
age
m
onthly te
m
p
e
r
ature
of m
a
xim
u
m
,
min
i
m
u
m
an
d
rain
fall, at lagged
on
e m
o
n
t
h
.
Tab
l
e
4
sho
w
s
th
e
b
e
st fitting
m
o
d
e
l for each state as
well as th
e
avera
g
e o
f
o
v
e
r
all states. The best
m
odel fo
r the ave
r
ag
e
o
v
erall states is
m
odel III d
u
e
to the least value o
f
BIC, wh
ich
equ
a
l to
91
3.64
,
with
th
e p-v
a
l
u
e o
f
th
e pr
e
v
i
o
us m
a
l
a
ri
a cases equal
s
.
0
17 a
nd
p-
val
u
e
of
r
a
i
n
fal
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PH
S I
S
SN
:
225
2-8
8
0
6
Mal
a
ri
a Di
sea
s
e
Di
st
ri
b
u
t
i
o
n
i
n
Su
d
a
n
U
s
i
n
g
Ti
me Seri
es ARIMA
Mo
del
(
M
oh
am
me
d I. Mus
a
)
13
less th
an
.0001
. Th
e states
o
f
Kh
ar
tou
m
an
d
K
a
ssala ar
e o
n
l
y sign
if
ican
t w
ith
t
h
e prev
iou
s
m
a
lar
i
a
cases
v
a
riab
le; th
e
best
m
o
d
e
l fo
r
Kh
artou
m
stat
e is m
o
d
e
l I,
wh
ich
B
I
C equ
a
l
s
1
,
12
7.3,
wh
il
e m
o
d
e
l II is
best for
Kassala state.
The
Northe
rn
and Red Sea st
ates ha
ve
no signi
ficance
with
pre
v
ious m
a
laria cases a
n
d
rainfal
l
i
n
t
h
e
di
f
f
ere
n
t
m
odel
s
;
ho
we
ver
,
t
h
e t
e
m
p
er
at
ure m
a
xim
u
m
and m
i
nim
u
m
are si
gni
fi
ca
nt
i
n
t
h
e N
o
rt
h
e
rn a
n
d
Red Sea states. Model II
wa
s the best
m
o
del for both
th
e No
rt
h
e
rn
and Red
Sea state
s
with
BIC equ
a
l to
7
8
8
.
92
an
d 753
.7
3, resp
ectively. Mo
d
e
l
VI was t
h
e
b
e
st
fitted
m
o
d
e
l fo
r
Ged
a
ref state with
BIC
eq
u
a
l t
o
92
7.
7
6
wi
t
h
a p-val
u
e .0
0
3
, <.
00
0
1
an
d .0
0
5
fo
r p
r
evi
o
us m
a
l
a
ria cases,
m
a
xi
m
u
m
and
m
i
ni
m
u
m
te
m
p
erature
,
re
spectively. In
m
odel II
th
e
p
-
v
a
lu
es
of rai
n
fall were sign
ifi
cant for all states exce
pt Khartoum
,
Kassala,
N
o
rt
hern, Rive
r
Nile and Re
d Sea
s
t
ates.
Table
2.
Forec
a
sting m
onthly
m
a
laria cases
of
Suda
n states
from
Janua
ry to
Decem
ber 2013
State
Forecasted Malar
i
a Cases
Total
Jan.
F
e
b.
March
April
May
June
Ju
ly
Aug.
Sep. O
c
t. Nov.
Dec.
Kassala
1682
3
1456
5
1703
1
1450
3
1500
2
1462
3
1561
2
1597
9
1741
1
1944
1
2035
5
1763
0
1989
75
Gedar
e
f
1130
6
1002
5
8908
1025
7
8941
9693
1173
3
1432
5
1677
1
1815
6
1367
4
8002
1417
91
Al
Gazir
a
h
5982
1
5782
4
5215
1
5587
2
5710
5
5583
4
5797
1
5989
5
6507
1
7512
9
6632
9
4581
3
7088
15
Sinnar
1596
7
1277
2
1462
1
1637
8
1869
1
1946
2
2231
1
2742
6
2946
5
2415
0
1823
6
1301
2
2324
91
Blue
Nile
1238
7
1521
5
1161
3
1381
6
1364
9
1620
0
2102
6
2434
3
2147
5
2408
5
1988
5
1482
4
2085
18
W
h
ite.
