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8/20/2019 Epidemiological Impact of a Genital Herpes Type 2 Vaccine for Young Females
1/22
Epidemiological Impact of a Genital Herpes Type 2 Vaccine for Young
Females• Yijun Lou ,
• Redouane Qesmi ,
• Qian Wang ,
• Marc Steben,
• Jianhong Wu,
• Jane M. Heffernan
• Published !ctober "", #$"#
• %!& "$."'(")journal.*one.$$+$#(
Abstract
-enital Her*es, hich is caused b/ Her*es Sim*le0 1irus2" or 2# 3HS12", 2#, *redominantl/
HS12#4 is a se0uall/ transmitted infection 3S5&4 that causes a chronic latent infection ith
outbrea6 e*isodes lin6ed to transmission. 7nti8iral thera*ies are effecti8e in reducing 8iral
shedding during these e*isodes, but are ineffecti8e as a hole since man/ outbrea6s are
as/m*tomatic or ha8e mild s/m*toms. 5hus, the de8elo*ment of a 8accine for genital her*es is
needed to control this disease. 5he 9uestion of ho to im*lement such a 8accine *rogram is an
im*ortant one, and ma/ be similar to the 8accination *rogram for Human Pa*illoma 1irus 3HP14
for /oung females. We ha8e de8elo*ed a mathematical model to describe the e*idemiolog/ of
8accination targeting /oung females against HS12#. 5he model *o*ulation is delineated ith
res*ect to age grou*, se0ual acti8it/ and infection status including oral infection of HS12",
hich ma/ affect 8accine efficac/. 7 threshold *arameter , hich determines the le8el of 8accine u*ta6e needed to eradicate HS12#, is found. :om*uter simulation shos that an
adolescent2onl/ 8accination *rogram ma/ be effecti8e in eliminating HS12# disease, hoe8er,
the success of e0tinction greatl/ de*ends on the le8el of 8accine u*ta6e, the 8accine efficac/, the
age of se0ual maturit/ and safe se0 *ractices. Hoe8er, the time course of eradication ould
ta6e man/ /ears. We also in8estigate the *re8alence of infection in the total *o*ulation and in
omen beteen ";'$ /ears of age before and after 8accination has been introduced, and sho
that the adolescent2onl/ 8accination *rogram can be effecti8e in reducing disease *re8alence in
these *o*ulations de*ending on the le8el of 8accine u*ta6e and 8accine efficac/. 5his ill also
result in a decrease of maternal2fetal transmission of HS12# infection. 7nother im*ortant, if
commonsense, conclusion is that 8accination of some females reduces infection in men, hich
then reduces infection in omen.
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Introduction
-enital her*es is one of the most *re8alent se0uall/ transmitted infections 3S5&4 in the orld. &t
is estimated that there are ne cases of genital her*es in :anada *er /ear ith
a**ro0imatel/ ne cases each da/
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7:7M2>#B 8accine su**orted b/ Sanofi Pasteur are undergoing clinical trials
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&n this *a*er, e de8elo* a mathematical model to e8aluate the effecti8eness of a 8accination
*rogram against HS12#. We focus our stud/ on a 8accination *rogram targeting female school
children aged "#;"+ /ears. !ur model also includes age structure and gender differences in
transmission. We also include 8ar/ing efficacies of the 8accine against HS12#, hich ma/ not be
effecti8e in indi8iduals that are HS12" *ositi8e. 5he details of our model and model assum*tions
are outlined in the ne0t section.
Methods
5he mathematical model, shon in Gig. ", illustrates ho genital her*es can s*read in a
*o*ulation. 5he *o*ulation is di8ided into com*artments de*ending on gender 3male or female4,
disease status 3infected or uninfected4, and susce*tibilit/ to the 8irus 3su*erscri*t denotes
*rotection4. 5he female *o*ulation is then further di8ided according to age 3children "';" /ears
old 3 4, and adults beteen ";'$ /ears of age 3 4 and o8er /ears of age 3 44
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5he mathematical model can be described as follos female children 3 4 enter the *o*ulation at
rate . Gemale children that are HS12" seronegati8e 3 4, 8accinated 3 4 and ac9uire immunit/
from the 8accine 3 4 mo8e to the 8accinated)*rotected class and all others remain in the non2
immune class 3 4. Since se8eral 8accine trails ha8e shon some success in *re8enting disease,
but onl/ in females that are HS12" and 2# negati8e, e incor*orate here the HS12" seronegati8e
*ro*ortion to account for this *ossible 8accine limitation
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#arameter Values
Parameter 8alues are listed in 5able " and are chosen so that the/ agree ith current :anadian
and orth 7merican statistics, and data re*orted in the medical literature. 5he mortalit/ rate is
assumed to be a**ro0imatel/ /ears", here /ears is the mean life e0*ectanc/ of
:anadians beteen #$$$;#$$
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Table ! $ist of notations and symbols!
