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O
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dels o
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p
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c
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lo
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m
e
a
su
re
s.
In
t
h
is
p
a
p
e
r,
we
in
v
e
sti
g
a
te
m
a
th
e
m
a
ti
c
a
l
m
o
d
e
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a
c
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ted
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n
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a
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ti
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t
o
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n
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ly
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e
h
o
w
th
e
sp
re
a
d
o
f
c
o
r
o
n
a
v
ir
u
s
d
ise
a
se
2
0
1
9
(
COV
ID
-
19
)
in
fe
c
ti
o
n
e
v
o
l
v
e
s
o
v
e
r
ti
m
e
.
In
th
e
p
ro
c
e
ss
o
f
c
o
n
s
tru
c
ti
n
g
a
m
a
th
e
m
a
ti
c
a
l
m
o
d
e
l
fo
r
COV
ID
-
1
9
,
t
h
e
re
a
re
m
a
n
y
p
a
ra
m
e
t
e
rs
wh
o
se
v
a
lu
e
s
a
re
n
o
t
y
e
t
k
n
o
wn
with
c
e
rtain
ty
.
Th
e
re
fo
re
,
t
h
e
e
x
te
n
d
e
d
Ka
lma
n
fil
ter
m
e
th
o
d
is
u
se
d
a
s
a
to
o
l
t
o
e
stim
a
te
th
e
se
p
a
ra
m
e
ters
in
a
n
e
ffo
rt
to
b
e
tt
e
r
u
n
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e
rsta
n
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th
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y
n
a
m
ics
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th
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a
d
a
n
d
e
v
o
lu
t
io
n
o
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th
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s
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ise
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se
.
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is
m
e
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o
d
h
e
lp
s
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li
g
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th
e
m
a
th
e
m
a
ti
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a
l
m
o
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l
with
e
x
isti
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g
e
m
p
iri
c
a
l
d
a
ta,
a
ll
o
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g
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s
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k
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te
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re
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ictio
n
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a
b
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t
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h
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rse
o
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th
e
CO
VID
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1
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p
a
n
d
e
m
ic
a
n
d
p
lan
m
o
re
p
re
c
ise
a
c
ti
o
n
s
to
a
d
d
re
ss
th
e
situ
a
ti
o
n
.
F
u
rth
e
rm
o
re
,
a
n
o
p
ti
m
a
l
c
o
n
tro
l
d
e
sig
n
is
a
p
p
li
e
d
t
o
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c
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th
e
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u
m
b
e
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ted
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ls
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e
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ti
n
g
se
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n
stra
teg
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v
in
g
a
c
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m
b
in
a
ti
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o
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lt
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d
u
c
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ti
o
n
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v
a
c
c
in
a
ti
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,
a
n
d
iso
lati
o
n
c
o
n
t
ro
ls.
T
h
e
sim
u
latio
n
re
su
lt
s
we
c
o
n
d
u
c
ted
in
d
ica
te
t
h
a
t
t
h
e
u
se
o
f
o
p
ti
m
a
l
c
o
n
tr
o
l
stra
teg
ies
c
a
n
lea
d
to
a
sig
n
ifi
c
a
n
t
d
e
c
re
a
se
in
th
e
n
u
m
b
e
r
o
f
i
n
d
i
v
id
u
a
ls
in
fe
c
ted
with
COV
ID
-
19.
K
ey
w
o
r
d
s
:
E
x
ten
d
ed
Kalm
a
n
f
ilter
Ma
th
em
atica
l m
o
d
el
Om
icr
o
n
Op
tim
al
co
n
tr
o
l
Par
am
eter
esti
m
atio
n
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Dew
i Su
h
ik
a
Dep
ar
tm
en
t o
f
Ma
th
em
atics,
Facu
lty
o
f
Ma
th
e
m
atics a
n
d
Na
tu
r
al
Scien
ce
s
,
I
n
s
titu
t T
ek
n
o
l
o
g
i Ban
d
u
n
g
B
an
d
u
n
g
,
I
n
d
o
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m
ail: 3
0
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2
0
0
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6
@
m
ah
asis
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.
itb
.
ac
.
id
1.
I
NT
RO
D
UCT
I
O
N
C
o
r
o
n
av
ir
u
s
d
is
ea
s
e
2
0
1
9
(
C
OVI
D
-
19)
f
ir
s
t
d
etec
ted
in
W
u
h
an
,
C
h
in
a
at
th
e
en
d
o
f
2
0
1
9
[
1
]
,
h
as
r
ap
id
ly
e
v
o
lv
ed
in
to
a
g
lo
b
al
p
an
d
em
ic,
d
is
r
u
p
tin
g
n
ea
r
l
y
al
l
asp
ec
ts
o
f
life
.
As
th
e
v
ir
u
s
s
p
r
ea
d
wo
r
ld
wid
e,
it
u
n
d
er
wen
t
s
ev
er
al
m
u
tatio
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s
lead
in
g
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th
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em
e
r
g
en
ce
o
f
v
a
r
ian
ts
s
u
ch
as
Alp
h
a
(
B
.
1
.
1
.
7
)
,
f
ir
s
t
id
en
tifie
d
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th
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Un
ited
Kin
g
d
o
m
o
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Dec
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m
b
er
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2
0
2
0
,
wh
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h
as
s
ev
er
al
m
u
tatio
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s
in
t
h
e
v
ir
al
s
p
ik
e
p
r
o
tein
e
n
h
an
ci
n
g
its
ab
ilit
y
to
attac
h
to
h
u
m
an
ce
lls
an
d
in
c
r
ea
s
in
g
tr
a
n
s
m
is
s
io
n
[
2
]
.
Fo
ll
o
win
g
th
e
Alp
h
a
v
ar
ia
n
t,
th
e
B
eta
v
ar
ian
t
(
B
.
1
.
3
5
1
)
was
r
ep
o
r
te
d
in
So
u
th
Af
r
ica
in
Dec
em
b
e
r
2
0
2
0
,
f
ea
tu
r
in
g
m
u
tatio
n
s
th
at
co
u
ld
p
o
ten
tially
im
p
ac
t
v
ac
cin
e
an
d
an
tib
o
d
y
ef
f
icac
y
[
3
]
.
Similar
ly
,
th
e
Gam
m
a
v
ar
ian
t
(
P.1
)
was
id
e
n
tifie
d
in
B
r
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il
o
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J
an
u
ar
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2
1
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2
0
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1
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an
d
th
e
Delta
v
ar
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t
(
B
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1
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6
1
7
.
2
)
,
k
n
o
wn
f
o
r
b
ein
g
m
o
r
e
co
n
tag
i
o
u
s
th
an
its
p
r
ed
ec
ess
o
r
s
,
r
aised
g
lo
b
al
co
n
ce
r
n
s
in
Ap
r
il
2
0
2
1
[
4
]
.
T
h
e
latest,
th
e
O
m
icr
o
n
v
ar
ian
t
(
B
.
1
.
1
.
5
2
9
)
,
w
as
f
ir
s
t
r
ep
o
r
ted
in
So
u
th
Af
r
ica
o
n
No
v
e
m
b
er
2
4
,
2
0
2
1
[
5
]
,
an
d
h
as
q
u
ick
l
y
b
ec
o
m
e
a
m
ajo
r
co
n
ce
r
n
d
u
e
to
its
n
u
m
e
r
o
u
s
m
u
tatio
n
s
,
s
o
m
e
p
r
ev
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u
s
ly
u
n
s
ee
n
,
wh
ich
co
n
tr
ib
u
te
to
its
f
aster
tr
an
s
m
is
s
io
n
r
ate
an
d
p
o
ten
tial
to
o
v
er
co
m
e
ex
is
tin
g
im
m
u
n
ity
[
6
]
.
T
h
ese
v
ar
ian
ts
h
av
e
n
o
t
o
n
ly
in
cr
ea
s
ed
th
e
co
m
p
lex
ity
o
f
co
n
tr
o
llin
g
th
e
v
ir
u
s
'
s
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ea
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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g
I
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N:
2088
-
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Op
tima
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tr
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a
teg
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a
s
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o
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ex
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d
ed
K
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filt
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ma
th
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…
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6301
b
u
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also
ch
allen
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f
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tiv
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estab
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p
u
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ea
lth
s
tr
ateg
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I
n
I
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d
o
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esia,
th
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wif
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p
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i
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ar
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as
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ated
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ain
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elm
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d
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atio
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al
h
ea
lth
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y
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tem
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co
m
p
licated
o
n
g
o
in
g
v
ac
cin
atio
n
ef
f
o
r
ts
[
7
]
.
Ma
th
em
atica
l
m
o
d
els
ar
e
cr
u
cial
to
o
ls
f
o
r
u
n
d
er
s
tan
d
in
g
an
d
m
an
ag
in
g
th
e
s
p
r
ea
d
o
f
th
e
C
OVI
D
-
19
v
ir
u
s
.
R
esear
ch
u
s
in
g
m
ath
e
m
atica
l
m
o
d
els
h
as
b
ee
n
c
o
n
d
u
c
ted
ex
ten
s
iv
ely
s
in
ce
th
e
p
an
d
em
ic
b
eg
a
n
.
T
h
ese
m
o
d
els
ar
e
u
s
ed
to
u
n
d
er
s
tan
d
v
ir
u
s
tr
an
s
m
is
s
io
n
,
p
r
e
d
ict
ep
id
em
io
lo
g
ical
tr
en
d
s
,
p
lan
in
ter
v
en
tio
n
s
,
a
n
d
m
ak
e
p
o
licy
d
ec
is
io
n
s
[
8
]
.
R
esear
ch
b
y
An
n
as
et
a
l.
[
9
]
d
ev
elo
p
e
d
an
s
u
s
ce
p
tib
le
–
e
x
p
o
s
ed
–
in
f
ec
tio
u
s
–
r
em
o
v
ed
(
SEI
R
)
m
o
d
el
th
at
in
co
r
p
o
r
ated
v
ac
cin
atio
n
an
d
i
s
o
latio
n
p
ar
am
eter
s
,
p
r
o
v
i
d
in
g
in
s
ig
h
ts
in
to
th
e
ef
f
ec
tiv
en
ess
o
f
th
ese
in
ter
v
en
tio
n
s
in
s
lo
win
g
th
e
s
p
r
ea
d
.
