one possible model of prevention (one county in sw) chatham is...
TRANSCRIPT
NW
NSW
CE
1996
124
257
99
243
1997
116
2231
01
6819
9818
134
758
3315
419
9940
713
216
0310
231
420
0033
711
011
2050
292
2001
362
141
903
161
396
2002
795
345
887
534
925
2003
3017
1791
4789
3599
5451
Tabl
e 1:
199
6 -2
003
Repo
rted
Flu
Cas
es in
Virg
inia
regi
ons:
N
W(1
) = N
orth
wes
t, N
(2) =
Nor
th, S
W(3
) = S
outh
wes
t, C
(4) =
Cen
tral,
E(5)
= E
aste
rn.
Rea
chin
g th
e C
omm
unit
yw
ith
Mat
hem
atic
al B
iolo
gyR
each
ing
the
Com
mun
ity
Rea
chin
g th
e C
omm
unit
yw
ith
Mat
hem
atic
al B
iolo
gyw
ith
Mat
hem
atic
al B
iolo
gyO
lgam
ary
Riv
era-
Mar
rero
or
iver
am@
mat
h.vt
.edu
Purp
ose
Purp
ose
Stud
ents
Lear
n ho
w to
app
ly b
asic
mat
hem
atic
al c
once
pts
to
mod
el re
al-w
orld
situ
atio
ns.
Teac
hers
Acq
uire
new
idea
s of
inte
grat
ing
non-
stan
dard
m
athe
mat
ics
into
the
clas
sroo
m.
Abs
trac
t Alg
ebra
Abs
trac
t str
uctu
res:
inve
rses
and
iden
titie
sPr
oper
ties o
f ope
ratio
ns: c
omm
utat
ive,
ass
ocia
tive,
di
stri
butiv
eFi
nite
fiel
ds: a
rith
met
ic a
nd fu
nctio
nsSo
ftw
are:
Disc
rete
Visu
aliz
erof
Dyn
amic
s(D
VD
)
Gra
ph T
heor
yG
raph
s: v
erte
x , w
eigh
ted
Adj
acen
cy m
atri
ces
Ver
tex
colo
ring
Path
s and
cyc
les:
shor
test
, eul
eria
n, h
amilt
onia
nSo
ftw
are:
Mat
hem
atic
al M
odeli
ng: U
sing
Gra
phs/
Mat
rices
(MM
)
Focu
s an
d To
pics
of t
he W
orks
hop
Focu
s an
d To
pics
of t
he W
orks
hop
To d
evel
op a
nd im
plem
ent a
mat
hem
atic
s w
orks
hop
for s
econ
dary
mat
hem
atic
s te
ache
rs a
nd h
igh
scho
ol
stud
ents
.
The
wor
ksho
p w
as d
esig
ned
to in
trod
uce
mat
hem
atic
al b
iolo
gy a
nd to
dem
onst
rate
inno
vativ
e w
ays
of te
achi
ng m
athe
mat
ics w
ith g
raph
ical
m
odel
ing
softw
are.
Vira
l Epi
dem
ic P
roje
ctVi
ral E
pide
mic
Pro
ject
Giv
en d
ata
of th
e nu
mbe
r of c
ases
of i
nflu
enza
Find
a m
odel
to p
redi
ct a
pos
sibl
e fu
ture
epi
dem
ic.
Find
a m
odel
to p
reve
nt th
e sp
read
of t
he in
fect
ion.
The
teac
hers
gen
erat
ed id
eas
to in
tegr
ate
stan
dard
mat
hem
atic
s an
d th
e to
pics
of t
he w
orks
hop
thro
ugh
inte
ract
ions
with
the
stud
ents
and
the
othe
r tea
cher
s.
Solu
tions
Solu
tions
One
pos
sibl
e m
odel
of p
redi
ctio
n
One
pos
sibl
e m
odel
of p
reve
ntio
n (o
ne c
ount
y in
SW
)
This
impl
ies
that
the
regi
ons N
W, S
W, a
nd C
are
like
ly to
ex
peri
ence
influ
enza
at e
pide
mic
leve
ls in
the
2005
/200
6 flu
seas
on.
A c
linic
will
be
cons
truc
ted
in th
e m
ost c
entr
al lo
calit
y in
the
iden
tifie
d co
unty
.
Dis
sem
inat
ion
of in
form
atio
n by
hea
lth s
peci
alis
ts is
one
w
ay to
pre
vent
spre
ad o
f the
flu. G
raph
4: H
amilt
onia
n ci
rcui
t for
one
pos
sible
ro
ute
for t
he s
peci
alist
s to
visit
eac
h ci
ty in
the
coun
ty.
The
rout
e st
arts
and
end
s at
the
clin
ic.
Con
clus
ions
Con
clus
ions
The
stud
ents
ext
ende
d th
eir p
robl
em s
olvi
ng a
nd
com
mun
icat
ion
skill
s.Th
e te
ache
rs e
xplo
red
way
s to
inco
rpor
ate
the
conc
epts
into
thei
r ow
n cl
assr
oom
s.A
ll pa
rtic
ipan
ts e
stab
lishe
d a
conn
ectio
n am
ong
mat
hem
atic
s, b
iolo
gy, m
odel
ing,
and
tech
nolo
gy.
Bra
ndil
yn S
tigl
erbs
tigl
er@
vbi.
vt.e
du
All
part
icip
ants
app
lied
thes
e co
ncep
ts to
an
epid
emio
logi
cal p
robl
em.
15
23
41
21
2
34
13
41
53
4
54
15
1
()
(1)
()
0
()
1
()
(1)
0(
)(
1)(
)
1(
)(
)
fx
xx
xx
fxx
fxx
xf
xx
xx
fx
xx
=+
++
++
=+
=+
++
=+
++
++
=+
++
5
2
Gra
ph 1
: Geo
grap
hic
rela
tions
hips
be
twee
n re
gion
s.
Varia
bles
= re
gion
s
Gra
ph 2
: Evo
lutio
n of
flu
epi
dem
ic
beha
vior
.
0 =
no e
pide
mic
1 =
epid
emic
Year
200
1
Pred
icte
d ye
ar
2005
NW
N S
W C
E
Gra
ph 3
: Ver
tex
colo
ring
of w
eigh
ted
grap
h fo
r the
cou
nty.
Tabl
e 2:
Sho
rtest
-pat
h m
atrix
for
driv
ing
times
bet
wee
n ci
ties
in th
e co
unty
.
Lette
r = c
ityN
umbe
r = s
horte
st d
rivin
g tim
e
The
min
imum
num
ber o
f sp
ecia
lists
nee
ded
are
3.
Cha
tham
is m
ost c
entr
al.
Ver
tex-
grap
hH
amilt
on c
ircui
t
Col
or =
spe
cial
ist
Refe
renc
esRe
fere
nces
DV
D: h
ttp:/
/dvd
.vbi
.vt.e
duM
M: h
ttp:/
/ww
w.le
arni
ngin
mot
ion.
com
Nat
iona
l Cou
ncil
for T
each
ers
of M
athe
mat
ics:
http
://w
ww
.nct
m.o
rgG
raph
theo
ry le
sson
s: ht
tp:/
/ww
w.u
tc.e
du/F
acul
ty/C
hris
toph
er-
Maw
ata/
pete
rsen
/les
son1
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