&t is assumed that the a8erage age of *rogression of female children to se0ual acti8it/ 3 4 is
beteen /ears
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higher *robabilit/ of entering into monogamous relationshi*s, and that the *robabilit/ of se0ual
acti8it/ out of these monogamous relationshi*s is small.
Similar to
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5he threshold can be e0*lained relati8e to the underl/ing biolog/ as follos hen an
infecti8e male is introduced into the *o*ulation, ne infected males can be made through three
*ossible *atha/s
hich corres*ond to the first, second and third terms of @9. 3"4 res*ecti8el/. Gor instance, using
the second *ath, e see that hen one infected male is introduced into the *o*ulation, the male
*roduces, on a8erage, infected /oung adult females aged ";'$ /ears during his
a8erage se0ual lifes*an 3 4. 5hese /oung adult females then gro into adult females
aged '$ /ears and older o8er their lifes*an at a rate and then each infected
older adult female *roduces, on a8erage, infected males during her se0ual
lifes*an . 5hus through the second *ath, the a8erage number of ne infected males
*roduced b/ a single infected male in a *o*ulation consisting onl/ of susce*tible females and
males is . With the *arameter 8alues listed in 5able ", the
basic re*roduction number is , that is, one infected male ma6es ".> ne infected
males 3or " infected female ma6es ".> ne infected females4 hen this indi8idual is introducedinto a *o*ulation com*osed onl/ of susce*tible males and females. &f e assume the *arameters
related to a 8accine *rogram are , , and , then the re*roduction
number becomes .
ote that a reduction in the infecti8it/ 3 4 ill also decrease . Moreo8er, in order to
eradicate HS12# from a *o*ulation, the 8accination *rogram must be effecti8e in
reducing 3see 5heorem 7' in 7**endi0 S" for theoretical results4. Grom @9. 3#4 e find
that this ill occur hen a critical 8accination threshold 3 4 is achie8ed, here
'umerical (imulations
7n adolescent2onl/ 8accination *rogram ma/ be effecti8e in eliminating HS12# 3Gig. #4.
Hoe8er, regardless of the 8accine efficac/ and u*ta6e, the time course of eradication ould
ta6e man/ decades 3Gig. '4. 7lso eradication ma/ not result 3Gig. '4. Gor similar 8accination
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u*ta6e to that of the HP1 8accination *rogram 3>';A$N4, HS12# elimination ma/ not be
achie8ed 3Gig. +a, solid line4. &f 8accine efficac/ is , or if the *ro*ortion of children that
are HS12")HS12# negati8e decreases 3 4, then eradication is more li6el/, but high 8accination
u*ta6e is still re9uired 3Gig. +a4. 7n im*ortant, if commonsense, conclusion is that 8accination of
some females reduces infection in men, hich then reduces infection in omen 3Gig. 'b,c4.
Figure 2! #re)alence of H(V*2 +ith different le)els of )accination!
Pre8alence of HS12# decreases as 8accine u*ta6e increases in the total *o*ulation 3solid line4,omen ages ";'$ /ears 3dot2dashed line4, omen ages o8er /ears 3dashed line4, omen
ages o8er /ears 3blac6 dotted line4 and men 3gra/ dotted line4. 1accine efficac/ 3 4 le8els are
assumed to be 3a4 and 3b4 res*ecti8el/. 5he *ro*ortion of females b/ age "# that are
HS12" and HS12# seronegati8e 3 4 is assumed to be .
doi"$."'(")journal.*one.$$+$#(.g$$#
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Figure ,! #re)alence of infection o)er time!
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Pre8alence of infection in the total *o*ulation 3to*4, omen ages o8er /ears 3bottom left4 and
men 3bottom right4 are shon hen 8accination is started at /ear " and is gi8en for BBB /ears.
1accination le8els, from to* to bottom, are $, "$, #$, '$, +$, >$, $, ($, A$, B$ and "$$N.
1accine efficac/ 3 4 is assumed to be and the *ro*ortion of females b/ age "# that are HS12
" and HS12# seronegati8e 3 4 is assumed to be .
doi"$."'(")journal.*one.$$+$#(.g$$'
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Figure -! Thresholds of )accination!
