Effectiveness assessment of vaccination policy against measles
epidemic in Japan using an age–time two-dimensional
Yusuke Maitani•Hirofumi Ishikawa
Received: 14 February 2011/Accepted: 8 April 2011/Published online: 7 May 2011
? The Japanese Society for Hygiene 2011
and young adult population in Japan, creating in a serious
social problem. Among the developed countries, Japan has
a relatively high incidence of measles. The objective of this
study was to assess the effect of improvements in the
vaccination policy against measles through simulations.
We developed an age–time two-dimensional
model for the transmission of measles to reflect an age
structure, enabling contact rate to be selected by age.
Introduction of the maternal immunity class into the model
allowed natural infection and vaccination to be discrimi-
nated along the course of an infant’s mother acquiring the
immunity, thereby resulting in an improved accuracy of the
simulations in infants. Several vaccination scenarios were
attempted in order to assess the influence of various vac-
cination policies on the prevention of a measles epidemic.
The results of this quantitative study indicated
that suppression of a measles outbreak requires the main-
tenance of high vaccine coverage and that a decline in
vaccine coverage may result in a measles epidemic.
The present standard immunization program
for measles will maintain an acceptable level of immunity
and is therefore associated with a low risk of an epidemic
after discontinuation of the third and fourth stages as
scheduled—as long as at least 90% vaccine coverage of the
first and second is maintained. The simulation results show
that discontinuation of the third and fourth stages of vac-
cination as scheduled should be accompanied by endeavors
In 2007, measles prevailed among the youth
to maintain appropriate high vaccine coverage of the first
and second stages.
Routine immunization program ? Age–time model ?
Measles ? Vaccination coverage ?
In 2007, measles prevailed among the youth and young
adult (teenagers and those in their 20s) population of Japan,
creating serious social problems, such as closure of college/
university classes. The incidence of measles in Japan has
been reported to be 10,000–30,000 per year , but the
actual incidence is estimated to be about tenfold higher
than the number of reported cases . The aim of this study
was to analyze the effect of improvements to the standard
vaccination program for measles, with a special focus on
the coverage of measles vaccination. Vaccination against
measles was incorporated into the national immunization
program in Japan in 1978, but in 1994 some children had
an allergic reaction due to sensitization to the gelatin
contained in the measles–mumps–rubella vaccine (MMR).
As a consequence, the measles vaccination policy was
modified, i.e., from mass immunization in schools to
individual immunization, and from obligatory to voluntary
immunization. This policy change has led to the ongoing
low vaccination coverage against measles that was imme-
diately detectable . Because it is feared that an outbreak
of measles will occur under these circumstances, a second
stage of measles vaccination was introduced into the rou-
tine immunization program in 2006. In 2008, a third and
fourth stage of measles vaccination were later added to the
routine immunization program for a limited period of
Y. Maitani ? H. Ishikawa (&)
Department of Human Ecology,
Graduate School of Environmental Science,
Okayama University, Okayama 700-8530, Japan
Environ Health Prev Med (2012) 17:34–43
5 years (2008–2012). The first to fourth stages of vacci-
nation were targeted at infants (1 year old), children 1 year
prior to starting elementary school (5–6 years old), students
in the first grade of junior high school (12–13 years old),
and students in the third grade of high school (17–18 years
old), respectively . Those autonomous local and regional
authorities that achieved high vaccination coverage in the
second stage did so by encouraging individual vaccination,
establishing a strong partnership with institutions, distrib-
uting leaflets, mailing postcards, posting notifications of
vaccination on city bulletin boards and posters, and
developing a system to target non-vaccinated individuals,
among others (Niigata, Odawara, Takamatsu, and Kura-
shiki cities, and Fukui and Akita prefectures) [3–8]. Those
authorities that achieved high vaccination coverage in the
third and the fourth stages had a program that involved
notification of individuals for vaccination, cooperation with
schools, and mass immunization against measles, among
others (Johetsu, Tsukuba, Hakodate, and Hamamatsu cit-
The World Health Organization (WHO) assesses the
numbers of measles patients and deaths attributable to
measles to be more than 30,000,000 and 875,000 each year,
respectively . In most developed countries, including the
USA and Korea, the law obliges parents to present a cer-
tificate of measles vaccination when their child enters
elementary school , which has resulted in a high vac-
cination coverage. Consequently, any outbreaks of measles
in such countries mainly occur among immigrants from
regions where measles is epidemic.