Nile
1600
7
2068
4
2349
2
2017
6
1278
8
1833
7
2972
3
2742
3
3285
4
2786
8
1197
2
1005
8
2513
82
N.
Gor
dofan
1540
0
1694
6
1693
1
1873
0
2219
2
2026
7
2411
5
2661
3
2924
2
2706
1
3275
0
2184
8
2720
95
S.
Gor
dofan
8661
7937
7330
7123
1066
1
1337
8
1438
1
1609
1
1309
3
1443
5
1154
6
5625
1302
61
S.
Dar
f
ur
6147
2715
4034
4192
3750
5565
7600
7729
8228
7418
5710
4056
6714
4
W
.
Dar
f
ur
1396
1055
959
667
538
937
1565
2050
3286
3245
2443
1236
1937
7
N.
Dar
f
ur
5323
3564
4271
5777
6103
6909
7752
8450
8326
9488
5596
5445
7700
4
Khar
tou
m
5608
8
4674
3
4831
1
5376
8
5079
8
3862
5
3668
1
3391
5
4949
6
6795
0
6747
0
4328
1
5931
26
Nile
River
9670
1013
7
8908
8302
9432
9563
1050
8
1051
1
1000
0
9794
8150
6986
1119
61
Nor
t
her
n
1719
2349
3463
1999
1307
2353
3415
2383
2608
3178
3262
1822
2985
8
Red
Sea
2059
2789
2595
2486
603
1544
1329
1238
907
1690
2254
1465
2095
9
Overall
States
2387
74
2253
20
2246
18
2340
46
2315
60
2332
90
2657
22
2783
71
3082
33
3330
88
2896
32
2011
03
3063
757
Table
3.
Forec
a
sting m
onthly
m
a
laria cases
of
Suda
n states
from
Janua
ry to
Decem
ber 2014
State
Forecasted Malar
i
a Cases
Total
Jan.
F
e
b.
March
April
May
June
Ju
ly
Aug.
Sep. O
c
t. Nov.
Dec.
Kassala
1598
2
1368
5
1613
2
1359
0
1407
6
1368
5
1466
2
1501
7
1643
6
1845
4
1935
6
1661
9
1876
94
Gedar
e
f
1089
0
9610
8492
9841
8525
9277
1131
8
1390
9
1635
5
1774
0
1325
8
7586
1368
01
Al
Gazir
a
h
5951
8
5753
0
5186
5
5559
5
5683
7
5557
4
5772
0
5965
3
6483
7
7490
3
6611
2
4560
5
7057
49
Sinnar
1559
0
1240
7
1425
9
1601
7
1833
2
1910
3
2195
2
2706
7
2910
8
2379
2
1787
9
1265
6
2281
62
Blue
Nile
1211
1
1495
2
1134
6
1355
1
1338
4
1593
5
2076
1
2407
8
2121
1
2382
1
1962
1
1456
1
2053
32
W
h
ite.
Nile
1564
8
2030
9
2310
9
1979
0
1240
1
1794
9
2933
5
2703
4
3246
6
2748
0
1158
3
9670
2467
74
N.
Gor
dofan
1488
1
1642
6
1641
1
1821
0
2167
2
1974
7
2359
5
2609
3
2872
2
2654
1
3223
0
2132
9
2658
57
S.
Gor
dofan
7254
7024
6684
6621
1023
7
1299
6
1402
1
1574
4
1275
2
1409
8
1121
0
5291
1239
32
S.
Dar
f
ur
6127
2658
3989
4143
3702
5516
7552
7680
8180
7370
5662
4008
6658
7
W
.
Dar
f
ur
1357
1002
913
617
490
888
1517
2002
3237
3197
2395
1188
1880
3
N.
