1. The
rate
of
vaccina.on
of
all
age
classes,
p,
is
a
func.on
of
.me
such
that:
See
Figure
3a.
Rou.ne
vaccina.on
of
babies
occurs
at
a
separate
rate
d.
Analysis
revealed
that
b
and
c
have
li@le
effect
on
the
propor.on
of
individuals
vaccinated
(see
V
in
Figure
3b),
therefore
only
a
is
varied
here.
Parameters
&
Methods
Introduc2on
The
meningi.s
belt
–
stretching
from
Senegal
to
Ethiopia
–
has
the
highest
incidence
of
meningococcal
meningi.s
in
the
world.
Meningi.s
frequently
causes
death
and
lifelong
disability,
as
well
as
serious
economic
drain
on
impacted
countries.
Epidemics
are
seasonal,
but
in
the
past
decade
have
become
more
frequent
and
irregular
and
have
spread
to
countries
farther
south.
A
conjugate
vaccine
against
meningococcal
serogroup
A,
which
causes
most
invasive
disease
in
the
African
meningi.s
belt,
was
introduced
in
2010
and
appears
to
have
significantly
reduced
carriage
and
incidence
of
serogroup
A
meningococcal
disease
in
vaccinated
communi.es
[1].
However,
serogroup
W
caused
a
major
outbreak
in
2000
and
2001
during
the
Hajj
–
a
Muslim
pilgrimage
to
Saudi
Arabia
–
in
a
popula.on
of
individuals
vaccinated
against
serogroups
A
and
C.
Pilgrims
brought
the
outbreak
strain
back
to
Africa,
where
it
con.nues
to
circulate
[2].
With
the
intensifica.on
of
serogroup
A
vaccina.on
in
the
meningi.s
belt,
there
is
concern
that
serogroup
W
could
replace
serogroup
A
as
the
major
cause
of
disease
in
the
region
[3].
In
meningococcal
meningi.s,
epidemics
of
invasive
disease
appear
to
be
driven
by
seasonal
fluctua.ons
in
carriage
prevalence
and
epidemics
are
almost
always
associated
with
high
levels
of
carriage
[4].
For
these
reasons,
understanding
the
dynamics
of
carriage
is
key
to
reducing
the
burden
of
invasive
disease.
Model
Discussion
These
results
suggest
that
rela.ve
transmissibility
of
strains
is
important
in
choosing
op.mal
vaccina.on
levels.
If
serogroup
W
is
more
transmissible
than
A,
vaccina.on
may
actually
increase
overall
meningococcal
carriage
because
vaccina.on
will
increase
the
number
of
suscep.ble
individuals
available
for
coloniza.on
by
W,
the
“stronger
compe.tor”
of
the
two.
If
serogroup
W
is
less
transmissible
than
A,
vaccina.on
will
decrease
overall
meningococcal
carriage.
This
model
also
suggests
that
low
or
intermediate
levels
of
vaccina.on
may
be
more
advantageous
in
reducing
overall
carriage
than
high
vaccina.on.
For
a
given
transmissibility
level,
increasing
vaccina.on
oen
results
in
higher
overall
carriage.
Interes.ngly,
vaccina.on
plays
the
greatest
role
in
reducing
carriage
of
serogroup
A
where
A
and
W
are
equally
transmissible.
This
is
probably
because
when
A
is
less
transmissible
than
W,
strain
compe..on
plays
an
important
role
in
decreasing
carriage
and
when
A
is
more
transmissible
than
W,
both
vaccina.on
and
strain
compe..on
are
less
effec.ve
at
reducing
carriage.
It
is
important
to
note
that
although
increased
carriage
is
linked
increased
rates
of
invasive
disease,
not
all
serogroups
are
equally
virulent
and
therefore
all
types
of
carriage
may
not
be
of
equal
concern.
If
serogroup
A
is
significantly
more
virulent
than
serogroup
W,
higher
vaccina.on
coverage
may
save
more
lives
even
though
it
may
result
in
higher
rates
of
carriage.
Using
an
age-­‐structured
version
of
this
model
would
allow
for
targe.ng
of
certain
age
classes
for
vaccina.on
and
differen.al
interac.on
between
age
groups.