An
o
th
er
s
tu
d
y
b
y
W
an
g
et
a
l
.
[
1
0
]
ad
a
p
ted
th
e
SEI
R
m
o
d
el
to
in
clu
d
e
c
o
m
p
ar
tm
en
ts
f
o
r
s
u
s
ce
p
tib
le
(
S)
,
ex
p
o
s
ed
(
E
)
,
in
f
ec
ted
(
I
)
,
h
o
s
p
italized
(
H)
,
an
d
r
em
o
v
ed
(
R
)
,
u
s
in
g
p
u
b
lic
d
at
a
f
r
o
m
W
u
h
an
.
T
h
is
m
o
d
el
wa
s
u
tili
ze
d
to
d
eter
m
in
e
th
e
in
itial d
ate
o
f
C
OVI
D
-
1
9
in
f
ec
tio
n
in
W
u
h
an
,
c
o
n
s
id
er
in
g
th
e
lack
o
f
in
f
o
r
m
atio
n
o
n
in
itial
co
n
d
itio
n
s
.
Su
n
et
a
l.
[
1
1
]
co
n
s
tr
u
cted
th
e
SEI
R
m
o
d
el
with
an
a
d
d
e
d
q
u
ar
a
n
tin
e
(
Q)
co
m
p
a
r
tm
en
t
to
ass
ess
th
e
im
p
ac
t
o
f
lo
ck
d
o
wn
m
ea
s
u
r
es
an
d
th
e
av
ailab
ilit
y
o
f
m
ed
ical
r
eso
u
r
ce
s
in
W
u
h
an
d
u
r
in
g
2
0
2
0
o
n
th
e
v
ir
u
s
'
s
d
y
n
am
ics
an
d
s
p
r
ea
d
.
T
h
e
r
esu
lts
in
d
icate
d
th
at
th
e
lo
n
g
er
th
e
l
o
ck
d
o
wn
was
im
p
lem
en
ted
in
W
u
h
an
,
th
e
f
ewe
r
p
eo
p
le
we
r
e
in
f
ec
ted
,
b
u
t
th
is
h
ad
im
p
licatio
n
s
f
o
r
o
th
er
ci
ties
in
C
h
in
a
an
d
ar
o
u
n
d
th
e
wo
r
ld
.
Ho
wev
er
,
d
esp
ite
th
ese
ad
v
an
ce
m
e
n
ts
,
cu
r
r
en
t
m
o
d
els
o
f
ten
s
tr
u
g
g
le
to
ad
ap
t
to
th
e
r
ap
i
d
ly
ev
o
l
v
in
g
d
y
n
am
ics
o
f
th
e
v
ir
u
s
,
esp
ec
ially
with
th
e
f
r
eq
u
e
n
t
em
er
g
e
n
ce
o
f
n
ew
v
ar
ian
ts
.
T
h
er
e
is
a
p
r
ess
in
g
n
ee
d
f
o
r
m
o
d
els
th
at
in
co
r
p
o
r
ate
r
ea
l
-
tim
e
d
ata,
wh
ich
co
u
ld
s
ig
n
if
ican
tly
im
p
r
o
v
e
th
e
ac
c
u
r
ac
y
o
f
p
r
ed
ictio
n
s
an
d
th
e
e
f
f
ec
tiv
en
ess
o
f
in
t
er
v
en
tio
n
s
.
T
h
e
c
o
n
c
e
p
t
o
f
o
p
ti
m
a
l
c
o
n
t
r
o
l
is
p
a
r
ti
c
u
l
a
r
l
y
r
e
l
e
v
a
n
t
i
n
m
an
a
g
i
n
g
d
y
n
a
m
i
c
s
y
s
t
e
m
s
l
i
k
e
p
a
n
d
e
m
i
c
s
,
w
h
e
r
e
i
t
a
i
m
s
t
o
i
d
e
n
t
i
f
y
t
h
e
m
o
s
t
e
f
f
e
ct
i
v
e
s
t
r
at
e
g
i
es
u
n
d
er
g
i
v
e
n
c
o
n
s
t
r
ai
n
t
s
[
1
2
]
.
M
a
n
y
r
e
s
e
a
r
c
h
e
r
s
h
a
v
e
u
t
i
l
i
z
e
d
o
p
t
i
m
a
l
c
o
n
t
r
o
l
t
h
e
o
r
y
t
o
a
d
d
r
e
s
s
i
n
f
e
c
t
i
o
u
s
d
is
e
as
e
c
o
n
t
r
o
l
is
s
u
es
.
Ma
d
u
b
u
e
z
e
e
t
a
l
.
[
1
3
]
i
n
v
e
s
ti
g
a
t
es
o
p
t
i
m
a
l
c
o
n
t
r
o
l
i
n
C
O
V
I
D
-
1
9
m
o
d
e
l
s
as
n
o
n
-
p
h
a
r
m
a
c
o
l
o
g
i
c
a
l
s
t
r
a
te
g
i
e
s
s
u
c
h
a
s
q
u
a
r
an
t
i
n
e
a
n
d
is
o
l
a
ti
o
n
.
S
w
e
il
a
m
e
t
a
l
.
[
1
4
]
e
x
p
l
o
r
e
s
o
p
t
i
m
a
l
c
o
n
t
r
o
l
as
m
e
d
i
ca
l
t
r
e
a
t
m
e
n
t
s
t
r
a
t
e
g
i
e
s
s
u
c
h
as
is
o
l
a
t
i
o
n
i
n
h
e
al
t
h
c
a
r
e
f
a
c
i
l
it
i
es
a
n
d
t
h
e
p
r
o
v
i
s
i
o
n
o
f
r
e
s
p
i
r
a
t
o
r
y
a
i
d
s
,
i
n
v
o
l
v
i
n
g
v
a
r
i
a
t
i
o
n
s
i
n
p
a
r
a
m
et
e
r
s
r
e
l
at
e
d
to
c
o
n
t
a
c
t
r
a
t
e
s
a
n
d
i
n
f
e
c
t
i
o
n
t
r
a
n
s
m
i
s
s
i
o
n
.
Dj
i
d
j
o
u
-
D
e
m
a
s
s
e
e
t
a
l
.
[
1
5
]
u
t
i
l
i
ze
s
o
p
t
i
m
a
l
c
o
n
t
r
o
l
t
h
e
o
r
y
t
o
e
x
p
l
o
r
e
t
h
e
b
e
s
t
s
t
r
at
e
g
y
t
h
a
t
c
a
n
b
e
i
m
p
l
e
m
e
n
t
e
d
w
h
i
l
e
a
w
a
i
t
i
n
g
t
h
e
v
a
c
c
i
n
e
b
y
s
e
e
k
in
g
a
s
o
l
u
t
i
o
n
t
h
a
t
m
i
n
i
m
i
z
e
s
t
h
e
n
u
m
b
e
r
o
f
d
e
a
t
h
s
a
n
d
t
h
e
c
o
s
t
s
r
e
s
u
lt
i
n
g
f
r
o
m
t
h
e
i
m
p
l
e
m
e
n
t
a
t
i
o
n
o
f
t
h
e
c
o
n
t
r
o
l
s
t
r
a
t
e
g
y
i
ts
e
l
f
.
T
h
e
i
r
f
i
n
d
i
n
g
s
s
h
o
w
t
h
a
t
s
u
c
h
a
s
o
l
u
t
i
o
n
l
e
a
d
s
t
o
a
n
i
n
c
r
e
a
s
i
n
g
l
e
v
e
l
o
f
c
o
n
t
r
o
l
p
e
a
k
i
n
g
a
r
o
u
n
d
t
h
e
1
6
th
m
o
n
t
h
f
r
o
m
t
h
e
o
n
s
e
t
o
f
t
h
e
e
p
i
d
e
m
i
c
,
f
o
l
l
o
w
e
d
b
y
a
s
t
e
a
d
y
d
e
c
l
i
n
e
u
n
t
i
l
t
h
e
v
a
c
c
i
n
e
is
i
m
p
l
e
m
e
n
te
d
.
L
i
a
n
d
G
u
o
[
4
]
e
m
p
l
o
y
e
d
o
p
t
i
m
a
l
c
o
n
t
r
o
l
b
y
i
m
p
l
e
m
e
n
t
i
n
g
a
v
a
c
c
i
n
a
t
i
o
n
co
n
t
r
o
l
s
t
r
a
t
e
g
y
i
n
a
m
o
d
e
l
w
i
t
h
C
O
V
I
D
-
1
9
m
u
t
a
t
i
o
n
s
(
D
el
ta
s
t
r
a
i
n
)
.
H
o
w
e
v
e
r
,
e
x
i
s
ti
n
g
m
o
d
e
l
s
h
a
v
e
n
o
t
s
p
e
ci
f
i
c
a
ll
y
a
d
d
r
e
s
s
e
d
t
h
e
c
h
a
ll
e
n
g
e
s
p
o
s
e
d
b
y
t
h
e
O
m
i
c
r
o
n
v
a
r
i
a
n
t
a
n
d
t
h
e
o
r
i
g
i
n
a
l
v
i
r
u
s
,
n
o
r
h
a
v
e
t
h
e
y
f
u
l
l
y
u
t
i
li
ze
d
t
h
e
p
o
t
e
n
t
i
a
l
o
f
r
e
al
-
t
i
m
e
d
ata
i
n
t
e
g
r
a
t
i
o
n
f
r
o
m
b
o
t
h
a
s
p
e
ct
s
.