Dar
f
ur
5460
3677
4369
5863
6182
6983
7823
8518
8393
9554
5662
5510
7799
4
Khar
tou
m
5420
6
4483
8
4638
2
5181
5
4882
1
3662
4
3465
5
3186
6
4742
3
6585
2
6534
9
4113
6
5689
67
Nile
River
9731
1017
5
8931
8315
9439
9565
1050
6
1050
8
9995
9788
8143
6979
1120
75
Nor
t
her
n
1625
2253
3366
1901
1208
2253
3314
2280
2505
3074
3156
1715
2865
0
Red
Sea
1881
2660
2426
2342
436
1389
1160
1074
735
1520
2078
1288
1898
9
Overall
States
2322
61
2192
06
2186
74
2282
11
2257
42
2274
84
2598
91
2725
23
3023
55
3271
84
2836
94
1951
41
2992
366
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:2252
-88
06
IJP
H
S
V
o
l
.
4,
No
. 1,
M
a
rc
h 20
1
5
:
7 – 1
6
14
Table
4.
ARIM
AX m
odels, malaria cases a
n
d clim
at
e factors
with
pre
v
ious m
a
laria cases in Sudan
Mo
del
Predic-
tor
Sta
t
es*
1 2
3 4
5 6
7 8
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
I Prev.
Max.
BIC
.017
112
7.3
.
0
0
01
911.
11
.03
106
7.0
.04
789.
37
<.00
01
996.
67
.006
851.
89
<.00
01
754.
63
<.00
01
<.00
01
103
4.6
<.00
01
<.00
01
929.
68
.001
<.00
01
942.
99
<.00
01
872.
50
<.00
01
786.
33
<.00
01
.003
865.
85
<.00
01
972.
15
<.00
01
.01
997.
39
<.00
01
925.
42
II Prev.
Min.
BIC
.016
112
7.4
<.00
01
911.
09
.04
.006
106
0.1
.03
788.
96
.
0
0
02
<.00
01
984.
12
.006
848.
74
<.00
01
753.
73
.
0
0
04
105
0.4
<.00
01
943.
42
<.00
01
986.
56
<.00
01
847.
87
<.00
01
787.
04
<.00
01
873.
45
<.00
01
974.
75
<.00
01
<.00
01
984.
36
<.00
01
.009
919.
13
III Prev.
Rain.
BIC
.015
112
7.5
<.00
01
911.
30
.04
106
6.4
793.
80
.002
.
0
0
01
972.
86
.003
851.
12
778.
30
<.00
01
103
0.4
<.00
01
.04
965.
30
.04
<.00
01
930.
92
.
0
0
03
<.00
01
856.
32
<.00
01
.04
784.
96
<.00
01
859.
43
<.00
01
.007
967.
03
<.00
01
.03
100
0.2
.017
<.00
01
913.
64
IV Prev.
Max.
Rain.
BIC
.02
113
1.4
.
0
0
02
915.
18
106
9.3
.04
793.
30
.04
<.00
01
974.
31
.006
854.
94
<.00
01
757.
94
.04
.03
.
0
0
09
102
9.2
.
0
0
01
.001
932.
61
.002
<.00
01
925.
30
<.00
01
<.00
01
847.
77
<.00
01
788.
41
<.00
01
863.
41
<.00
01
.01
969.
69
<.00
01
.001
.002
990.
86
.001
<.00
01
.
0
0
07
920.
22
V Prev
.
Min.
Rain.
BIC
.02
113
1.5
.
0
0
01
915.
17
.016
106
4.5
.03
792.
90
<.00
01
<.00
01
958.
98
.005
852.
44
<.00
01
755.
10
<.00
01
103
3.5
<.00
01
.007
941.
68
.04
<.00
01
934.
49
<.00
01
<.00
01
827.
44
<.00
01
.04
786.
77
<.00
01
860.
28
<.00
01
.002
968.
64
<.00
01
<.00
01
984.
94
.01
.002
914.
76
VI Prev
.
Max.