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1accination thresholds for eradication de*end on the efficac/ of the 8accine 3to*4, age of
se0ual maturit/ 3bottom left4 and rate of transmission 3bottom right4. 3a4 5hreshold cur8es
de*ending on 8accine efficac/ for three le8els of HS12" and HS12# negati8e children 3 >$, >
and B>N, solid line, dashed line, dot2dashed line res*ecti8el/4 at the time of 8accination. 7ll
lines denote threshold corres*onding to a 8accine immunogenecit/ of B>N. 3b4 5hreshold cur8es
de*ending on age of se0ual maturit/ for three le8els of 8accine efficac/ 3 >$, ($ and B$N,
dashed line, solid line, dot2dashed line res*ecti8el/4 5he 8ertical line at age #> re*resents the
ma0imum age at hich age of se0ual maturit/ could be achie8ed to sustain a *o*ulation. 3c4
5hreshold cur8es de*ending on reduced transmission rates 3 , to 4 for three le8els of
8accine efficac/ 3 >$, ($ and B$N, dashed line, solid line, dot2dashed line res*ecti8el/4.
doi"$."'(")journal.*one.$$+$#(.g$$+
5o aid in the reduction of HS12# *re8alence, education *rograms about genital her*es ma/ be
im*lemented. 5hese *rograms ill ha8e an im*ortant effect if 8accination u*ta6e or if the
efficac/ of the 8accine is lo. 7 *ossible effect of these *rograms is an increase in the a8erageage of *rogression of children to se0ual acti8it/. Gig. +b demonstrates that as the a8erage age of
se0ual maturit/ 3 4 increases, the *ro*ortion of females needed to 8accinate to eradicate
HS12# decreases. Hoe8er, eradication ithout 8accination ould not be feasible since it is
im*ossible for the age of se0ual maturit/ to be high 3Gig. +b4 as *o*ulations ould not be
sustained. 7lso, e8en ith high le8els of efficac/ 3 4 8accination is unli6el/ to eradicate HS12#
since 8er/ high le8els of 8accine u*ta6e, hich are greater than hat is seen in HP1, are
re9uired.
7nother *ossible effect of education *rograms is an increase in safe se0 *ractices. 5his includes
the use of condoms, and can include the use of anti8irals in those infected ith HS12#. 5he use
of condoms ha8e been routinel/ recommended for the *re8ention of transmission of se0uall/
transmitted diseases such as HS12# $N
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demonstrates that for similar 8accination u*ta6e to that of the HP1 8accination *rogram 3>';
A$N4, HS12# *re8alence can be reduced b/ , hoe8er, this reduction in *re8alence can
still ta6e man/ decades to achie8e 3Gig. '4.
Figure .! %eduction in pre)alence!
1accination thresholds for reduction in *re8alence b/ are shon for three different
le8els of 8accine efficac/ 3 >$, ($ and B$N, dashed line, solid line, dot2dashed line
res*ecti8el/4.
doi"$."'(")journal.*one.$$+$#(.g$$>
Pregnant females infected ith genital HS12# 3*articularl/ those ith a *rimar/ infection4 can
transmit infection to the neonate, hich can lead to serious neonatal com*lications, such as
neurologic *roblems and e8en death. 5hus, it is im*ortant to consider the im*act of 8accination
on the *re8ention of HS12# in the child2bearing age grou*. Gig. # shos the *re8alence of
infection in omen o8er ";'$ /ears of age before and after 8accination has been introduced
3dot2dashed line4. Since the majorit/ of *regnant mothers are from this age grou*, this
demonstrates that the adolescent2onl/ 8accination *rogram results in a decrease in the number of
infected *regnant females. 5his ill in turn result in a decrease of maternal2fetal transmission of
HS12# infection.
&ntensi8e sensiti8it/ anal/ses can be *erformed in 8arious a/s to determine hich *arameters
*la/ a major role in affecting the *redicted results. We *erform the sensiti8it/ anal/sis b/ using
the Latin H/*ercube Sam*ling 3LHS4 *rocess, hich is numericall/ com*uted using the method
described in
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calculated. PR:: 8alues *ro8ide a measure of the relationshi* beteen model in*uts and out*uts
and are *articularl/ useful for such relationshi*s that are nonlinear but monotonic. PR:: 8alues
range beteen " and " ith the sign determining hether an increase in the *arameter 8alue
ill decrease 34 or increase 3O4 the s*ecified model out*ut. 5he PR:: results for disease
*re8alence in the total *o*ualtion are shon in Gig. . 5his figure indicates that the transmission
rates and *arameters related to the 8accination *rograms 3 , , 4 are statisticall/ significant
3ith 4. &n contrast, the *rogression rates and are relati8el/ insignificant.