T
h
is
s
tu
d
y
ai
m
s
to
ad
d
r
ess
th
ese
lim
itatio
n
s
b
y
en
h
a
n
cin
g
t
h
e
r
esp
o
n
s
iv
en
ess
o
f
th
e
SEI
R
m
o
d
el
t
o
ch
an
g
es
in
v
ir
u
s
tr
an
s
m
is
s
io
n
d
y
n
am
ics
th
r
o
u
g
h
th
e
in
teg
r
atio
n
o
f
th
e
ex
ten
d
ed
Kalm
a
n
f
ilter
a
n
d
o
p
tim
a
l
co
n
tr
o
l
s
tr
ateg
ies.
T
h
is
ap
p
r
o
ac
h
is
d
esig
n
e
d
t
o
n
o
t
o
n
ly
i
m
p
r
o
v
e
th
e
ad
a
p
tab
ilit
y
o
f
o
u
r
m
o
d
els
b
u
t
also
to
p
r
o
v
id
e
m
o
r
e
e
f
f
ec
tiv
e
an
d
t
im
ely
r
esp
o
n
s
es
to
th
e
p
a
n
d
e
m
ic'
s
ch
allen
g
es.
Sp
ec
if
ically
,
we
f
o
cu
s
o
n
th
e
ap
p
licatio
n
o
f
th
ese
ad
v
an
ce
d
tech
n
iq
u
es
to
m
an
a
g
e
p
o
p
u
la
tio
n
s
th
at
h
av
e
b
ee
n
v
ac
cin
ate
d
,
aim
in
g
to
r
e
f
in
e
th
e
co
n
tr
o
l stra
teg
ies ag
ain
s
t
C
OVI
D
-
1
9
m
o
r
e
ef
f
ec
tiv
ely
.
T
h
e
n
ex
t
p
ar
t
o
f
th
is
p
ap
er
will
d
escr
ib
e
th
e
m
eth
o
d
o
lo
g
y
we
u
s
e,
in
clu
d
in
g
d
etails
ab
o
u
t
th
e
in
teg
r
atio
n
o
f
t
h
e
ex
ten
d
ed
Kalm
an
f
ilter
a
n
d
th
e
d
e
v
elo
p
m
en
t
o
f
o
p
tim
al
c
o
n
tr
o
l
s
tr
ateg
ies.
W
e
will
p
r
esen
t
s
im
u
latio
n
r
esu
lts
to
d
em
o
n
s
tr
ate
th
e
ef
f
ec
tiv
en
ess
o
f
th
is
ap
p
r
o
ac
h
in
r
ed
u
cin
g
t
h
e
s
p
r
ea
d
o
f
C
OVI
D
-
1
9
.
Su
b
s
eq
u
en
tly
,
th
e
d
is
cu
s
s
io
n
will c
r
itiq
u
e
th
ese
r
esu
lt
s
in
th
e
co
n
tex
t o
f
ex
is
tin
g
liter
atu
r
e
an
d
th
eir
im
p
ac
t o
n
p
u
b
lic
h
ea
lth
p
o
licy
.
T
h
e
co
n
c
lu
s
io
n
will
s
u
m
m
ar
ize
th
e
s
ig
n
if
ican
t
f
i
n
d
in
g
s
an
d
p
r
o
p
o
s
e
d
ir
ec
tio
n
s
f
o
r
f
u
tu
r
e
r
esear
ch
in
th
is
f
ield
.
2.
M
E
T
H
O
D
I
n
c
o
n
s
t
r
u
c
t
i
n
g
a
m
a
t
h
e
m
a
t
i
ca
l
m
o
d
e
l
,
a
p
p
r
o
p
r
i
a
t
e
a
s
s
u
m
p
t
i
o
n
s
a
r
e
n
e
e
d
e
d
t
o
m
a
k
e
t
h
e
m
o
d
e
l
s
i
m
p
l
e
r
,
e
a
s
i
e
r
t
o
a
n
a
l
y
z
e
,
u
n
d
e
r
s
ta
n
d
,
a
n
d
i
m
p
l
e
m
e
n
t
.
F
u
r
t
h
e
r
m
o
r
e
,
o
n
e
o
f
t
h
e
i
m
p
o
r
t
a
n
t
c
h
a
l
l
e
n
g
e
s
i
n
m
a
t
h
e
m
at
i
c
al
m
o
d
e
l
s
is
d
e
t
e
r
m
i
n
i
n
g
p
a
r
a
m
e
t
e
r
v
a
l
u
es
b
a
s
e
d
o
n
d
at
a
,
r
eq
u
i
r
i
n
g
o
p
t
i
m
i
z
a
ti
o
n
m
e
t
h
o
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i
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f
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e
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s
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w
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i
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lt
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o
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r
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t
e
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h
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r
e
f
f
e
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t
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v
e
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ess
in
c
o
n
t
r
o
l
l
i
n
g
t
h
e
o
u
t
b
r
e
a
k
.
T
h
e
r
e
s
e
a
r
c
h
m
e
t
h
o
d
o
l
o
g
y
is
i
l
l
u
s
t
r
at
e
d
i
n
F
i
g
u
r
e
1
.
2
.
1
.
Da
t
a
co
llect
io
n
I
n
th
is
s
tu
d
y
,
C
OVI
D
-
1
9
d
at
a
co
llectio
n
was
ca
r
r
ied
o
u
t
b
y
o
b
tain
in
g
d
aily
d
ata
f
r
o
m
th
e
Hea
lth
Dep
ar
tm
en
t
f
o
r
th
e
p
er
io
d
f
r
o
m
Feb
r
u
ar
y
6
to
Ma
y
5
,
2
0
2
2
,
s
p
ec
if
ically
f
o
r
th
e
DKI
J
ak
ar
ta
p
r
o
v
i
n
ce
.
T
h
e
co
llected
d
ata
i
n
clu
d
es
th
e
n
u
m
b
er
o
f
n
ew
ca
s
es,
ac
tiv
e
ca
s
es,
v
ac
cin
atio
n
s
,
q
u
ar
an
tin
es,
r
ec
o
v
er
ies,
a
n
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
14
,
No
.
6
,
Dec
em
b
e
r
20
24
:
6
3
0
0
-
6
3
1
2
6302
d
ea
th
s
th
at
o
cc
u
r
r
ed
ea
c
h
d
a
y
d
u
r
i
n
g
th
e
p
er
io
d
.
T
h
e
u
s
e
o
f
th
is
d
ata
aim
s
to
a
n
aly
ze
th
e
tr
en
d
s
in
v
ir
u
s
s
p
r
ea
d
,
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
in
ter
v
en
tio
n
s
ap
p
lied
,
an
d
th
e
d
y
n
am
ics
o
f
ca
s
e
ch
an
g
es
in
th
e
co
m
m
u
n
ity
.
T
h
is
in
f
o
r
m
atio
n
is
cr
u
cial
f
o
r
u
n
d
er
s
tan
d
in
g
th
e
ch
a
r
ac
ter
is
tics
o
f
C
OVI
D
-
1
9
s
p
r
ea
d
in
th
e
r
eg
io
n
a
n
d
s
er
v
es
as a
b
asis
f
o
r
f
u
r
th
e
r
h
ea
lth
p
o
licy
d
ec
is
io
n
s
.
Fig
u
r
e
1
.
R
esear
ch
p
r
o
ce
s
s
d
iag
r
am
f
o
r
th
e
o
p
tim
izatio
n
o
f
t
h
e
m
ath
em
atica
l m
o
d
el
o
f
C
O
VI
D
-
19
2
.
2
.
F
o
rm
ula
t
e
a
m
a
t
hema
t
i
ca
l m
o
del o
f
CO
VID
-
19
I
n
th
is
p
ap
er
,
th
e
m
o
d
el
em
p
l
o
y
ed
is
p
r
o
v
id
ed
with
ass
u
m
p
tio
n
s
as
p
r
o
b
lem
co
n
s
tr
ain
ts
t
o
f
ac
ilit
ate
th
e
co
n
s
tr
u
ctio
n
o
f
th
e
m
o
d
el.
T
h
e
ass
u
m
p
tio
n
s
u
tili
ze
d
ar
e
i)
T
h
e
av
er
ag
e
b
ir
th
r
ate
is
e
q
u
al
to
th
e
av
er
ag
e
d
ea
th
r
ate,
s
o
th
e
to
tal
p
o
p
u
lat
io
n
is
co
n
s
tan
t
;
ii)
T
h
e
p
o
p
u
latio
n
is
clo
s
ed
.
T
h
er
e
is
n
o
m
o
v
em
en
t
(
m
ig
r
atio
n
,
m
o
b
ilit
y
)
to
o
r
f
r
o
m
th
e
o
b
s
er
v
ed
ar
ea
;
iii)
E
v
er
y
h
u
m
an
b
ein
g
b
o
r
n
en
ter
s
a
s
u
s
ce
p
tib
le
p
o
p
u
latio
n
;
iv
)
I
n
d
iv
id
u
als
wh
o
h
av
e
r
ec
ei
v
ed
th
e
v
ac
cin
e
b
u
t
h
a
v
e
n
o
t
y
et
g
en
er
ated
a
n
tib
o
d
ies
m
i
g
h
t sti
ll
b
e
s
u
s
ce
p
tib
le
to
in
f
ec
tio
n
.
W
h
en
th
e
v
ac
ci
n
e
d
o
es
not
o
f
f
er
f
u
ll
im
m
u
n
ity
ag
ain
s
t
th
e
v
ir
u
s
,
v
ac
cin
at
ed
in
d
iv
id
u
als
ca
n
r
em
ain
at
r
is
k
o
f
c
o
n
tr
ac
tin
g
th
e
d
is
ea
s
e
[
1
6
]
;
v
)
I
n
f
ec
tio
n
with
th
e
Om
icr
o
n
v
ar
ian
t
is
tr
an
s
m
itted
th
r
o
u
g
h
co
n
tact
with
in
d
iv
id
u
als
ca
r
r
y
in
g
th
is
v
ar
ian
t,
wh
er
ea
s
in
f
ec
tio
n
with
th
e
o
r
ig
in
al
s
tr
ain
s
o
cc
u
r
s
v
ia
co
n
tact
with
in
d
iv
id
u
als
in
f
ec
ted
with
th
o
s
e
s
tr
ain
s
.