In recent years, most individuals have acquired immu-
nity to measles by vaccination. Because the antibody titer
acquired by vaccination is low compared with that by nat-
ural infection, the possibility of re-infection with measles
emerges in teenagers and in young adults in their 20s .
There have been several studies on a mathematical
model for the transmission of measles [15–20]. In this
study, we developed an age–time two-dimensional model
for the transmission of measles to reflect an age structure,
thereby enabling the selection of contact rate by age. We
analyzed vaccination policy and the influence of vaccina-
tion coverage through model simulations. To make the
model more precise, we developed the model to be able to
distinguish maternal immunity derived from a mother who
acquired immunity by natural infection from that derived
from a mother who acquired immunity by vaccination
because most mothers have acquired the antibody against
measles by vaccination in recent years. We also used epi-
demiological classes comprising individuals with low
antibody titer so as to be able to estimate the change in the
number of individuals with low antibody titer because any
increase in the number of such individuals may cause an
outbreak of measles.
The results of simulation indicated that the suppression
of a measles outbreak requires the maintenance of high
vaccine coverage, that a decline in vaccine coverage may
cause a measles epidemic, and that the present routine
immunization program of measles will maintain a low risk
of an epidemic even after discontinuation of the third and
fourth stages as scheduled—as long as at least 90% vaccine
coverage of the first and second stages is maintained.
Materials and methods
Okayama city, the capital of Okayama prefecture (popu-
lation 674,746 in 2005 ), was almost equivalent in
terms of vaccine coverage against measles to Japanese
national average, and Kurashiki city in Okayama prefecture
(population 469,377 in 2005 ) achieved high vaccine
coverage in the second vaccination of measles [22, 23].
Okayama city and Kurashiki city were chosen as targeted
regions in this study. The levels of measles vaccine cover-
age in Okayama city, Kurashiki city, and the mean coverage
of the whole country in 2008 are shown in Table 1.
Progress in symptom of measles
The clinical symptoms of measles progress from catarrh
(2–4 days) to rash (3–4 days), and then to a convalescence
period (3–4 days) after a latent period of 8–12 days [24,
25]. Any severe complication, such as brain inflammation
or pneumonia, may cause patient mortality. In this study,
we adopted 5 days as the infection period and 10 days as
the latent period, while we adopted 10 days as the infection
period and 16 days as the latent period for modified mea-
sles patients [24, 25].
Maternal immunity declines approximately 6 months after
birth on average . A study on the antibody titer of
Table 1 Mean percentage of vaccination coverage (from April 2008
to March 2009)
LocationStage of routine immunization by measles
First (%) Second (%)Third (%)Fourth (%)
Okayama city 92.994.690.477.9
Kurashiki city 96.395.788.976.3
Derived from National Institute of Infectious Diseases, 2008 [22, 23]
Environ Health Prev Med (2012) 17:34–4335
children in Belgium  reported that (1) the maternal
immunity of an infant born to a mother who had acquired
immunity by vaccination was lower and also lost earlier
than that of an infant born to a mother who had been
infected with measles and (2) the loss of maternal immu-
nity was not affected by the infant’s weight, breast feeding,
the educational level of the mother, or delivery by cesarean
operation. In our study, the initial antibody titer of maternal
immunity in an infant by the gelatin particle agglutination
(PA) assay was assumed to be at one of two levels, i.e.,
PA = 64 or 128, according to whether the maternal
immunity derived from the mother acquired immunity by
vaccination or by natural infection, respectively. The
maternal immunity was also assumed to decline exponen-
tially (Table 2).
Decline in the antibody titer over time
Prior to the introduction of mass immunization against
measles, most people acquired measles immunity by nat-
ural infection . However, in recent years, the majority
have acquired measles immunity through vaccination, the
antibody titer from which is lower than that acquired by
natural infection. Owing the decline in antibody titer over
time, the infection risk of measles should increase in
youths who have been immunized by measles vaccination
, which lead to a measles epidemic. On the other hand,
both Christenson et al.  and Edmonson et al. 
reported that the immunity acquired by natural infection
also decreases in the long term, even though it is called
lifetime immunity. It is generally considered that an anti-
body titer level of at least PA C 128—and preferably
PA C 256—is necessary to avoid being infected by the
measles virus , while a titer level of PA B 64 conveys
a risk of measles infection (modified measles). Therefore,
we categorized recovered and vaccinated individuals into
two subsets according to the antibody titer: PA C 128 or
PA B 64.
