SEEMEDJ 2021, VOL 5, NO. 1 Imported Infections Versus Herd Immunity Gaps
1 Southeastern European Medical Journal, 2021; 5(1)
Original article
Imported Infections Versus Herd Immunity Gaps; A Didactic
Demonstration of Compartment Models Through the Example of a
Minor Measles Outbreak in Hungary 1
Katalin Böröcz *1, Ákos Markovics 2, Zsuzsanna Csizmadia 1, Joseph Najbauer 1, Timea Berki 1, Peter
Németh 1
1 Department of Immunology and Biotechnology, Clinical Centre, University of Pécs Medical School, Pécs,
Hungary
2 Department of General and Physical Chemistry, Faculty of Natural Sciences, University of Pécs, Pécs,
Hungary
*Corresponding author: Katalin Böröcz, borocz.katalin@pte.hu
Received: Feb 1, 2021; revised version accepted: Mar 15 2021; published: Apr 28, 2021
KEYWORDS: MMR, vaccine, humoral antibody, epidemics, SEIR model
Abstract
Introduction: In Hungary, where MMR vaccine coverage is 99%, in 2017, a minor measles epidemic
started from imported cases due to two major factors – latent susceptible cohorts among the
domestic population and the vicinity of measles-endemic countries. Suspended immunization
activities due to the COVID-19 surge are an ominous precursor to a measles resurgence. This
epidemiological demonstration is aimed at promoting a better public understanding of
epidemiological data.
Materials and Methods: Our previous MMR sero-epidemiological measurements (N of total measles
cases = 3919, N of mumps cases = 2132, and N of rubella cases = 2132) were analyzed using open-
source epidemiological data (ANTSZ) of a small-scale measles epidemic outbreak (2017, Hungary).
A simplified SEIR model was applied in the analysis.
Results: In case of measles, due to a cluster-specific inadequacy of IgG levels, the cumulative
seropositivity ratios (measles = 89.97%) failed to reach the herd immunity threshold (HIT Measles =
92–95%). Despite the fact that 90% of overall vaccination coverage is just slightly below the HIT,
unprotected individuals may pose an elevated epidemiological risk. According to the SEIR model,
≥74% of susceptible individuals are expected to get infected. Estimations based on the input data of
a local epidemic may suggest an even lower effective coverage rate (80%) in certain clusters of the
population.
Conclusion: Serological survey-based, historical and model-computed results are in agreement. A
practical demonstration of epidemiological events of the past and present may promote a higher
awareness of infectious diseases. Because of the high R0 value of measles, continuous large-scale
monitoring of humoral immunity levels is important.
(Böröcz K, Markovics Á, Csizmadia Z, Najbauer J, Berki T, Németh P. Imported Infections Versus Herd
Immunity Gaps; A Didactic Demonstration of Compartment Models Through the Example of a Minor
Measles Outbreak in Hungary. SEEMEDJ 2021; 5(1); 1-16)
SEEMEDJ 2021, VOL 5, NO. 1 Imported Infections Versus Herd Immunity Gaps
2 Southeastern European Medical Journal, 2021; 5(1)
Introduction
Testing of acquired immunity and effectiveness
of vaccination against infectious diseases has
been increasingly important in the design of
preventive public health strategies. Resurgence
in measles cases in the United States and across
Europe has occurred, including in individuals
vaccinated with two doses of the vaccine (1).
According to the Centers for Disease Control
and Prevention (CDC), World Health
Organization (WHO) and United Nations
International Children’s Emergency Fund
(UNICEF), measles has already been a global
issue and now it has been aggravated by
disrupted immunization protocols due to the
COVID-19 pandemic (2–5). All six WHO regions
have reported disrupted immunization activities,
with major adverse effects on routine
immunization and mass vaccination campaigns
(4). According to CDC reports, in 2020, more than
117 million children were at the risk of missing
out on measles vaccines as a consequence of
the COVID-19 surge (2). Measles immunity gaps
resulting from suspended immunization
activities are an ominous precursor to a measles
resurgence (4). In Ukraine, one of Hungary’s
neighboring countries that was already endemic
for measles, vaccination has been interrupted in
many regions (3). Regarding Europe, ECDC
surveillance data have indicated an
exceptionally high number of measles cases in
2018, 2019 and 2020 in EU/EEA countries.
Vaccination remains one of the safest and most
effective interventions available in public health
for the primary prevention of infectious diseases,
resulting in both direct and indirect immunity in
individuals vaccinated (herd immunity) (6–8).
Even though a safe and effective two-dose
measles/MMR vaccination schedule has been
available in Europe since the 1960s, maintaining
high vaccine coverage is still difficult, despite
the fact that in Hungary, the MMR vaccine is
mandatory and consequently the vaccine
coverage is estimated to be at 98-99%.
According to our previous publications (9,10) and
in agreement with the results obtained by our
colleagues (11), there are latent immunization
gaps in certain age (or immunization) clusters of
the Hungarian population, with predominance of
the ~35-45-year-old adults. These are
individuals who form a significant portion of the
active labor force of the country, for instance
health care workers (HCWs).