I
t
i
s
im
p
o
r
tan
t
to
n
o
te
th
at
s
u
s
ce
p
tib
le
in
d
iv
id
u
als
wh
o
co
m
e
in
to
co
n
tact
with
t
h
o
s
e
in
f
ec
ted
wi
th
th
e
o
r
ig
i
n
al
v
ir
u
s
m
a
y
co
n
t
r
ac
t
th
at
v
ir
u
s
b
u
t
will
n
o
t
b
e
co
m
e
in
f
ec
ted
with
th
e
Om
icr
o
n
v
a
r
ian
t
u
n
less
ex
p
o
s
ed
t
o
it
s
p
ec
if
ically
[
1
7
]
;
v
i)
T
r
a
n
s
m
is
s
io
n
o
cc
u
r
s
th
r
o
u
g
h
in
te
r
ac
tio
n
s
b
etwe
en
s
u
s
ce
p
tib
le
an
d
in
f
e
cted
in
d
iv
id
u
als
[
1
8
]
;
an
d
v
i
i)
I
n
d
iv
id
u
als
wh
o
ar
e
r
ec
o
r
d
ed
as
co
n
f
ir
m
e
d
p
o
s
itiv
e
if
d
ec
lar
ed
c
u
r
ed
ar
e
ass
u
m
ed
to
b
e
im
m
u
n
e
to
C
O
VI
D
-
19.
2
.
3
.
P
a
ra
m
et
er
estima
t
io
n
E
x
ten
d
ed
Kalm
an
f
ilter
(
E
KF)
is
an
alg
o
r
ith
m
d
esig
n
ed
to
esti
m
ate
s
tates
in
n
o
n
lin
ea
r
d
y
n
am
ic
s
y
s
tem
s
an
d
is
r
ep
r
esen
ted
b
y
(
1
)
.
(
)
=
(
(
)
)
(
1
)
wh
er
e
(
.
)
d
en
o
tes
th
e
n
o
n
lin
ea
r
s
y
s
tem
f
u
n
ctio
n
.
B
y
d
is
cr
eti
zin
g
(
1
)
i
n
tim
e
d
o
m
ain
,
we
ca
n
o
b
tain
th
e
d
is
cr
ete
-
tim
e
m
o
d
el:
+
1
=
+
(
)
(
2
)
wh
er
e
r
ep
r
esen
ts
th
e
s
y
s
tem
s
tate
at
tim
e
p
o
in
t
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Op
tima
l c
o
n
tr
o
l str
a
teg
ies b
a
s
ed
o
n
ex
te
n
d
ed
K
a
lma
n
filt
er in
ma
th
ema
tica
l
…
(
Dewi S
u
h
ika
)
6303
T
h
e
s
tep
s
o
f
t
h
e
ex
ten
d
ed
Ka
lm
an
f
ilter
alg
o
r
ith
m
p
r
o
ce
e
d
as
f
o
llo
ws,
af
ter
c
o
n
v
e
r
tin
g
(
1
)
in
to
its
d
is
cr
ete
f
o
r
m
.
a.
L
in
ea
r
ize
th
e
s
y
s
tem
m
o
d
el
(
1
)
,
r
esu
ltin
g
in
t
h
e
J
ac
o
b
ian
m
a
tr
ix
.
b.
I
n
itializatio
n
o
f
ea
ch
s
tate
v
ar
iab
le
an
d
p
ar
am
eter
wh
e
n
=
0
f
o
r
t
h
e
s
y
s
tem
m
o
d
el
(
1
)
.
c.
Dete
r
m
in
e
th
e
in
itial v
alu
e
o
f
th
e
er
r
o
r
co
v
a
r
ian
ce
̂
0
b
ased
o
n
[
1
9
]
.
̂
0
=
[
(
0
−
̂
0
)
(
0
−
̂
0
)
]
d.
C
alcu
late
th
e
p
r
ed
icted
s
tate
u
s
in
g
̂
−
=
̂
−
1
.
e.
Dete
r
m
in
e
th
e
er
r
o
r
co
v
ar
ian
c
e
v
alu
e
o
b
tain
ed
u
s
in
g
th
e
eq
u
atio
n
,
−
=
−
1
+
ℚ
f.
Nex
t is th
e
co
r
r
ec
tio
n
s
tag
e.
C
alcu
late
Kalm
an
g
ain
b
ased
o
n
th
e
f
o
llo
win
g
eq
u
atio
n
,
=
(
−
+
ℛ
)
−
1
,
with
is
th
e
o
b
s
er
v
atio
n
m
atr
ix
.
g.
Up
d
ate
s
tate
esti
m
ates b
ased
o
n
th
e
f
o
llo
win
g
eq
u
atio
n
,
̂
=
̂
−
+
(
−
̂
−
)
h.
C
alcu
late
th
e
er
r
o
r
co
v
ar
ian
ce
u
s
in
g
th
e
f
o
ll
o
win
g
eq
u
atio
n
,
=
[
−
]
−
R
ep
ea
t step
s
(
a
)
-
(
d
)
u
n
til all
iter
atio
n
s
ar
e
p
r
o
ce
s
s
ed
an
d
th
e
v
alu
es c
o
n
v
e
r
g
e.
2
.
4
.
O
pti
m
a
l
c
o
ntr
o
l
Nu
m
er
ically
s
o
lv
in
g
th
is
o
p
tim
al
co
n
tr
o
l
p
r
o
b
lem
u
tili
zin
g
Po
n
tr
y
ag
in
'
s
m
in
im
u
m
p
r
in
cip
le
in
v
o
lv
es
d
ev
elo
p
in
g
an
alg
o
r
ith
m
to
g
en
er
ate
an
ap
p
r
o
x
im
ate
o
p
tim
al
co
n
tr
o
l
s
o
lu
tio
n
.
T
h
e
o
p
tim
al
s
y
s
tem
en
co
m
p
ass
es
s
tate
eq
u
atio
n
s
,
alo
n
g
with
th
eir
in
itial
co
n
d
itio
n
s
,
co
s
tate
eq
u
atio
n
s
,
an
d
ass
o
ciate
d
tr
an
s
v
er
s
ality
co
n
d
itio
n
s
,
as
w
ell
as
o
p
tim
al
co
n
tr
o
l
c
h
ar
ac
te
r
is
tics
.
T
h
is
co
n
tr
o
l
p
r
o
b
lem
c
an
b
e
s
o
lv
ed
u
s
in
g
th
e
b
ac
k
war
d
-
f
o
r
war
d
s
wee
p
alg
o
r
ith
m
as in
[
1
2
]
,
[
2
0
]
,
in
th
e
f
o
llo
win
g
m
an
n
e
r
:
a.
Div
id
e
th
e
tim
e
in
ter
v
al
[
0
,
]
in
to
eq
u
ally
s
p
ac
ed
s
u
b
in
ter
v
als.
C
r
ea
te
v
ec
to
r
s
=
(
1
,
2
,
…
,
6
)
an
d
=
(
1
,
2
,
…
,
6
)
to
ap
p
r
o
x
im
ate
th
e
s
tate
an
d
c
o
s
tate
v
ar
iab
les.
b.
I
n
itialize
th
e
v
alu
es
o
f
1
,
2
,
an
d
3
f
o
r
th
e
e
n
tire
tim
e
in
ter
v
al,
s
ettin
g
1
(
0
)
=
2
(
0
)
=
3
(
0
)
=
0
.
T
h
e
v
ec
to
r
s
1
,
2
,
an
d
3
r
ep
r
esen
t c
o
n
tr
o
l a
p
p
r
o
x
im
atio
n
s
at
tim
e
.
c.
Star
tin
g
with
th
e
i
n
itial
co
n
d
itio
n
1
=
(
0
)
=
0
an
d
th
e
v
alu
es
i
n
1
,
2
,
an
d
3
,
s
tate
d
if
f
er
e
n
tial
eq
u
atio
n
is
s
o
lv
ed
f
o
r
war
d
wi
th
r
esp
ec
t
to
tim
e
u
s
in
g
t
h
e
4
th
o
r
d
e
r
R
u
n
g
e
-
Ku
tta
m
et
h
o
d
.
T
h
is
p
r
o
v
id
es
a
n
u
m
er
ical
esti
m
ate
f
o
r
t
h
e
s
tate
d
ev
elo
p
m
en
t.
d.
Usi
n
g
th
e
tr
an
s
v
er
s
ality
co
n
d
i
tio
n
+
1
=
(
)
=
0
an
d
th
e
v
ec
to
r
v
alu
es
1
,
2
,
3
,
an
d
,
s
o
lv
e
th
e
co
s
tate
eq
u
atio
n
b
ac
k
war
d
in
tim
e
u
s
in
g
th
e
4
th
-
o
r
d
er
R
u
n
g
e
-
Ku
tta
m
eth
o
d
.
T
h
is
p
r
o
v
id
es
a
n
u
m
er
ical
esti
m
ate
f
o
r
th
e
co
s
tate.
e.
T
h
e
co
n
tr
o
l
v
alu
es
1
,
2
,
an
d
3
ar
e
u
p
d
ated
b
y
s
u
b
s
titu
tin
g
th
e
s
tate
an
d
co
s
tate
v
alu
es
in
to
th
e
o
p
tim
al
co
n
tr
o
l c
h
a
r
ac
ter
izatio
n
.
f.
Nex
t,
a
co
n
v
er
g
e
n
ce
ch
ec
k
i
s
ca
r
r
ied
o
u
t.
I
f
th
e
v
alu
e
o
f
th
e
v
ar
iab
le
b
ein
g
ca
lcu
lated
in
th
e
c
u
r
r
e
n
t
iter
atio
n
an
d
th
e
v
alu
e
in
th
e
p
r
ev
io
u
s
iter
atio
n
a
r
e
q
u
ite
cl
o
s
e
o
r
co
n
v
er
g
e,
t
h
en
th
e
v
al
u
e
o
f
th
e
v
ar
ia
b
le
in
th
e
cu
r
r
en
t
iter
atio
n
is
c
o
n
s
id
er
ed
an
ac
ce
p
tab
le
s
o
lu
tio
n
.