This
analysis
could
also
benefit
from
the
use
of
a
neutral
null
model,
which
displays
both
ecological
neutrality,
meaning
that
the
number
of
hosts
infected
by
a
par.cular
number
of
strains
(0,
1,
2…)
is
independent
of
strain
iden.ty,
and
popula.on
gene.c
neutrality,
meaning
that
it
is
possible
to
choose
parameters
that
guarantee
a
stable
arbitrary
frequency
of
strains
[6].
The
advantage
of
the
neutral
null
model
is
that
it
does
not
assume
stable
coexistence
of
strains,
and
therefore
is
not
biased
towards
predic.on
of
serotype
replacement
or
non-­‐replacement.
Finally,
given
the
importance
of
rela.ve
transmissibility
in
selec.ng
an
op.mal
vaccina.on
strategy,
it
would
be
valuable
to
derive
key
epidemiological
parameters
β
(transmissibility)
and
r
(rate
of
recovery
from
carriage)
for
both
serogroups.
It
should
be
emphasized
that
this
model
does
not
produce
quan.ta.ve
predic.ons,
but
instead
provides
qualita.ve
insight
into
the
effect
of
vaccina.on
on
the
compe..ve
landscape.
References
1.Daugla,
D.
et
al.
Effect
of
a
serogroup
A
meningococcal
conjugate
vaccine
(PsA–TT)
on
serogroup
A
meningococcal
meningi.s
and
carriage
in
Chad:
a
community
study.
The
Lancet
383,
40–47
(2014).
2.Harrison,
L.
H.,
Tro@er,
C.
L.
&
Ramsay,
M.
E.
Global
epidemiology
of
meningococcal
disease.
Vaccine
27,
Supplement
2,
B51–B63
(2009).
3.Caugant,
D.
A.
&
Nicolas,
P.
Molecular
surveillance
of
meningococcal
meningi.s
in
Africa.
Vaccine
25,
Supplement
1,
A8–A11
(2007).
4.Irving,
T.
J.,
Blyuss,
K.
B.,
Colijn,
C.
&
Tro@er,
C.
L.
Modelling
meningococcal
meningi.s
in
the
African
meningi.s
belt.
Epidemiol.
Infect.
140,
897–905
(2012).
5.Tro@er,
C.
L.,
Gay,
N.
J.
&
Edmunds,
W.
J.
Dynamic
Models
of
Meningococcal
Carriage,
Disease,
and
the
Impact
of
Serogroup
C
Conjugate
Vaccina.on.
Am.
J.
Epidemiol.
162,
89–100
(2005).
6.Lipsitch,
M.,
Colijn,
C.,
Cohen,
T.,
Hanage,
W.
P.
&
Fraser,
C.
No
coexistence
for
free:
Neutral
null
models
for
mul.strain
pathogens.
Epidemics
1,
2–13
(2009).
Op:mal
Vaccina:on
for
Meningococcal
Serogroup
A
in
the
African
Meningi:s
Belt
Laura
Cooper
ENV
304
Disease
Ecology,
Economics
and
Policy
Name
Meaning
Value
Range
Unit
Comment
μ
Natural
birth
and
death
rate
0.00032
1/week
Fixed.
Life
expectancy
around
60
years.
βA
Transmission
rate
of
carriage
0.113
1/week
Fixed.
Calculated
from
es.mated
R0
of
1.36.
[5]
βW
Transmission
rate
of
carriage
0.103-­‐0.123
1/week
Considered
values
smaller
and
larger
than
βA
that
did
not
result
in
compe..ve
exclusion
of
strains.
rA,
rW
Rate
of
loss
of
carriage
0.0833
1/week
Fixed.
Carriage
lasts
12
weeks.
[5]
d
Propor.on
of
newborns
vaccinated
0-­‐1
None
No
newborn
vaccina.on
used
for
calcula.on
of
end
states
–
li@le
change
in
carriage
reduc.on.
γ
Rate
of
loss
of
vaccine
protec.on
0.0038
1/week
Fixed.