Between January 2017 and May 2019, there were
76 reported measles cases in Hungary (12), 54 of
which were reported between 21 February and
22 March 2017 (13). Because of the recent
outbreaks worldwide, not only of measles, but
also mumps and rubella (MMR) infections, and
because of waning of immunity over time after
vaccination (14–17), the importance of
continuous MMR seroepidemiological screening
is evident.
Suboptimal vaccine effectiveness in certain
clusters of the population has a negative impact
on overall vaccination coverage. Small-scale
outbreaks suggest that certain measles
vaccines – applied during the early phases of the
Hungarian vaccination history – failed to elicit
the desired immunological response. The
resulting immunization gap(s) raise the concern
of potential further outbreaks (9,11). The 2020
COVID-19 outbreak called attention to the
importance of mathematical modelling of
epidemics (18). Based on a reliable model, the
timescale and economic impact of the disease
can be predicted and preventive
countermeasures can be taken (19). Through the
example of the measles epidemic in Makó (2017,
southeast Hungary), we demonstrated that, in
possession of key epidemiological data (e.g. R0
value, estimated vaccination coverage of a given
population, number of infected and recovered
individuals and duration of the epidemic), a
simple open-source mathematical model can
give a good approximation of the course of an
infection and may provide better general
compliance with protective measures.
Materials and Methods
Experimental work
In this seroepidemiological survey, we
combined the data from our previous findings
with recent measurements, including anti-
SEEMEDJ 2021, VOL 5, NO. 1 Imported Infections Versus Herd Immunity Gaps
3 Southeastern European Medical Journal, 2021; 5(1)
measles, -mumps and -rubella antibody level
(IgG) determination. Measurements were
performed on the automated Siemens BEP 2000
Advance® platform (Siemens AG, Germany),
using our self-developed ELISA assays
validated by well-established commercial kits,
as previously described (9,10). Indirect
immunofluorescent microscopy was used a
reference (Euroimmun, Germany).
In case of large-scale seroepidemiological
measurements, a serum bank consisting of
anonymous patient sera was used (N of total
measles cases = 3919, N of mumps cases = 2132,
and N of rubella cases = 2132) (Ethical License
number 2015/5726). Nationally representative
samples included randomly selected clinical
residual samples, with the exclusion criteria of
neonates, children under the vaccination age
and severely immunocompromised patients.
Samples were collected from the Department of
Laboratory Medicine (University of Pécs, Clinical
Centre). Serum samples were from all listed age
groups participating in this study and they were
categorized based on past changes introduced
in measles and MMR immunization schedules.
Age group determination was based on the
landmarks in the history of measles and MMR
vaccination schedules in Hungary (Figure 1).
Human sera were stored in the accredited
laboratory of the Department of Immunology
and Biotechnology (University of Pécs, Medical
School, Pécs, Hungary) according to quality
assurance criteria (ISO 17025).
Population-level result evaluation and
seropositivity ratio assessment was performed
in relation to the concept of herd immunity
threshold (HIT) values (HIT Measles = 92–95%,
HIT Mumps = 85–90%, HIT Rubella = 83–86). The
study relies on the full virus antigen repertoire-
based indirect ELISA method. Therefore, it must
be considered a good surrogate, rather than an
absolute correlate marker for immunity – as far
as Plotkin’s nomenclature is considered
normative (20–22). We examined vaccination
group-related infection- and vaccine-induced
antibody titres using the following software:
SPSS, Origin Pro, Excel.
SEIR model example and input data
A small-scale measles outbreak in Hungary in
2017 raised questions about the vaccination
coverage rate in the country. Experimental
results supported the theory of ineffective
vaccines, as previously mentioned (9). In spite of
its limitations, it seemed reasonable to set up a
SEIR model calculation in order to see whether
a few percent decrease in effective vaccination
could result in a local epidemic. To demonstrate
the disease spread in a well-immunized
population where latent immunity gaps may be
present, input data were based on the data of
the 2017 measles outbreak in Makó, southeast
Hungary. The following parameters were used
to perform the calculations:
Population (N): The epidemic was linked to the
small-town hospital. During that year, 65
physicians were responsible for medical
attendance of the estimated 30,000 inhabitants
of Makó and the surrounding villages. In our
model, a population of N = 400-1,000 people
was assumed, including patients, health-care
workers and family members.
Number of infected individuals (I): A total of 29
cases were reported.
Incubation time and contagious period: The
incubation time for measles ranges from 10 to 12
days on average, an infected person can be
contagious even 1-2 days before the first
characteristic symptoms are visible, up to 4 days
after the rashes appear. In our model, the
incubation time (Tinc) was assumed to be 10
days, whereas the contagious period (Tcont)
parameters were determined by equations (5)
and (6).