T
h
is
in
d
icate
s
th
at
th
e
alg
o
r
ith
m
h
as
co
n
v
er
g
ed
o
r
is
ap
p
r
o
ac
h
in
g
th
e
o
p
tim
al
s
o
lu
tio
n
.
I
f
n
o
t,
th
e
alg
o
r
ith
m
r
etu
r
n
s
to
s
tep
2
f
o
r
th
e
n
ex
t
iter
atio
n
.
T
h
is
p
r
o
ce
s
s
is
r
ep
ea
ted
iter
at
iv
ely
u
n
til
th
e
n
u
m
er
ical
s
o
lu
t
io
n
co
n
v
e
r
g
es
to
th
e
o
p
tim
al
s
o
lu
tio
n
o
f
th
e
g
iv
en
o
p
tim
al
co
n
tr
o
l
p
r
o
b
lem
.
T
h
is
m
eth
o
d
is
a
co
m
b
in
atio
n
o
f
f
o
r
wa
r
d
an
d
b
ac
k
war
d
ap
p
r
o
ac
h
es
to
f
in
d
o
p
tim
al
co
n
tr
o
l
u
s
in
g
th
e
4
th
o
r
d
e
r
R
u
n
g
e
-
K
u
tta
n
u
m
er
ical
m
eth
o
d
.
T
h
e
f
o
r
war
d
ap
p
r
o
ac
h
in
v
o
lv
es
s
im
u
latin
g
th
e
s
tate
d
y
n
am
ics
f
o
r
war
d
in
tim
e
u
s
in
g
in
iti
al
g
u
ess
es
f
o
r
th
e
co
n
tr
o
l
v
ar
iab
les,
wh
ile
th
e
b
ac
k
war
d
ap
p
r
o
ac
h
in
v
o
lv
es
ad
ju
s
tin
g
th
ese
co
n
tr
o
l
v
ar
ia
b
les
b
ased
o
n
th
e
d
is
cr
ep
an
c
ies
o
b
s
er
v
ed
in
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
14
,
No
.
6
,
Dec
em
b
e
r
20
24
:
6
3
0
0
-
6
3
1
2
6304
d
esire
d
s
tate
tr
ajec
to
r
y
.
T
h
r
o
u
g
h
iter
ativ
e
r
ef
in
em
e
n
t
o
f
co
n
tr
o
ls
,
th
is
m
eth
o
d
ef
f
ici
en
tly
ad
d
r
ess
es
th
e
ch
allen
g
es
o
f
n
o
n
-
lin
ea
r
ities
an
d
c
o
n
s
tr
ain
ts
in
c
o
n
tr
o
l
s
y
s
tem
s
,
en
s
u
r
in
g
ac
cu
r
ac
y
an
d
s
tab
ilit
y
in
th
e
co
m
p
u
ted
s
o
lu
tio
n
s
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
Resul
t
o
f
t
he
CO
VID
-
1
9
m
o
del
I
n
th
e
C
OVI
D
-
1
9
m
o
d
el,
th
e
p
o
p
u
latio
n
(
)
is
ca
teg
o
r
ized
i
n
to
eig
h
t
d
is
tin
ct
c
o
m
p
ar
tm
e
n
ts
to
b
etter
u
n
d
er
s
tan
d
an
d
s
im
u
late
th
e
s
p
r
ea
d
o
f
th
e
v
ir
u
s
an
d
its
v
ar
ian
ts
.
T
h
e
co
m
p
ar
tm
en
t
(
)
r
ep
r
esen
ts
th
e
s
u
b
p
o
p
u
latio
n
o
f
in
d
iv
id
u
als
wh
o
ar
e
s
u
s
ce
p
tib
le
to
th
e
v
ir
u
s
an
d
h
av
e
n
o
t
b
ee
n
v
ac
cin
at
ed
.
1
(
)
an
d
2
(
)
d
en
o
te
in
d
iv
id
u
als
wh
o
h
av
e
b
ee
n
ex
p
o
s
ed
to
th
e
o
r
ig
i
n
al
C
OVI
D
-
1
9
v
ir
u
s
an
d
t
h
e
Om
icr
o
n
v
a
r
ian
t,
r
esp
ec
tiv
ely
.
(
)
in
clu
d
es
th
o
s
e
wh
o
h
av
e
r
ec
eiv
ed
v
ac
cin
a
tio
n
s
.
1
(
)
an
d
2
(
)
ar
e
s
u
b
s
ets
o
f
th
e
p
o
p
u
latio
n
in
f
ec
ted
with
th
e
o
r
ig
in
al
v
ir
u
s
a
n
d
th
e
Om
icr
o
n
v
a
r
ian
t,
r
esp
ec
tiv
ely
.
(
)
r
e
f
er
s
to
t
h
o
s
e
wh
o
ar
e
s
ev
er
ely
in
f
ec
ted
a
n
d
cu
r
r
en
tly
h
o
s
p
italized
,
wh
ile
(
)
r
ep
r
esen
ts
in
d
iv
id
u
als
wh
o
h
av
e
r
ec
o
v
er
ed
f
r
o
m
th
e
in
f
ec
tio
n
,
h
ig
h
lig
h
tin
g
th
e
d
y
n
am
ics
an
d
in
ter
ac
tio
n
s
b
etwe
en
d
if
f
er
en
t
s
tag
es
o
f
th
e
d
is
ea
s
e
w
ith
in
th
e
p
o
p
u
latio
n
.
T
h
u
s
,
th
e
to
tal
p
o
p
u
latio
n
is
g
iv
en
b
y
,
(
)
=
(
)
+
1
(
)
+
2
(
)
+
(
)
+
1
(
)
+
2
(
)
+
(
)
+
(
)
T
h
e
m
ath
em
atica
l
m
o
d
el
f
o
r
t
h
e
s
p
r
ea
d
o
f
C
OVI
D
-
1
9
alo
n
g
with
co
n
tr
o
l
i
n
p
u
t
ca
n
b
e
s
e
en
in
th
e
f
o
llo
win
g
s
y
s
tem
:
̇
(
)
=
−
1
1
(
1
−
1
(
)
)
−
2
2
(
1
−
1
(
)
)
−
(
1
+
2
(
)
)
−
̇
1
(
)
=
1
1
+
1
1
1
−
1
1
−
1
̇
2
(
)
=
2
2
+
2
2
2
−
2
2
−
2
̇
(
)
=
(
1
+
2
(
)
)
−
1
1
1
−
2
2
2
−
̇
1
(
)
=
1
1
−
3
(
)
1
−
1
1
−
1
̇
2
(
)
=
2
2
−
3
(
)
2
−
2
2
−
2
̇
(
)
=
3
(
)
1
+
3
(
)
2
−
3
−
̇
(
)
=
1
1
+
2
2
+
3
−
(
3
)
an
d
th
e
e
x
p
lan
atio
n
o
f
th
e
p
ar
am
eter
s
in
m
o
d
el
(
3
)
ar
e
p
r
o
v
i
d
ed
in
T
a
b
le
1
.
T
h
e
co
n
tr
o
l
v
ar
iab
le
1
(
)
r
ep
r
ese
n
ts
h
ea
lth
e
d
u
ca
tio
n
p
r
o
v
id
e
d
to
in
d
iv
id
u
al
with
th
e
ai
m
o
f
en
h
an
cin
g
th
eir
u
n
d
er
s
tan
d
in
g
o
f
p
er
s
o
n
al
h
ea
lth
co
n
d
itio
n
s
,
d
is
ea
s
e
p
r
ev
e
n
tio
n
ef
f
o
r
ts
,
an
d
s
tep
s
to
m
ain
tain
o
p
tim
al
h
ea
lth
.
T
h
e
co
n
tr
o
l
v
ar
iab
le
2
(
)
r
ep
r
esen
ts
th
e
v
ac
c
in
atio
n
in
ter
v
e
n
tio
n
,
wh
ic
h
is
in
ten
d
ed
to
m
itig
ate
an
d
m
an
ag
e
th
e
tr
a
n
s
m
is
s
io
n
o
f
C
OVI
D
-
1
9
b
y
in
cr
ea
s
in
g
th
e
v
ac
cin
atio
n
co
v
er
ag
e
a
m
o
n
g
th
e
p
o
p
u
latio
n
.
T
h
e
c
o
n
tr
o
l
v
ar
ia
b
le
3
(
)
is
th
e
is
o
latio
n
r
ate
g
iv
e
n
to
1
an
d
2
with
th
e
aim
o
f
r
e
d
u
cin
g
th
e
in
f
ec
ted
p
o
p
u
latio
n
o
f
1
an
d
2
.
T
h
e
b
asic r
ep
r
o
d
u
ctio
n
n
u
m
b
e
r
(
0
)
is
g
iv
en
b
y
,
0
=
{
(
1
(
+
)
+
1
1
(
+
)
)
1
1
,
(
2
(
+
)
+
2
2
(
+
)
)
2
3
}
.
D
i
s
ea
s
e
-
f
r
e
e
c
o
n
d
i
ti
o
n
s
o
c
c
u
r
if
t
h
e
d
i
s
e
a
s
e
is
n
o
t
e
n
d
e
m
i
c
o
r
i
n
f
e
c
t
i
o
n
h
a
s
n
o
t
o
c
c
u
r
r
e
d
,
n
a
m
e
l
y
w
h
e
n
0
<
1
.
E
n
d
e
m
i
c
c
o
n
d
i
t
i
o
n
s
o
c
c
u
r
i
f
t
h
e
d
i
s
e
as
e
is
n
o
t
e
n
d
e
m
i
c
o
r
i
n
f
ec
t
i
o
n
h
a
s
n
o
t
o
c
c
u
r
r
e
d
,
n
a
m
e
l
y
w
h
e
n
0
>
1
.
3
.
2
.