5
years
of
protec.on.
p
Rate
of
vaccina.on
of
general
popula.on
See
Table
3
and
Figure
3a
1/week
See
below.
ϵ
Seasonal
forcing
term
0-­‐1
None
No
seasonal
forcing
used
for
calcula.on
of
end
states.
φ
Vaccine
efficacy
against
carriage
acquisi.on
0.6
None
Fixed.
Vaccine
protects
against
90%
of
carriage
acquisi.on.
Table
2.
Carriage
Model
Parameters
Class
Meaning
S
Unvaccinated
suscep.ble
individuals
SV
Vaccinated
suscep.ble
individuals
A
Unvaccinated
individuals
carrying
serogroup
A
AV
Vaccinated
individuals
carrying
serogroup
A
W
Unvaccinated
individuals
carrying
serogroup
W
WV
Vaccinated
individuals
carrying
serogroup
W
Table
1.
Carriage
model
classes
! ! = ! ∗ exp
− ! − ! !
2!!
!
!
! ! = !!(1 + ! ∗ cos 2!" )!
!
!"
!"
= !! ! ! ! + !" + !"# − (!! + ! + !(!))!!
!
!"#
!"
= ! ! ! + 1 − ! !! ! !" ! + !" − ! + !! + ! !"!
!
!"
!"
= !! ! ! ! + !" + !"! − (!! + ! + !(!))!!
!
!"#
!"
= ! ! ! + !! ! !" ! + !" − ! + !! + ! !"!
!
!"
!"
= ! 1 − ! + !!! + !!! + !"# − !! ! ! ! + !" − !! ! ! ! + !" − !"!
!
!"#
!"
= !! + !!!" + !!!" − 1 − ! !! ! !! ! + !" − !! ! !! ! + !" − (! + !)!!!
!
!!
!"
= !! + !(!)(1 − !) − (! + !)!!
!
!
Name! Meaning! Value!
Range!
Unit! Comment!
!! Natural!birth!and!death!rate! 0.00032! 1/week! Fixed.!Life!expectancy!around!
60!years.!
!!, !!! Transmission!rate!of!carriage! 0.113! 1/week! Fixed.!Calculated!from!
estimated!R0!of!1.36.!
!!,!!!! Rate!of!loss!of!carriage! 0.0833! 1/week! Fixed.!Carriage!lasts!12!weeks.!
d! Proportion!of!newborns!
vaccinated!
0L1! None! !
!! Rate!of!loss!of!vaccine!protection! 0.0038! 1/week! Fixed.!5!years!of!protection.!
p! Rate!of!vaccination!of!general!
population!
See!! 1/week! !
!! Seasonal!forcing!term! 0L1! None! !
!! Vaccine!efficacy!against!carriage!
acquisition!
0L1! None! !
!
Name
Value
Range
Meaning
a
0-­‐0.1
Maximum
vaccina.on
effort
b
30
“Lag”
–
propor.onal
to
start
.me
of
campaign
c
10
Propor.onal
to
length
of
campaign
Table
3.
VaccinaFon
campaign
model
parameters
[
p(t)
]
0 100 200 300 400
0.00.20.40.6
Weeks
Proportion
V
A
W
0 100 200 300 400
0.000.030.06
Weeks
p
Figure
3.
Time
series
predicFon
a.
p,
the
rate
of
vaccina.on,
as
a
func.on
of
.me.
Parameter
values
–
a=.05,
b=30,
c=10
b.
Propor.on
vaccinated
shown
in
black
(V).
Carriers
of
W
shown
in
blue
and
carriers
of
A
shown
in
red,
with
and
without
seasonal
forcing.
Parameter
values
–
βW=0.113,
d=0,
ϵ=0.8
or
0,
φ=0.6,
A0=W0=0.13.
a.
Percent
Decrease
in
Carriage
of
Serogroup
A
c.
Percent
Increase
in
Carriage
of
Serogroup
W
d.
Percent
Change
in
Overall
Carriage
a,
c,
and
d
calculated
in
rela.on
to
carriage
levels
aer
zero
vaccina.on.