Model for the transmission of measles
In this study, an age–time two-dimensional model for the
transmission of measles was constructed. In this model, the
steps of age and time are treated at daily intervals where
age ranges from 0 to 100 years. The population is divided
into several epidemiological classes and subclasses: sus-
ceptible (S), maternal immunity (M), exposed (E, Em; Em
is the exposed class developing modified measles), infec-
tious (I, Im; Im is the infectious class consisting of those
with modified measles), recovered (R, Rw; Rw is the
recovered class with weak immunity), and vaccinated (V).
An infant younger than 1.5 years of age who has never
been infected with measles nor inoculated with measles
vaccine belongs to the maternal immunity class or to the
susceptible class according to his/her mother having
immunity to measles or not, respectively; in addition,
maternal immunity class is subdivided into maternal
immunity derived from a vaccination (M1) and maternal
immunity derived from natural infection (M2). When an
infant loses maternal immunity, he/she moves to the
S-class. The recovered class includes a subclass with weak
immunity (Rw) in that the antibody titer starts to deterio-
rate (PA B 64). The vaccinated class is further classified
into one of three subclasses: (1) V1, individuals who were
vaccinated only once and have effective immunity
(PA C 128); (2) V1w, individuals who were vaccinated
once at a stage at which they still had maternal immunity or
individuals with deteriorated antibody titer (PA B 64)
acquired by a single vaccination; (3) V2, individuals who
were vaccinated more than two times. The infection of an
Table 2 Assumed values of the model parameters
Description Age (months)Assumed value (per day)
The rate of loss of maternal immunity
Mother acquired immunity by vaccination 0–60.0122
Mother acquired immunity by infection 0–60.0063
DescriptionAge (years)Assumed value (per day)
The probability of coefficient of infection (b)
The rate of loss of immunity acquired by infection
0–1001.0 9 10-3
5.56 9 10-6
2.78 9 10-6
6.89 9 10-5
1.43 9 10-5
The rate of second vaccine failure (one-time vaccination)1–10
The proportion of primary vaccine failure–5%
36Environ Health Prev Med (2012) 17:34–43
individual belonging to the S-class with measles transfers
him/her to the I-class through the E-class, while the
infection of an individual belonging to V1w- or Rw-class
with measles transfers him/her to the Im-class through Em.
Recovery leads to transfer from the I- or Im-class to the
R-class. The model scheme is shown in Fig. 1. The
assessed values of the model parameters are shown in
Relative contact rate
The force of infection at age a is dependent on the contact
rates with infectious individuals at age a0for all a0. It is
assumed that the contact rate among students in the same
school year in primary and junior high schools is the
highest and that among students in consecutive school
years is the second highest, while that among adults or
among adults and children is fairly low. We have assigned
the relative contact rate rc(a, a0) between individuals at
ages a and a0in comparison with the highest contact rate.
Full details of relative contact rates are shown in Fig. 2.
Therefore, the force of infection at age a is given by the
where b is a probability coefficient of infection; the
assumed value of b refers to Table 2.
f a ð Þ ¼ b
ðÞ I a0
ð Þ þ Im a0
In order to analyze the influence of various vaccination
coverages on the prevention of measles epidemic, we pre-
pared several vaccination scenarios. As the standard level,
we adopted the vaccination policy of Okayama city in 2008,
consisting of vaccination coverage of one to four stages,
which was similar to the average vaccination coverage
nationwide [22, 23]. In baseline scenario 1, a vaccination
coverage of one to four stages is maintained as the standard
level during 2008–2012. In scenario 2, the vaccination
coverage of one to four stages is maintained in accordance
with the vaccination coverage of one to four stages in
Kurashiki city in 2008, which achieved a high coverage in
average [22, 23]. We also prepared high and low levels of
vaccination coverage in comparison with the standard level
in scenarios 3 and 4, respectively. To analyze the validity of
the current vaccination policy in which the third and fourth
stages are limited to 5 years (2008–2012), in scenarios 5–7,
2018, and three levels of vaccination coverage are provided
in these scenarios. All scenarios are summarized in Table 3.
The population size for each scenario is fixed as the popu-
lation of Okayama city in 2005, 674,746, to compare simu-
lation results among scenarios easily.