Resul
t
o
f
pa
ra
m
et
er
esti
m
a
t
i
o
n us
ing
ex
t
ended K
a
lm
a
n f
ilte
r
B
ef
o
r
e
esti
m
atin
g
th
e
C
OVI
D
-
1
9
s
p
r
ea
d
m
o
d
el
u
s
in
g
th
e
ex
ten
d
ed
Kalm
an
f
ilter
(
E
KF)
,
d
is
cr
etiza
tio
n
will
b
e
ca
r
r
ied
o
u
t
f
i
r
s
t.
Dis
cr
etiza
tio
n
its
el
f
aim
s
to
o
b
tain
th
e
f
o
r
m
o
f
th
e
eq
u
atio
n
in
a
d
is
cr
ete
s
tate
[
2
1
]
.
T
h
is
i
s
b
ec
au
s
e
th
e
E
KF
m
eth
o
d
is
a
s
y
s
t
em
m
o
d
el
th
at
u
s
es
m
ea
s
u
r
em
en
ts
an
d
a
d
is
cr
ete
tim
e
s
y
s
tem
m
o
d
el.
I
n
th
e
C
OVI
D
-
1
9
m
o
d
el
(
3
)
,
it
will
b
e
d
is
cr
etize
d
u
s
in
g
a
f
o
r
war
d
f
in
ite
d
if
f
er
en
ce
m
eth
o
d
f
o
r
c
h
an
g
es
in
v
ar
ia
b
les
o
v
er
tim
e.
T
h
e
f
o
llo
win
g
is
a
d
is
cr
etiza
tio
n
o
f
th
e
C
OVI
D
-
1
9
d
is
ea
s
e
tr
an
s
m
is
s
io
n
m
o
d
el:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Op
tima
l c
o
n
tr
o
l str
a
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ies b
a
s
ed
o
n
ex
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d
ed
K
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er in
ma
th
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tica
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…
(
Dewi S
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ika
)
6305
+
1
=
+
(
−
1
1
−
2
2
−
−
)
∆
1
+
1
=
1
+
(
1
1
+
1
1
1
−
1
1
−
1
)
∆
2
+
1
=
2
+
(
2
2
+
2
2
2
−
2
2
−
2
)
∆
+
1
=
+
(
−
1
1
−
2
2
2
−
)
∆
1
+
1
=
1
+
(
1
1
−
3
1
−
1
1
−
1
)
∆
2
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1
=
2
+
(
1
2
−
3
2
−
2
2
−
2
)
∆
+
1
=
+
(
2
1
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3
2
−
3
−
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∆
+
1
=
+
(
1
1
+
2
2
+
3
−
)
∆
.
(
4
)
T
h
e
d
is
cr
ete
m
o
d
el
(
4
)
ca
n
b
e
s
im
p
lifie
d
in
to
th
e
f
o
r
m
o
f
a
n
o
n
lin
ea
r
f
u
n
ctio
n
as:
+
1
=
+
(
)
wh
er
e
is
th
e
s
y
s
tem
s
tate
at
tim
e
p
o
in
t
.
I
n
m
o
d
el
(
4
)
a
n
ew
s
tate
v
ar
iab
le,
̇
1
=
0
,
̇
2
=
0
,
̇
=
0
,
̇
1
=
0
,
̇
2
=
0
,
̇
1
=
0
,
̇
2
=
0
̇
3
=
0
d
an
̇
3
=
0
.
Nex
t,
t
o
f
o
r
m
a
s
y
s
tem
m
o
d
el,
i
n
(
4
)
a
s
to
ch
asti
c
f
ac
to
r
in
th
e
f
o
r
m
o
f
n
o
is
e
is
ad
d
ed
as:
+
1
=
+
(
−
1
−
2
2
−
−
)
∆
+
1
1
+
1
=
1
+
(
1
1
+
1
1
1
−
1
−
)
∆
+
+
2
2
+
1
=
2
+
(
2
2
+
2
2
2
−
2
2
−
2
)
∆
+
3
+
1
=
+
(
−
1
1
−
2
2
2
−
)
∆
+
4
1
+
1
=
1
+
(
1
1
−
3
1
−
1
1
−
1
)
∆
+
5
2
+
1
=
2
+
(
1
2
−
3
2
−
2
2
−
2
)
∆
+
6
+
1
=
+
(
3
1
+
3
2
−
3
−
)
∆
+
7
+
1
=
+
(
1
1
+
2
2
+
3
−
)
∆
+
8
1
+
1
=
1
+
9
2
+
1
=
2
+
10
+
1
=
+
11
1
+
1
=
1
+
12
2
+
1
=
2
+
13
1
+
1
=
1
+
14
2
+
1
=
2
+
15
3
+
1
=
3
+
16
3
+
1
=
3
+
17
(
5
)
wh
er
e
∆
is
th
e
ch
an
g
e
in
tim
e
with
∆
=
0
.
01
.
is
s
y
s
tem
n
o
is
e
in
a
s
y
s
tem
m
o
d
el
th
at
is
n
o
r
m
a
lly
d
is
tr
ib
u
ted
with
ze
r
o
m
ea
n
an
d
co
v
ar
ia
n
ce
ℚ
o
r
ca
n
b
e
wr
itten
w
~
(
0
,
ℚ
)
.
I
t
is
ass
u
m
ed
th
at
th
e
p
ar
am
eter
s
to
b
e
esti
m
ated
ar
e:
1
,
2
,
,
1
,
2
,
1
,
2
,
2
,
3
,
an
d
3
as
a
c
o
n
tin
u
o
u
s
p
iece
wis
e
f
u
n
ctio
n
s
with
ju
m
p
s
ev
er
y
d
ay
,
o
b
tain
ed
i
n
o
n
e
d
ay
th
e
v
alu
e
s
1
,
2
,
,
1
,
2
,
1
,
2
,
2
,
3
,
an
d
3
ar
e
co
n
s
tan
t,
s
o
t
h
at
eq
u
atio
n
s
1
+
1
=
1
,
2
+
1
=
2
,
+
1
=
,
1
+
1
=
1
,
2
+
1
=
2
,
1
+
1
=
1
,
2
+
1
=
2
,
3
+
1
=
3
,
an
d
3
+
1
=
3
s
atis
f
ies.
I
n
th
e
p
r
o
ce
s
s
o
f
p
ar
am
eter
esti
m
atio
n
with
ex
ten
d
ed
Kalm
an
f
ilter
,
it
is
a
co
m
m
o
n
p
r
ac
tice
to
in
tr
o
d
u
ce
a
d
d
itio
n
al
p
a
r
am
et
er
s
as
n
ew
s
tate
v
ar
iab
les.
E
q
u
atio
n
(
5
)
is
a
s
y
s
tem
m
o
d
el,
wh
ile
th
e
m
ea
s
u
r
em
en
t m
o
d
el
is
:
=
+
wh
er
e
is
th
e
s
y
s
tem
n
o
is
e
in
th
e
m
ea
s
u
r
em
en
t
m
o
d
el
wh
i
ch
is
n
o
r
m
ally
d
is
tr
ib
u
ted
with
ze
r
o
m
ea
n
an
d
co
v
ar
ian
ce
ℛ
o
r
u
s
u
ally
wr
itten
v
~
(
0
,
ℛ
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
14
,
No
.
6
,
Dec
em
b
e
r
20
24
:
6
3
0
0
-
6
3
1
2
6306
T
h
e
C
m
atr
ix
f
o
llo
ws
th
e
av
aila
b
le
d
ata
wh
ich
in
clu
d
es
,
1
,
2
,
,
1
,
2
,
,
an
d
.
T
h
e
s
to
ch
asti
c
f
ac
to
r
in
th
e
f
o
r
m
o
f
n
o
is
e
co
n
tain
ed
in
th
e
e
q
u
atio
n
is
g
en
e
r
ated
f
r
o
m
a
n
u
m
b
er
o
f
r
an
d
o
m
n
u
m
b
er
s
f
r
o
m
th
e
co
m
p
u
ter
th
r
o
u
g
h
th
e
MA
T
L
AB
p
r
o
g
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am
.
T
h
e
n
o
is
e
g
en
er
ated
is
ass
u
m
ed
to
h
av
e
a
n
o
r
m
al
d
is
tr
ib
u
tio
n
with
a
m
ea
n
o
f
ze
r
o
wh
ile
th
e
n
o
is
e
v
ar
ian
ce
is
as
s
u
m
ed
to
b
e
co
n
s
tan
t
at
ℚ
an
d
ℛ
.
B
y
f
o
llo
win
g
th
e
alg
o
r
ith
m
s
tep
s
in
s
u
b
s
ec
t
io
n
2
.
3
,
esti
m
atio
n
r
esu
lts
ar
e
o
b
tain
ed
wh
ich
ca
n
b
e
s
ee
n
in
T
ab
le
1
.
Valid
atin
g
th
e
co
n
s
tr
u
cted
m
o
d
el'
s
ac
cu
r
ac
y
en
tails
co
m
p
ar
in
g
n
u
m
er
ical
s
im
u
latio
n
o
u
tco
m
es
with
ac
tu
al
d
ata
o
b
tain
ed
f
r
o
m
th
e
DKI
J
ak
a
r
ta
Hea
lth
Ser
v
ice
f
r
o
m
Feb
r
u
ar
y
0
5
t
o
Ma
y
05
,
2
0
2
2
.
T
h
e
f
o
llo
win
g
is
a
g
r
ap
h
co
m
p
ar
in
g
th
e
in
f
ec
ted
p
o
p
u
latio
n
f
r
o
m
t
h
e
r
esu
lts
o
f
th
e
n
u
m
er
ical
s
i
m
u
latio
n
with
th
e
d
ata
s
h
o
wn
in
Fig
u
r
e
2
.
T
ab
le
1
.
E
s
tim
atio
n
r
esu
lts
o
f
s
ev
er
al
p
ar
am
eter
s
with
th
e
ex
ten
d
ed
Kalm
an
f
ilter
(
E
KF)
P
a
r
a
me
t
e
r
D
e
scri
p
t
i
o
n
R
e
s
u
l
t
E
K
F
R
e
f
e
r
e
n
c
e
s
1
Tr
a
n
sm
i
ssi
o
n
r
a
t
e
o
f
t
h
e
o
r
i
g
i
n
a
l
v
i
r
u
s
0
.