5hese results highlight the im*ortance of 8accine u*ta6e, 8accine efficac/, HS12" and HS12#
status, and safe se0 in the control of genital her*es. 5he PR:: results for HS12# *re8alence in
men, adult and older omen, and the control re*roduction number are similar to that shon
in Gig. .
Figure /! (enstiti)ity analsysis!
5he *artial ran6 correlation coefficients are shon using the total *o*ulation as the inde0.
doi"$."'(")journal.*one.$$+$#(.g$$
"iscussion
-enital her*es is one of the most *re8alent se0uall/ transmitted diseases in the orld. :urrentl/,
the de8elo*ment of a 8accine againt HS12#, the main cause of genital her*es, is a major focus of
stud/. We ha8e de8elo*ed a model of HS12# transmission that delineates the *o*ulation b/
gender and age, to factors that ha8e been shon to be effecti8e *redictors of HS12# ris6, to
assess the efficac/ of a 8accination *rogram against HS12# similar to the 8accination *rogram
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alread/ im*limented against HP1. ?sing this model e ha8e found that eradication of HS12#
ma/ be achie8able, hoe8er, this feasibilit/ of eradication de*ends on se8eral factors.
Girstl/, eradication greatl/ de*ends on the rate of 8accine u*ta6e and the efficac/ conferred b/
the 8accine. 1accine u*ta6e needs to be 8er/ high 3 4 e8en if the 8accine is 8er/ effecti8e
in inducing *rotection against the disease. Hoe8er, e8en if 8accine u*ta6e is high, eradication
ill not be seen for se8eral decades.
5he *ossibilit/ of eradication also de*ends on education *rograms that ma/ dela/ the age of
se0ual maturit/ and increase the le8el of safe se0 *ractices. &n these cases, hoe8er, 8accination
u*ta6e still needs to be 8er/ high and ma/ e0ceed hat is actuall/ achie8able.
7lthough eradication ill be difficult to achie8e, the 8accination *rogram can be effecti8e in
reducing disease *re8alence to a large e0tent. Reduction le8els of can be achie8ed,
hoe8er, these also greatl/ de*end on the 8accine efficac/ and the time since the initiation of the
8accination *rogram.
7n e0tension of the current model ma/ be to stud/ the effects of 8accination in age grou*s less
than "+ /ears of age 3and *erha*s infants4 here HS12" *re8alence is decreased, and stud/ the
effects of a 8accine that is onl/ *artiall/ affected b/ HS12" *re8alence. Foth of these scenarios
can be com*ared to a 8ariation in *arameter . ?sing the current model e see that the
*ro*ortion of children needed to 8accinate to eradicate HS12# is decreased considerabl/ hen
increases.
7nother future direction ma/ be to stud/ the effects of booster 8accines in adult females, since
8accine induced immunit/ to HS12# ma/ ane o8er time. Gurther delineation of the *o*ulation
including oral infection 8ersus genital infection and se0ual *reference ma/ also be im*ortant
hen considering the number of booster 8accinations re9uired and the time beteen them.
7 limitation of the current model is e do not model 8ar/ing rates of 8irus shedding. HS12#
infection is actuall/ characteriCed b/ ra*id e*isodes of as/m*tomatic shedding *unctuated b/
increased 9uantities of 8irus
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HS12# ould not be *ossible ith 8accines that merel/ decrease s/m*toms and the fre9uenc/ of
recurrences, since transmission is still *ossible in these instances.
(upporting Information
7**endi0S".*df
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Mathematical analysis of the model! 5he mathematical model is formulated as a s/stem of
ordinar/ differential e9uations. We find the model e9uilibria, the basic re*roducti8e ratio, and
*ro8ide some local and global stabilit/ anal/sis of the model. Justification of the S& frameor6 is
also *ro8ided.
Mathematical analysis of the model! 5he mathematical model is formulated as a s/stem of
ordinar/ differential e9uations. We find the model e9uilibria, the basic re*roducti8e ratio, and
*ro8ide some local and global stabilit/ anal/sis of the model. Justification of the S& frameor6 is
also *ro8ided.
doi"$."'(")journal.*one.$$+$#(.s$$"
3P%G4
Ac0no+ledgments
5he authors ould li6e to than6 Professors Pauline 8an den %riessche and Robert Smith for
their hel*ful insights on the de8elo*ment of the mathematical model. We ould also li6e to than6
the anon/mous re8ieers for their su**orti8e comments.
Author &ontributions
:oncei8ed and designed the e0*eriments QW RQ JMH JW MS. Performed the e0*eriments
QW RQ YL JMH. 7nal/Ced the data QW RQ YL JMH. :ontributed reagents)materials)anal/sis
tools QW RQ 5L JMH JW MS. Wrote the *a*er QW RQ YL JMH JW MS.
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