Min.
Rain.
BIC
.029
113
5.4
.007
916.
80
<.00
01
<.00
01
105
0.4
796.
87
.03
<.00
01
.001
958.
04
.007
.03
853.
53
759.
17
.008
.002
.04
102
9.8
.003
<.00
01
.005
927.
76
<.00
01
<.00
01
.04
909.
61
.001
<.00
01
.008
821.
46
<.00
01
787.
03
.04
.01
<.00
01
860.
39
<.00
01
.007
972.
44
.
0
0
07
.01
792.
44
.001
.001
.003
924.
30
4. DIS
C
USSI
ON
4.1.
Malaria T
i
me Series Model
Th
e
p
r
esen
t st
u
d
y
ado
p
t
ed
the season
al
ARIMA m
o
d
e
l and fitted
th
e m
a
la
ria cases
for each
state as
well as the
overall states. The differe
n
t AR
IMA m
odels
were
found for di
ffe
rent stat
es, this indicates that
each group
ha
s an indivi
dua
l
m
a
laria
trend. T
h
ese
res
u
lts are consiste
nt with t
hose
of se
ve
ral pre
v
ious
st
udi
es,
s
u
ch
a
s
[
11]
,
w
h
o
fo
un
d t
h
e e
x
i
s
t
e
nce
of
di
ffe
ren
t
AR
IM
A m
o
d
e
l
s
of
t
i
m
e-seri
es anal
y
s
i
s
f
o
r t
h
e
endem
i
c areas
of Bhuta
n
. T
h
e
prese
n
t st
udy found t
h
at
the
West states, s
u
ch as
N.
Dar
f
u
r
,
S.
Da
r
f
u
r
,
W.
Dar
f
u
r
an
d S.
Go
rd
o
f
an
, l
o
ca
t
e
d i
n
gr
o
up
I
V
, ha
ve t
h
e sa
m
e
m
odel
t
r
end, an
d,
henc
e,
t
h
ere i
s
a sim
ilari
t
y
of
m
a
l
a
ri
a di
sease t
r
ansm
i
ssi
on
fo
r t
h
ese
st
at
es. I
n
c
ont
ra
st
, t
h
e
ot
her
AR
I
M
A m
odel
i
s
not
c
o
nsi
s
t
e
nt
wi
t
h
t
h
i
s
assum
p
tion. S
o
m
e
states, despite thei
r ge
ographical rem
o
teness, a
r
e loca
ted
in
on
e
g
r
ou
p, wh
ile th
e ad
j
acen
t
states are located in differ
e
n
t
groups.
Kha
r
toum
and Al Gazirah stat
es are adjacent and located in group I,
whi
c
h al
so i
n
cl
udes t
h
e p
r
e
s
ence o
f
t
h
e No
rt
he
rn st
at
e i
n
t
h
e sam
e
gr
o
u
p
,
des
p
i
t
e
bei
ng ge
o
g
ra
phi
cal
l
y
located
far
from
these states. Sinnar a
n
d Blue
Nile st
ates located in group II ha
ve t
h
e
sam
e
m
odel, whi
c
h
border each
other while Kass
ala and N. Gordofa
n
had
the
sam
e
m
odel but diffe
re
nt geogra
phical loc
a
tions.