09717
Est
i
m
a
t
i
o
n
2
Tr
a
n
sm
i
ssi
o
n
r
a
t
e
o
f
t
h
e
o
mi
c
r
o
n
v
i
r
u
s
0
.
1097
Est
i
m
a
t
i
o
n
V
a
c
c
i
n
a
t
i
o
n
r
a
t
e
s
0
.
1053
Est
i
m
a
t
i
o
n
1
A
n
t
i
b
o
d
i
e
s
ma
y
n
o
t
h
a
v
e
b
e
e
n
f
o
r
me
d
b
y
v
a
c
c
i
n
e
r
e
c
i
p
i
e
n
t
s a
g
a
i
n
st
t
h
e
o
r
i
g
i
n
a
l
v
i
r
u
s a
f
t
e
r
2
8
d
a
y
s.
0
.
05
[
1
7
]
2
A
n
t
i
b
o
d
i
e
s
ma
y
n
o
t
h
a
v
e
f
o
r
m
e
d
i
n
v
a
c
c
i
n
e
r
e
c
i
p
i
e
n
t
s
a
g
a
i
n
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t
h
e
O
mi
c
r
o
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v
i
r
u
s a
f
t
e
r
2
8
d
a
y
s.
0
.
33
[
2
2
]
1
Th
e
r
a
t
e
o
f
c
h
a
n
g
e
o
f
i
n
d
i
v
i
d
u
a
l
e
x
p
o
su
r
e
s fr
o
m
1
t
o
1
0
.
1052
Est
i
m
a
t
i
o
n
2
Th
e
r
a
t
e
o
f
c
h
a
n
g
e
o
f
i
n
d
i
v
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d
u
a
l
e
x
p
o
su
r
e
s
2
t
o
2
0
.
1053
Est
i
m
a
t
i
o
n
1
R
e
c
o
v
e
r
y
r
a
t
e
o
f
e
a
c
h
c
o
mp
a
r
t
me
n
t
1
0
.
04659
Est
i
m
a
t
i
o
n
2
R
e
c
o
v
e
r
y
r
a
t
e
o
f
e
a
c
h
c
o
mp
a
r
t
me
n
t
2
0
.
05587
Est
i
m
a
t
i
o
n
3
R
e
c
o
v
e
r
y
r
a
t
e
o
f
e
a
c
h
c
o
mp
a
r
t
me
n
t
0
.
05134
Est
i
m
a
t
i
o
n
3
i
so
l
a
t
i
o
n
r
a
t
e
0
.
659
Est
i
m
a
t
i
o
n
Fig
u
r
e
2
.
C
OVI
D
-
1
9
m
o
d
el
s
i
m
u
latio
n
m
atch
in
g
g
r
ap
h
with
r
ea
l d
ata
3
.
3
.
Desig
n o
ptim
a
l c
o
ntr
o
l
I
n
th
is
s
u
b
s
ec
tio
n
,
we
will
b
e
ap
p
ly
in
g
o
p
tim
al
co
n
tr
o
l
tech
n
iq
u
es
to
th
e
C
OVI
D
-
1
9
m
o
d
el
(
3
)
.
T
h
e
o
b
jectiv
e
o
f
th
is
o
p
tim
al
co
n
tr
o
l
is
to
m
in
im
ize
th
e
p
er
f
o
r
m
an
ce
in
d
ex
with
th
e
g
o
al
o
f
r
ed
u
cin
g
th
e
p
o
p
u
latio
n
s
1
(
)
an
d
2
(
)
,
wh
ich
is
f
o
r
m
u
lated
as (
6
)
,
(
1
,
2
,
3
)
=
∫
(
1
(
)
+
2
(
)
+
1
2
1
1
2
(
)
+
1
2
2
2
2
(
)
+
1
2
3
3
2
(
)
)
0
(
6
)
with
1
,
2
,
d
a
n
3
r
esp
ec
tiv
ely
ar
e
t
h
e
weig
h
t
co
n
s
tan
ts
o
f
th
e
co
n
tr
o
l
v
ar
iab
les
in
th
e
f
o
r
m
o
f
co
s
ts
f
o
r
h
ea
lth
ed
u
ca
tio
n
(
1
)
,
v
ac
cin
atio
n
(
2
)
,
an
d
is
o
latio
n
(
3
)
.
r
ep
r
esen
ts
th
e
en
d
tim
e
o
f
th
e
o
b
s
er
v
atio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Op
tima
l c
o
n
tr
o
l str
a
teg
ies b
a
s
ed
o
n
ex
te
n
d
ed
K
a
lma
n
filt
er in
ma
th
ema
tica
l
…
(
Dewi S
u
h
ika
)
6307
Ou
r
p
r
im
ar
y
f
o
c
u
s
is
o
n
id
en
ti
f
y
in
g
th
e
o
p
tim
al
co
n
tr
o
l
(
1
∗
,
2
∗
,
3
∗
)
s
u
ch
th
at
(
1
∗
,
2
∗
,
3
∗
)
=
1
,
2
,
3
∈
(
1
,
2
,
3
)
wh
er
e
=
{
(
1
,
2
,
3
)
|
(
)
is
L
e
b
e
s
q
ue
me
a
s
ura
b
l
e
on
[
0
,
1
]
,
(
=
1
,
2
,
3
)
}
.
B
ased
o
n
s
y
s
tem
(
3
)
an
d
in
d
ex
p
e
r
f
o
r
m
an
ce
in
(
6
)
,
a
H
am
ilto
n
ian
f
u
n
ctio
n
ca
n
b
e
f
o
r
m
ed
as:
ℋ
=
ℋ
(
(
)
,
(
)
,
(
)
)
=
1
+
2
+
1
2
1
1
2
(
)
+
1
2
2
2
2
(
)
+
1
2
3
3
2
(
)
+
1
(
Λ
−
(
1
−
1
(
)
)
1
−
(
1
−
1
(
)
)
1
2
−
(
1
+
2
(
)
)
−
)
+
2
(
(
1
−
1
(
)
)
1
1
+
(
1
−
1
)
1
1
1
−
1
1
−
1
)
+
4
(
(
1
+
2
(
)
)
−
(
1
−
1
(
)
)
1
1
1
−
(
1
−
1
(
)
)
2
2
2
−
)
+
5
(
1
1
−
3
(
)
1
−
1
2
−
1
)
+
6
(
2
2
−
3
(
)
2
−
2
2
−
2
)
+
7
(
3
(
)
1
+
3
(
)
2
−
3
−
)
+
8
(
1
1
+
2
2
+
3
−
)
.
wh
er
e
(
)
=
(
(
)
,
1
(
)
,
2
(
)
,
(
)
,
1
(
)
,
2
(
)
,
(
)
,
(
)
)
is
s
tate
s
y
s
tem
(
3
)
an
d
,
=
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
ar
e
th
e
ad
jo
in
t
v
ar
iab
les o
r
co
s
tate
v
ar
iab
le.
Th
eo
r
em
1
.
Su
p
p
o
s
e
g
i
v
en
th
e
s
o
lu
tio
n
s
(
)
,
1
(
)
,
2
(
)
,
(
)
,
1
(
)
,
2
(
)
,
(
)
,
(
)
o
f
th
e
s
tate
s
y
s
tem
(
3
)
a
n
d
o
p
tim
al
co
n
tr
o
l
p
air
s
(
1
∗
,
2
∗
,
3
∗
)
,
th
er
e
e
x
is
t
co
s
tate
v
ar
ia
b
les
,
=
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
wh
ich
f
u
lf
ill
th
e
f
o
llo
win
g
a
d
jo
in
t sy
s
tem
:
̇
1
=
(
1
−
2
)
1
1
(
1
−
)
(
1
−
1
)
+
(
1
−
3
)
2
2
(
1
−
)
(
1
−
1
)
+
(
1
−
4
)
(
1
+
2
)
+
1
̇
2
=
(
1
+
)
2
−
1
5
̇
3
=
(
2
+
)
3
−
2
6
̇
4
=
(
4
−
2
)
1
1
1
(
1
−
)
(
1
−
1
)
+
(
4
−
3
)
2
2
2
(
1
−
)
(
1
−
1
)
+
4
̇
5
=
−
1
+
(
1
−
2
)
1
(
1
−
1
)
(
1
−
1
)
+
(
4
−
2
)
1
1
(
1
−
1
)
(
1
−
1
)
+
5
(
3
+
1
+
)
−
3
7
−
1
8
̇
6
=
−
1
+
(
1
−
3
)
2
(
1
−
2
)
(
1
−
1
)
+
(
4
−
3
)
2
2
(
1
−
2
)
(
1
−
1
)
+
6
(
3
+
2
+
)
−
3
7
−
2
8
̇
7
=
7
(
3
+
)
−
3
8
̇
8
=
8
.
T
h
e
c
o
s
t
at
e
e
q
u
at
i
o
n
s
y
s
t
e
m
r
e
l
a
t
e
d
t
o
t
h
e
o
p
ti
m
a
l
c
o
n
t
r
o
l
s
(
1
∗
,
2
∗
,
,
3
∗
)
∈
a
n
d
s
a
ti
s
f
y
i
n
g
t
h
e
t
r
a
n
s
v
e
r
s
al
i
ty
c
o
n
d
i
t
i
o
n
s
(
)
,
=
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
.
A
s
a
r
es
u
l
t
,
t
h
e
o
p
ti
m
a
l
c
o
n
t
r
o
ls
a
r
e
o
b
t
a
i
n
e
d
as
:
1
∗
=
{
0
,
{
1
,
1
1
(
(
2
−
1
)
1
1
+
(
3
−
1
)
2
2
+
(
2
−
4
)
1
1
1
+
(
3
−
4
)
2
2
2
)
}
}
2
∗
=
{
0
,
{
1
,
(
1
−
4
)
2
}
}
3
∗
=
{
0
,
{
1
,
(
5
−
7
)
1
+
(
6
−
7
)
2
3
}
}
.