The age–time two-dimensional model was programmed by
Intel Visual Fortran on Microsoft Visual Studio to work on
any computer using the Microsoft Windows platform
(Microsoft, Redwood, WA). In all scenarios, the initial
values of epidemiological classes were determined on the
basis of data on the age distribution of measles PA antibody
positivity in Japan in 2006  and coverage of measles
immunization by age group (nationwide) in 2006 ;
simulations proceed during 2006–2007 by using the cov-
erage of immunization in the respective year [34, 35];
thereafter, simulations proceed during 2008–2018 accord-
ing to a scenario. For baseline scenario 1, the progression of
the sectional distributions of epidemiological classes by
Fig. 1 Model scheme. For
definition of epidemiological
classes/subclasses refer to
section Model for the
transmission of measles
Environ Health Prev Med (2012) 17:34–43 37
month-old age (0–100 years of age) in March in 2008,
2013, and 2018, which were obtained by the simulation, are
shown in Fig. 3a, b, c, respectively. The proportions of
susceptible and low antibody titer classes (S, Rw, V1w) in
youths and young adults (aged 10–25 years) as of March in
2013 and 2018 were estimated as 5.9 and 3.4%,
respectively. The sectional distributions in Fig. 3d, e are
limited to these three classes to show the details of the
progression in the situation of youths and younger adults
(\25 years old) as of March in 2013 and 2018, respectively.
We first compared scenario 2, that is, a higher vacci-
nation coverage situation in Kurashiki city in the first and
Fig. 2 Relative contact rates by
Number of scenarioScenario Stage of vaccination
First (%)Second (%) Third (%)Fourth (%)
1. Okayama city
2008–201292.9 94.690.4 77.9
2008–201296.395.7 88.9 76.3
3. High level
4. Low level
2008–201290.0 90.080.0 70.0
5. Okayama city
6. High level
2013–201895.0 95.090.0 80.0
7. Low level
2008–201290.0 90.0 80.070.0
38Environ Health Prev Med (2012) 17:34–43
second stages of routine immunization, with baseline sce-
nario 1. According to the result of the simulation, the ratio
of the total number of youths and young adults at an age of
10–25 as of March, 2013 who had no or insufficient
immunity (S, Rw, V1w) between scenarios 2 and 1 was
0.95:1, and the ratio as of March, 2018 fell to 0.57:1
We then prepared two scenarios, namely, 3 and 4, with
high and low levels of vaccination coverage, respectively,
where the third and the fourth stages of measles vaccina-
tion are discontinued in 2013. The aim of these scenarios
was to examine how variation introduced in vaccination
coverage would influence the number of individuals
potentiality susceptible to measles virus infection. The
Fig. 3 The sectional distributions of epidemiological classes in
March in scenario 1 (Okayama city). a 2008, b, d 2013, c, e 2018.
d, e Limited to susceptible (S) and low antibody titer classes (Rw,
V1w). PA particle agglutination assay. The axis of ordinates shows
the number of population by month-old age
Environ Health Prev Med (2012) 17:34–43 39
ratios for the total numbers of youths and young adults at
an age of 10–25 years as of March, 2013 who had no or
insufficient immunity (S, Rw, V1w) in scenarios 3 and 4 to
that in baseline scenario 1 were assessed as 0.71:1 and
0.99:1, respectively (Fig. 5).
Finally, in scenarios 5–7, we extended the third and the
fourth stages of measles vaccination until 2018. According
to the results of the simulations, the proportions of indi-
viduals belonging to susceptible and low antibody titer
classes (S, Rw, V1w) at an age 10–25 years as of March,
2018, for scenarios 1, 3, and 4 with the third and fourth
stages discontinued in 2013 were estimated at 3.4, 2.2, and
4.0%, respectively, while those proportions for scenarios 5,
6, and 7 with the third and fourth stages extended until
2018 were estimated at very low levels of 1.3, 0.76, and
2.2%, respectively. The progress of the sectional distribu-
tions of these three classes by month-old age as of March in
2018 for scenarios 6 and 7 are shown in Fig. 6a, b,
respectively; the progression for scenario 5 is omitted
because of its similarity to Fig. 6a.
In this study, we constructed an age–time two-dimensional
model for the transmission of measles that was formulated
by a system of partial differential equations. This model is
able to describe the changes in numbers in epidemiological
classes for both age and time in detail and can also
precisely track changes in the vaccination schedule of
measles so that a simulation of the model can assess the
effect of various vaccination methods.