Intere
stingly, s
o
m
e
high m
a
la
ria rate states are close to
the
very low m
a
lar
i
a rate states (see Figure 1). T
hus
,
di
ffe
re
nt
m
a
l
a
r
i
a AR
IM
A m
o
del
s
we
re
det
ect
ed al
o
ng
wi
t
h
states that
ha
ve the
sam
e
malaria rate and
sim
ila
r
cl
im
at
e vari
abl
e
s. Thi
s
res
u
l
t
i
s
sup
p
o
r
t
e
d b
y
[11]
wh
o co
n
c
l
ude
d t
h
at
t
h
e endem
i
c di
st
rict
s i
n
B
hut
an d
i
d no
t
follow
the hypothesis, wh
ich assum
e
that the areas
near t
o
each
ot
he
r a
r
e expected to have sim
ilar
disease
transm
ission patterns accordi
ng to their s
p
atial and clim
atic similarity in ter
m
s
of spatial location. The
d
i
fferen
ce in t
h
e m
a
laria tren
d b
e
t
w
een
st
ates, resu
lts fro
m
th
e v
a
riab
i
lity o
f
m
a
laria
treatm
e
n
t
d
i
ag
no
sis
cont
rol
progra
mmes between states and
bet
w
een urban and
rural are
a
within
state. As
well as a
number
of
fact
or
s
pl
ay
ed
rol
e
i
n
ur
ba
n
m
a
l
a
ri
a epi
d
e
m
i
c
s such a
s
c
onst
r
uct
i
o
n
o
f
new
u
r
ban
col
oni
es
wi
t
h
o
u
t
sui
t
a
bl
e
facilities fo
r drain
a
g
e
, influx
o
f
refug
ees, in
su
fficien
t
su
pp
l
y
o
f
drug
s, also
th
e m
i
g
r
atio
n
fro
m
ru
ral to urb
a
n
4
.
2
.
Climate Va
ria
b
ility
a
n
d Ma
l
a
ria
Mo
del
Th
e tim
e series AR
IMAX mo
d
e
l
was fitted to
t
h
e m
a
laria
cases
with
prev
iou
s
m
a
laria cases and
pre
d
i
c
t
o
r
vari
a
b
l
e
s i
n
cl
u
d
ed
(
a
vera
ge m
ont
h
l
y
t
e
m
p
erat
ure of m
a
xim
u
m
,
m
i
nim
u
m
and
rai
n
fal
l
l
a
g
g
e
d
at
a
p
e
ri
o
d
of on
e m
o
n
t
h
)
. Th
e lag
g
e
d
on
e m
o
n
t
h
to
th
e cli
m
at
e v
a
riab
ility is
lo
g
i
cal fo
r th
e p
e
riod
tak
e
n
b
y
th
e
m
o
squito a
n
d
vector life cycl
e [13].
The
pre
v
ious m
ont
h’s
malaria cases indicate t
h
e level of hum
a
n re
servoir
within the area
, while clim
ate
factors
,
suc
h
as te
m
p
erature
and
rainfall are
im
portant fa
ctors that are directly
related
with
the growth of
v
e
cto
r
s and
m
o
squ
ito
es.
Malaria cases in the states of
Kha
r
toum
and Kassala ha
ve
only been affect
ed by th
e previous m
a
laria c
a
ses;
th
is in
d
i
cates th
at th
e cli
m
ate
v
a
riab
ility d
i
d
n
o
t
affect
m
a
l
a
ria tran
sm
issi
o
n
. Th
is resu
lt ag
rees
with
prev
iou
s
st
udi
es
on
cl
i
m
at
e vari
abl
e
s
and t
h
e t
r
a
n
s
m
i
ssi
on o
f
Fa
lcip
a
r
um
m
a
lar
i
a in Ne
w Hal
f
, easter
n
S
u
da
n [
1
3]
.
Him
e
id
an
co
nclu
d
e
s t
h
at tem
p
eratu
r
e, relativ
e hu
m
i
d
i
t
y
an
d
water irrig
a
tion
are no
t sign
ifican
t i
n
conc
urre
nce
with the
pres
ent study.
T
h
e clim
atic fac
t
ors
for
Khart
oum
and Ka
s
s
ala states we
re
not
si
gni
fi
ca
nt
, w
h
i
c
h can be i
n
t
e
rp
ret
e
d as t
h
e
m
a
l
a
ri
a
t
r
ans
m
i
ssi
on bei
n
g m
a
n-m
a
de t
h
rou
g
h
ur
ba
n m
a
l
a
ri
a.