3
.
4
.
Resul
t
o
f
n
um
er
ica
l sim
ula
t
io
n
I
n
th
is
s
u
b
s
ec
tio
n
,
we
co
n
d
u
ct
n
u
m
er
ical
s
im
u
latio
n
s
o
n
m
o
d
els
b
o
th
with
o
u
t
an
d
wit
h
co
n
tr
o
l
m
ea
s
u
r
es
to
illu
s
tr
ate
th
e
im
p
o
r
tan
ce
o
f
im
p
lem
en
tin
g
c
o
n
tr
o
l
s
tr
ateg
ies.
Op
tim
al
c
o
n
tr
o
l
s
im
u
latio
n
is
ca
r
r
ied
o
u
t
u
s
in
g
th
e
f
o
r
war
d
-
b
ac
k
war
d
s
wee
p
alg
o
r
ith
m
.
T
h
e
p
ar
am
eter
v
alu
es
u
s
ed
in
t
h
e
s
im
u
latio
n
ar
e
in
T
ab
le
1
.
T
h
e
weig
h
t
v
alu
es
u
s
ed
ar
e
1
=
10
,
2
=
20
,
an
d
2
=
20
an
d
o
b
s
er
v
ati
o
n
tim
e
0
≤
≤
150
d
ay
s
.
I
n
th
is
p
a
p
er
,
t
h
r
ee
c
o
n
tr
o
l
s
ce
n
ar
io
s
a
n
d
s
ev
e
n
co
n
tr
o
l
s
tr
ateg
ies
ar
e
p
r
esen
ted
,
en
co
m
p
ass
in
g
a
co
m
b
in
atio
n
o
f
h
ea
lth
ed
u
ca
tio
n
(
1
(
)
)
,
v
ac
cin
atio
n
(
2
(
)
)
,
an
d
is
o
latio
n
m
ea
s
u
r
es
(
3
(
)
)
.
−
S
c
e
n
a
r
i
o
1
c
o
n
s
is
ts
o
f
s
i
n
g
l
e
co
n
t
r
o
l
s
,
n
a
m
e
l
y
s
t
r
a
t
e
g
y
1
(
h
e
al
t
h
e
d
u
c
a
ti
o
n
c
o
n
t
r
o
l
)
,
s
t
r
a
te
g
y
2
(
v
a
c
c
i
n
a
ti
o
n
)
,
a
n
d
s
t
r
a
t
e
g
y
3
(
is
o
l
a
ti
o
n
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
14
,
No
.
6
,
Dec
em
b
e
r
20
24
:
6
3
0
0
-
6
3
1
2
6308
−
Scen
ar
io
2
co
n
s
is
ts
o
f
d
o
u
b
le
co
n
tr
o
ls
,
th
er
e
ar
e
s
tr
ateg
y
4
(
co
m
b
in
ed
h
ea
lth
ed
u
ca
tio
n
an
d
v
ac
cin
atio
n
co
n
tr
o
l)
,
s
tr
ateg
y
5
(
h
ea
lth
e
d
u
ca
tio
n
an
d
is
o
latio
n
c
o
n
tr
o
l)
,
an
d
s
tr
ateg
y
6
(
v
ac
cin
atio
n
an
d
is
o
latio
n
co
n
tr
o
l)
.
−
Scen
ar
io
3
is
s
tr
ateg
y
7
,
th
r
ee
co
n
tr
o
l in
p
u
ts
o
f
h
ea
lth
ed
u
ca
t
io
n
,
v
ac
cin
atio
n
,
an
d
is
o
latio
n
.
I
n
Fig
u
r
e
3
,
co
n
tr
o
l
r
e
p
r
esen
t
s
th
e
ch
an
g
e
in
c
o
n
tr
o
l
∗
with
tim
e.
No
te
th
at
in
itially
th
e
o
p
tim
al
co
n
tr
o
l
1
∗
(
h
ea
lth
ed
u
ca
tio
n
)
ta
k
es
a
m
ax
im
u
m
v
alu
e
at
∈
[
0
.
65
]
,
th
en
at
tim
e
∈
[
65
,
150
]
th
e
o
p
tim
al
co
n
tr
o
l
v
al
u
e
1
∗
b
eg
in
s
to
d
ec
r
e
ase
u
n
til
o
n
d
a
y
1
5
0
we
o
b
tai
n
φ
1
∗
=
0
.
I
n
o
p
tim
al
c
o
n
tr
o
l
2
∗
(
v
ac
ci
n
atio
n
)
tak
es
a
m
ax
im
u
m
v
alu
e
at
∈
[
0
.
5
]
,
th
en
at
tim
e
∈
[
5
,
150
]
th
e
o
p
tim
al
co
n
tr
o
l
v
alu
e
2
∗
b
eg
in
s
to
d
ec
r
ea
s
e
u
n
til
d
ay
1
5
0
we
o
b
tain
2
∗
=
0
.
Me
a
n
wh
ile,
th
e
o
p
tim
al
co
n
tr
o
l
3
∗
(
i
s
o
latio
n
)
tak
es
a
m
a
x
im
u
m
v
a
lu
e
at
∈
[
0
.
95
]
,
th
en
at
tim
e
∈
[
95
,
150
]
th
e
o
p
tim
al
co
n
tr
o
l
v
alu
e
3
∗
b
eg
in
s
to
d
ec
r
ea
s
e
u
n
til
o
n
d
ay
1
5
0
we
o
b
tain
3
∗
=
0
.
T
h
is
m
ea
n
s
th
at
in
itial
ly
th
e
co
n
tr
o
l
ef
f
o
r
t
is
ca
r
r
ied
o
u
t
in
f
u
ll,
th
en
th
e
co
n
tr
o
l
v
alu
e
d
ec
r
ea
s
es
g
r
ad
u
ally
u
n
til th
e
en
d
o
f
th
e
o
b
s
er
v
atio
n
r
ea
ch
es z
er
o
.
T
o
p
er
f
o
r
m
a
co
m
p
r
eh
e
n
s
iv
e
co
m
p
ar
is
o
n
o
f
all
av
ailab
le
co
n
tr
o
l
s
tr
ateg
ies,
an
im
p
o
r
ta
n
t
s
tep
is
to
ca
lcu
late
th
e
to
tal
n
u
m
b
er
o
f
in
f
ec
ted
in
d
iv
id
u
als
(
T
I
I
)
as
well
as
th
e
to
tal
ca
s
es
av
er
t
ed
(
T
C
A)
f
o
r
ea
ch
s
tr
ateg
y
.
I
n
o
th
er
wo
r
d
s
,
it
is
n
ec
ess
ar
y
to
e
v
alu
ate
th
e
ef
f
ec
tiv
en
ess
o
f
ea
ch
co
n
tr
o
l
s
tr
ateg
y
to
ass
ess
its
ab
ilit
y
to
r
ed
u
ce
th
e
n
u
m
b
er
o
f
p
eo
p
le
i
n
f
ec
ted
a
n
d
th
e
n
u
m
b
er
o
f
ca
s
es th
at
ca
n
b
e
p
r
ev
en
ted
.
=
∫
(
1
(
)
+
2
(
)
)
0
a
n
d
=
∫
(
̂
1
(
)
+
̂
2
(
)
−
(
1
(
)
+
2
(
)
)
)
0
,
wh
er
e
(
̂
1
(
)
+
̂
2
(
)
)
r
ep
r
esen
ts
th
e
n
u
m
b
er
o
f
in
f
ec
ted
in
d
i
v
id
u
als
wi
th
o
u
t
co
n
tr
o
l
m
ea
s
u
r
es,
(
1
(
)
+
2
(
)
)
d
en
o
te
th
e
in
f
ec
ted
in
d
iv
id
u
als
with
co
n
tr
o
l
s
tr
ateg
y
[
4
]
.
T
h
e
o
u
tc
o
m
es
o
f
all
co
m
p
u
tatio
n
s
ar
e
p
r
esen
ted
in
T
a
b
le
2
.
I
n
s
in
g
le
in
p
u
t
co
n
tr
o
l
s
ce
n
ar
i
o
s
,
o
n
ly
is
o
latio
n
co
n
tr
o
l
s
h
o
wed
a
s
ig
n
if
ican
t
r
ed
u
ctio
n
i
n
th
e
n
u
m
b
e
r
o
f
in
f
ec
ted
i
n
d
iv
id
u
als
co
m
p
ar
ed
to
h
ea
lth
ed
u
ca
tio
n
an
d
v
ac
cin
atio
n
co
n
tr
o
ls
.
T
h
is
r
ed
u
ctio
n
o
cc
u
r
r
e
d
b
ec
au
s
e,
in
m
o
d
el
(
3
)
,
is
o
latio
n
co
n
tr
o
l
is
d
ir
ec
tly
ap
p
lied
to
alr
ea
d
y
in
f
ec
ted
in
d
iv
id
u
al
s
,
th
u
s
ac
ce
ler
atin
g
th
e
d
ec
r
ea
s
e
in
th
e
n
u
m
b
er
o
f
in
f
ec
ted
in
d
iv
i
d
u
als
as
s
h
o
wn
in
Fig
u
r
e
4
.
I
n
t
h
e
d
o
u
b
le
in
p
u
t
co
n
tr
o
l
s
ce
n
a
r
io
in
Fig
u
r
e
5
,
co
m
b
in
in
g
is
o
latio
n
co
n
tr
o
l
with
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s
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ch
as
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o
r
h
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lth
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,
h
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ter
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n
u
m
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in
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iv
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th
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r
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ip
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u
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o
f
th
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th
r
ee
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m
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e
s
p
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th
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o
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tr
o
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h
as p
r
o
v
en
s
u
cc
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f
u
l in
ad
d
r
ess
in
g
th
e
C
OVI
D
-
1
9
p
an
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cin
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Fig
u
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u
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Op
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atio
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(
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n
d
is
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e
C
OVI
D
-
1
9
p
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ic
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ateg
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if
ican
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ile
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,
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