The maternal immunity class in infancy was introduced
into the model. A vaccine at the first stage is unsuccessful
during the period of preservation of maternal immunity
. On the other hand, an infant is faced with a risk of
infection with the measles virus when his/her maternal
maternal immunity as due to natural infection or vaccina-
tion in the course of the mother acquiring the immunity
because maternal immunity derived from a mother
obtained by vaccination is lower and lost earlier than that
derived from a mother infected with measles [27, 28]. The
introduction of this distinction in maternal immunity con-
tributes to improving the accuracy of simulations in infants.
In recent years, most mothers have acquired immunity by
vaccination; therefore, this distinction has the additional
advantage of the model automatically reflecting the rela-
tionship between the abundance of vaccinated mothers and
the strength of maternal immunity in a long-term
Since the measles virus has a high infectivity, the basic
reproduction number was estimated at high levels: 26.33
(Delhi, 1987), 12.76 (Kenya, 1984), 68.78 (Cameroon,
1975)  and so on . We simply assigned the relative
contact rate among individuals by age in comparison to the
highest contact rate among students of the same school
year in elementary and junior high schools. The value of
Fig. 4 The sectional distributions of three epidemiological classes (S, Rw, V1w) in March in scenario 2 (Kurashiki city). a 2013, b 2018. The
axis of ordinates shows the number of population by month-old age
40Environ Health Prev Med (2012) 17:34–43
the probability coefficient of infection (b) was chosen so
that the model reflects an actual situation in terms of
incidence. Further demographical studies on human
behavior may contribute to the accuracy of the transmis-
For a measles epidemic to be prevented, it is necessary
to prevent an increase in the pool of individuals susceptible
to the measles virus. Insufficient coverage of measles
vaccination for several years in Japan is considered to be
the cause of an outbreak in 2007 . The result of our
simulation showed that a high level of vaccine coverage
(scenario 3) would lead directly to a reduction in the
number of individuals who have no or low antibody titer,
while the low level of vaccine coverage (scenario 4) would
not lead to an increase in the number of such individuals,
thereby indicating that the difference in the number of
vaccinated individuals between the standard level (scenario
1) and the low level may correspond to the number of
infections in scenario 4.
A considerable number of infants are left unvaccinated
when there is only one opportunity for routine immuni-
zation against measles. A second failure of the one-time
vaccination policy over time may increase the risk of
infection with measles [29, 30]. On the occasion of the
measles outbreak in 2007, students with a low antibody
titer were found attending several colleges [38, 39]. A
reinforced routine immunization program with the intro-
duction of third and fourth stages, which was limited to a
term of 5 years, had an effect on the suppression of mea-
sles. We examined the effect of the discontinuance of the
third and fourth stages. For those scenarios based on the
present routine immunization policy, the proportions of
Fig. 5 The sectional distributions of epidemiological classes in March in scenarios 3 (a, b; high vaccination coverage) and 4 (c, d; low
vaccination coverage). a, c 2013, b, d 2018. The axis of ordinates shows the number of population by month-old age
Environ Health Prev Med (2012) 17:34–4341
individuals belonging to susceptibly low antibody titer
classes in 2018 at an age of 10–25 years decreased to
2–3% in scenarios 1 and 3, or the proportion was main-
tained at 4% in scenario 4, while for scenarios 5–7 in
which the third and fourth stages were extended, the pro-
portions decreased to 1–2%. The results of this quantitative
study indicate that the suppression of measles outbreak
requires the maintenance of high vaccine coverage and that
a decline in vaccine coverage may result in a measles
The present routine immunization program of measles
will maintain a low risk of an epidemic after the discon-
tinuation of the third and fourth stages as scheduled, as
long as at least 90% vaccine coverage of the first and
second stages is maintained. Therefore, the simulation
results support discontinuation of the third and fourth
stages of vaccination as scheduled so long as endeavors are
continued to maintain appropriate high vaccine coverage of
the first and second stages.
Among the developed countries Japan has a relatively
high incidence of measles, and it is also held responsible
for the export of measles to measles-free countries.
Therefore, it is important to implement a measles-elimi-
nation program at the national level.
Aid from the Japan Society for the Promotion of Science (21540129)
and a Grant-in-Aid from the Ministry of Health, Labour and Welfare
of Japan (H20-Sinkou-ippan-013).
This work was supported in part by a Grant-in-
Conflict of interest
There are no conflicts of interest.
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