[
1
6
]
r
e
v
ealed
t
h
at urb
a
n m
a
l
a
r
i
a is asso
ciated
w
ith so
cio-
eco
l
o
g
i
cal and
so
cio-
economic f
acto
r
s, su
ch as
b
i
o
m
ass facto
r
s, qu
ality o
f
ho
u
s
i
n
g
and
top
ograph
i
cal
. Th
e rai
n
fall was no
t sign
ifican
t in
North
e
rn, Riv
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PH
S I
S
SN
:
225
2-8
8
0
6
Mal
a
ri
a Di
sea
s
e
Di
st
ri
b
u
t
i
o
n
i
n
Su
d
a
n
U
s
i
n
g
Ti
me Seri
es ARIMA
Mo
del
(
M
oh
am
me
d I. Mus
a
)
15
Nile and
Red Sea states to
th
e
tran
sm
issio
n
of m
a
laria, th
is is b
ecau
s
e
o
f
th
e lack
o
f
rainfall in
th
ese areas;
th
e
avera
g
e an
n
u
al
rai
n
fal
l
was ar
ou
n
d
4.
4
7
m
m
,
0.
28m
m
and 6.
35m
m
for t
h
e R
i
ver Ni
l
e
, N
o
rt
her
n
an
d R
e
d
Sea
states, res
p
ectively, com
p
are
d
to the a
n
nua
l avera
g
e
of a
n
ove
rall area
exceedi
n
g 26
mm, this resul
t
agree
s
with
[3
]
who
rev
ealed
th
at t
h
e m
i
n
i
m
u
m
rain
fall req
u
i
re
m
e
nt
fo
r
deve
l
opm
ent
m
o
sq
ui
t
o
t
o
t
r
a
n
sm
i
ssi
on
m
a
l
a
ri
a was ar
ou
n
d
8
0
m
m
per m
ont
h f
o
r t
h
ree m
ont
hs
of
r
a
i
n
. T
h
e N
o
rt
h
e
rn a
n
d R
e
d
Se
a st
at
es di
d
not
hav
e
any significa
nt of m
a
laria
cases with the pre
v
ious m
a
lari
a
cases, similar t
o
stu
d
i
es[1
1, 17
], th
is resu
lt can
be
expl
ai
ne
d t
h
at
t
h
ese t
w
o st
at
es (N
ort
h
er
n a
n
d R
e
d Se
a)
ha
ve sm
alles
t
m
a
laria cases com
p
ared to the
rest of
th
e Sud
a
n
ex
cep
t
Sou
t
h
Darfu
r, in
add
itio
n th
ere are v
a
ri
o
u
s
so
cio-eco
n
o
m
ic facto
r
s, su
ch
as immig
r
atio
n
fro
m
ru
ral to
u
r
b
a
n
and
po
pu
l
a
tio
n
attitu
d
e
s. Gen
e
rally, th
ere are v
a
riation
s
in
th
e i
m
p
act o
f
cli
m
a
tic f
acto
r
s
fo
r t
h
e sp
read
of m
a
l
a
ri
a amon
g st
at
es i
n
Suda
n, t
h
i
s
re
su
l
t
i
s
consi
s
t
e
nt
wi
t
h
a num
ber of
pre
v
i
o
us s
t
udi
e
s
suc
h
as[
6
]
,
w
h
o i
n
vest
i
g
at
ed
t
h
e associ
at
i
o
n
bet
w
ee
n a
u
t
o
r
e
gres
si
ve (
n
u
m
ber of m
a
l
a
ri
a out
pat
i
e
nt
s
du
ri
n
g
th
e p
r
ev
iou
s
time p
e
rio
d
), season
ality an
d
cli
m
a
t
e v
a
riab
ility, an
d
th
e num
b
e
r o
f
m
o
n
t
hly
malaria o
u
t
patien
t
s
in
East Africa. Zho
u
fo
und
t
h
at th
ere was
a h
i
gh
sp
atial v
a
riation
in
t
h
e sen
s
itiv
ity of m
a
laria o
u
t
patien
t
n
u
m
b
e
rs t
o
cli
m
ate flu
c
tu
atio
n
s
in th
e
h
i
gh
land
s, and
t
h
at cli
m
ate v
a
riab
ility p
l
ayed
an
im
p
o
r
tan
t
ro
le in
malaria ep
id
emics in
th
e East African
h
i
gh
land
s.