Beta
W:Beta
A
on
the
horizontal
axis
is
the
ra.o
of
rela.ve
transmissibility
of
the
serogroups:
at
BetaW:BetaA
equals
1,
the
serogroups
are
assumed
to
be
equally
transmissible.
On
the
ver.cal
axis
is
the
maximum
popula.on
vaccine
coverage
level
achieved
before
waning
(see
Fig.3a).
Model
was
run
for
the
equivalent
of
5
years.
Parameter
values
–d=0,
φ=.9,
A0=W0=0.13.
a.
Increased
vaccina.on
results
in
decreased
carriage
of
serogroup
A.
When
W
is
less
transmissible
than
A
(BetaW:BetaA
less
than
1)
reduc.on
in
carriage
of
A
requires
higher
levels
of
vaccina.on.
The
greatest
reduc.ons
in
carriage
occur
where
A
and
W
are
equally
transmissible.
b.
Carriage
of
serogroup
W
increases
with
increasing
vaccina.on
against
serogroup
A
and
with
increasing
transmissibility
of
serogroup
W.
c.
Vaccina.on
has
the
greatest
effect
on
carriage
of
W
when
transmissibility
is
low.
When
serogroup
W
is
more
transmissible
than
A,
vaccina.on
results
in
li@le
addi.onal
increase
in
carriage.
d.
In
most
cases,
vaccina.on
results
in
a
net
decrease
in
meningococcal
carriage.
At
high
levels
of
vaccina.on
where
W
is
moderately
more
transmissible
than
A
(darkest
green),
vaccina.on
results
in
a
small
net
increase
in
carriage.
b.
Final
Carriage
of
Serogroup
W
Figure
5.
Effect
of
VaccinaFon
Depends
on
Coverage
and
RelaFve
Transmissibility
of
Serogroup
W
Carriage
Results
a.
b.
! ! = !!(1 + ! ∗ cos 2!" )!
!
!"
!"
= !! ! ! ! + !" + !"# − (!! + ! + !(!))!!
!
!"#
!"
= ! ! ! + 1 − ! !! ! !" ! + !" − ! + !! + ! !"!
!
!"
!"
= !! ! ! ! + !" + !"# − (!! + ! + !(!))!!
!
!"#
!"
= ! ! ! + !! ! !" ! + !" − ! + !! + ! !"!
!
!"
!"
= ! 1 − ! + !!! + !!! + !"# − !! ! ! ! + !" !!
−!! ! ! ! + !" − !"!
!
!"#
!"
= !" + !!!" + !!!" − 1 − ! !! ! !" ! + !" !!
−!! ! !" ! + !" − (! + !)!"!
!
Figure
2.
Carriage
model
equaFons
A
S
W
AV
SV
WV
Carriage
status
Vaccina.on
status
p
ϒ
p
ϒ
p
ϒ
βA
rA
(1-­‐φ)βA
rA
βW
rW
βW
rW
μ(1-­‐d)
μd
To
inves.gate
the
effects
of
serogroup
A
vaccina.on
on
meningococcal
disease
in
a
community
with
circula.on
of
both
serogroups
A
and
W,
a
compartment
model
of
carriage
and
vaccina.on
was
constructed.
This
model
assumes
no
co-­‐carriage
of
strains
[5].
The
vaccine
is
known
to
protect
against
acquisi.on
of
serogroup
A
carriage
[1]
but
no
cross-­‐protec.ve
immunity
is
assumed
[5].
Figure
1.
Compartment
model
of
carriage
transmission
and
vaccinaFon
Li@le
serogroup-­‐specific
data
is
available
on
key
epidemiological
parameters,
although
these
could
be
es.mated
from
private
serogroup-­‐specific
incidence
data
as
part
of
a
further
inves.ga.on.
For
this
simula.on,
the
same
general
parameters
were
used
as
baseline
values
for
both
serogroups
A
and
W
and
the
effects
of
poten.al
differences
in
transmissibility
of
the
two
were
examined.
The
effect
of
two
other
parameters
not
shown
below
were
also
inves.gated.