[11
]
,
u
s
i
ng m
ont
hl
y
m
a
l
a
ri
a cases and t
h
e m
e
t
e
orol
o
g
i
cal
dat
a
i
n
seve
n
m
a
l
a
ri
a endem
i
c di
st
ri
ct
s, fo
u
nd t
h
at
t
h
e m
e
an m
a
xim
u
m
tem
p
erat
ur
e l
a
g
g
ed at
one m
ont
h
was
a stro
ng
po
sitiv
e pred
ictor of in
creased
m
a
l
a
ria cases fo
r fo
ur d
i
stricts. [1
1, 17
] u
s
ed
ARIMA m
o
d
e
ls with
seaso
n
al
com
pone
nt
s, a
n
d s
easo
n
al
m
u
l
t
i
p
l
i
cat
i
v
e aut
o
re
gressi
ve i
n
t
e
gr
at
ed m
ovi
ng
avera
g
e (
S
AR
IM
A
)
m
o
d
e
ls were co
m
p
ared
o
n
mo
n
t
h
l
y ti
m
e
series o
f
d
i
stri
ct
malaria cases fo
r t
h
eir ab
ility
to
pred
ict th
e nu
m
b
er
of m
a
l
a
ri
a cases one t
o
f
o
ur m
ont
hs ahea
d. [
1
7]
co
ncl
u
ded t
h
at
t
h
e addi
t
i
on
of rai
n
fal
l
as a cova
ri
at
e im
prov
e
d
t
h
e p
r
edi
c
t
i
o
n
of
sel
ect
ed
(s
easo
n
al
)
AR
I
M
A m
odel
s
i
n
s
o
m
e
di
st
ri
ct
s but
w
o
rse
n
ed
pre
d
i
c
t
i
on
i
n
ot
her
districts.
5.
CO
NCL
USI
O
N
The tim
e
serie
s
seasonal ARIMA
m
odel showed that
the
r
e are four distinc
t
m
odels acros
s the study
area; there
f
ore, any m
a
laria cont
rol
programme
m
u
st
be t
r
eat
ed sepa
rat
e
l
y
. The a
v
era
g
e
m
ont
hl
y
m
a
xim
u
m
te
m
p
eratu
r
e, min
i
m
u
m
te
m
p
eratu
r
e an
d rai
n
fall are
pred
ict
o
r v
a
riab
les; t
h
e
ARIM
AX
m
o
d
e
l illu
strated
t
h
at
diffe
re
nt states res
p
o
n
d
ed
to
diffe
re
nt
m
odels. Som
e
states only show sign
ificance
to
previous m
a
laria cases
,
wh
ile o
t
h
e
r states ap
p
e
ar significan
t to
pred
i
c
to
r vari
ables
.
The AR
IMA
m
odel used by
the pre
s
ent study can
be useful
to ot
her diseases such
as
de
ngue.
Howe
ver, furt
her resea
r
c
h
is recommende
d to forecasting
malaria
usi
n
g
ot
he
r
va
ri
abl
e
s s
u
c
h
as
t
h
e m
a
l
a
ri
a cont
rol
p
r
o
g
ra
m
m
e
, im
m
i
grat
i
on
bet
w
ee
n a
n
d
wi
t
h
i
n
st
at
es a
n
d
beha
vi
o
r
of
p
o
pul
at
i
o
n.
ACKNOWLE
DGE
M
ENTS
We a
r
e
grat
ef
ul
t
o
t
h
e M
a
l
a
y
s
i
a
n Tec
hni
c
a
l
C
o
o
p
er
ation
Pr
o
g
ram
(M
TCP)
fo
r
fina
nc
ial sup
p
o
rt;
many thanks t
o
the Econom
i
cs and Social Research
B
u
re
au (ESR
B
)
, M
i
ni
st
ry
of Sci
e
nce an
d Tec
h
n
o
l
o
gy
Sudan.
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