Varying
vaccine
efficacy(φ)
versus
rela.ve
transmissibility
produces
similar
outcomes
as
those
presented
in
Figure
5.
Rou.ne
vaccina.on
of
newborns
(d)
decreased
the
rate
of
waning
of
popula.on-­‐wide
immunity
following
the
campaign,
but
had
li@le
effect
on
carriage,
probably
because
of
the
rela.vely
short
.me
frame
considered
(five
years).
85% 90% 95%
Carriage 6 Weeks Post Vaccination
Phi
0.000000.00015
Figure
4.
Carriage
of
A,
Six
Weeks
Post-­‐VaccinaFon
Vaccine
efficacy,
φ,
was
es.mated
from
data
documen.ng
the
post-­‐vaccina.on
reduc.on
in
carriage
[1].
Model
outputs
(green)
were
closest
to
observed
data
(black)
at
a
vaccine
efficacy
of
90%.
0.72
0.68
0.63
0.58
0.52
0.44
0.36
0.26
0.14
0
accineCoverage
% Change in Carriage
−20 −10 0
0.72
0.68
0.63
0.58
0.52
0.44
0.36
0.26
0.14
0
ccineCoverage
0 100 300 500
0.91
0.92
0.94
0.95
0.96
0.97
0.98
0.99
1.01
1.02
1.03
1.04
1.05
1.06
1.08
1.09
0.86
0.85
0.83
0.81
0.78
0.75
0.72
0.68
0.63
0.58
0.52
0.44
0.36
0.26
0.14
0
Beta W:Beta A
VaccineCoverage
0 100 300 500
0.91
0.92
0.94
0.95
0.96
0.97
0.98
0.99
1.01
1.02
1.03
1.04
1.05
1.06
1.08
1.09
0.86
0.85
0.83
0.81
0.78
0.75
0.72
0.68
0.63
0.58
0.52
0.44
0.36
0.26
0.14
0
Beta W:Beta A
VaccineCoverage
−20 −10 0
0.91
0.92
0.94
0.95
0.96
0.97
0.98
0.99
1.01
1.02
1.03
1.04
1.05
1.06
1.08
1.09
0.86
0.85
0.83
0.81
0.78
0.75
0.72
0.68
0.63
0.58
0.52
0.44
0.36
0.26
0.14
0
Beta W:Beta A
VaccineCoverage
0 20 40 60 80
0.72
0.68
0.63
0.58
0.52
0.44
0.36
0.26
0.14
0
ccineCoverage
0 20 40 60 80
>99.995%
>99.99%
>99%
>95%
>90%
>80%
>50%
0.91
0.92
0.94
0.95
0.96
0.97
0.98
0.99
1.01
1.02
1.03
1.04
1.05
1.06
1.08
1.09
0.86
0.85
0.83
0.81
0.78
0.75
0.72
0.68
0.63
0.58
0.52
0.44
0.36
0.26
0.14
0
Beta W:Beta A
VaccineCoverage
Final Carriage of W
0.05 0.15 0.25
0.72
0.68
0.63
0.58
0.52
0.44
0.36
0.26
0.14
0
ccineCoverage
Final Carriage of W
0.05 0.15 0.25
Conclusions
What
are
the
effects
of
serogroup
A
vaccinaFon
on
carriage
of
serogroup
A?
• Higher
vaccina.on
decreases
carriage
of
A
regardless
of
rela.ve
transmissibility.
• Carriage
of
A
is
decreased
most
where
W
is
more
transmissible
than
A.
• Vaccina.on
contributes
most
to
the
decrease
in
carriage
of
A
where
W
and
A
are
equally
transmissible.
On
carriage
of
serogroup
W?
• Carriage
of
W
increases
with
increasing
vaccine
coverage
and
where
W
is
more
transmissible
than
A.
• Vaccina.on
contributes
most
to
the
increase
in
carriage
where
W
is
less
transmissible
than
A.
On
overall
carriage?
• In
most
cases,
vaccina.on
results
in
modest
decreases
in
overall
carriage.
• Greatest
decreases
in
carriage
occur
at
lower
vaccina.on
coverage
and
where
W
is
less
transmissible
than
A.