Reproduction rate ranging from 12 to 18 can be
found in the literature and both values were
tested. The higher value is applicable to
communities where no social distancing is
present and the ratio of vaccinated or
immunized inhabitants is low. In Central Europe,
the use of the lower value seems more rational,
although this specific epidemic was kept mainly
in a hospital, where circumstances promote the
spread of the infection. In this case, the start of
SEEMEDJ 2021, VOL 5, NO. 1 Imported Infections Versus Herd Immunity Gaps
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the outbreak was defined as the possible first
day of the first patient’s infection, while the
model was set to stop after the recovery of the
last infected person. When it comes to large-
scale epidemics, a different approach is used. If
no new cases are found after a certain period,
the outbreak is over. This time period is usually
determined by the incubation time, with a
calculation method suggested by the WHO.
Based on the ELISA antibody measurements, it
can be assumed that only ~90% of the Hungarian
population has effective immunization, which is
under the theoretical 92-94% of HIT. In the
model, 90% of seroprevalence was assumed,
but lower values were also tested subsequently.
No additional vaccinated (V) compartment was
created and immunized individuals were treated
as recovered. Vital dynamics was disregarded
due to the short period of the epidemic. Death
rate was not taken into consideration either, as
no fatalities were observed during the
Hungarian outbreak. Calculations were
performed using Microsoft Excel Visual Basic
Application (VBA), but the graphs were plotted in
Origin. VBA is a built-in feature of the Microsoft
Office Suite with several limitations, but its
prevalence and the user-friendly computer
language makes it suitable for educational
purposes.
Results
Changes and historical data regarding
epidemics in the Hungarian measles/MMR
vaccination schedule (23–25) have been plotted
on a timeline in order to evaluate
seroepidemiological data accordingly. Figure 1
shows changes in measles and MMR vaccination
schedules in Hungary since the introduction of
the vaccine (1969). High age-specific attack rates
characterizing major epidemics (1980-81 and
1988-89) along with 93%-99% of vaccine
coverage evidence insufficiencies of the early
vaccination program.
Figure 1. Measles and MMR vaccination schedules in Hungary
(a) Vaccination against measles was introduced in Hungary in 1969. (b) From 1969 to 1974, a single dose of measles
vaccine was administered in mass campaigns to persons aged 9-27 months. (c) After vaccination was
implemented, the incidence rate decreased until 1973-74, when large epidemics occurred primarily in
unvaccinated 6-9-year-olds. (d) The recommended age for vaccination was 10 months until 1978, when it was
changed to 14 months. (e) After the 1980-81 epidemic, persons born between 1973 and 1977, who received vaccine
when the recommended age was 10 months, were revaccinated. (f) The 1988-89 epidemic mainly affected persons
aged 17-21, who had been targeted to receive vaccine during mass campaigns in the first years of the vaccination
program in Hungary. After 1989, children were re-vaccinated at the age of 11 with a monovalent measles vaccine
in a scheduled manner. Also, in 1989, the rubella vaccine was introduced. (g) In 1990, measles-rubella bivalent
vaccines were introduced. (h) The administration of the first vaccine at the age of 14 months lasted from 1978 to
1991. Also, in 1991, the measles-mumps-rubella trivalent vaccine was introduced. (i) In 1992, the administration of
the first MMR vaccine was shifted to 15 months of age. (j) In 1996, the MERCK MMR II vaccine (Enders’ Edmonston
SEEMEDJ 2021, VOL 5, NO. 1 Imported Infections Versus Herd Immunity Gaps
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strain, live attenuated) was introduced. (k) In 1999, measles-mumps-rubella revaccination replaced the monovalent
measles vaccine. Also, in 1999, the GSK PLUSERIX vaccine (Measles Schwarz Strain) was introduced. (l) In 2003, the
GSK PRIORIX vaccine was introduced. (m) Between 2004 and 2005, the MERCK MMR II vaccine was used. (n)
Between 2006 and 2010, the GSK PRIORIX vaccine was in use. (o) Starting from 2011, we have been using a Sanofi-
MSD product, MMRvaxPro (Measles virus Enders’ Edmonston strain, live, attenuated), for vaccination and
revaccination of children. GSK PRIORIX is still on the market, commonly used for vaccination in adulthood. (p)
Between January 2017 and December 2019, there were 76 reported measles cases in Hungary (according to ECDC
Surveillance reports). (Source of information: MMWR Weekly October 06, 1989 / 38(39); 665-668, International
Notes Measles – Hungary, http://www.vacsatc.hu, https://www.ecdc.europa.eu)
Figure 2 shows the age or vaccination group-
specific seropositivity and seronegativity ratios
for measles, mumps and rubella. The lowest
seropositivity ratios in terms of anti-measles
antibody titres (IgG) were observed in the groups
‘Vaccinated between 1969-1977’ (87.56%) and
‘Vaccinated between 1978-1987’ (78.48%). These
results are further confirmed by the
abovementioned vaccine insufficiencies of the
relative periods, described in Figure 1. Regarding
the mumps and rubella seroepidemiological
survey, in terms of humoral antibody levels, all
vaccination groups satisfied the requirements
necessary for the achievement of herd
immunity.
(a) Measles
(b) Mumps
(c) Rubella
Figure 2. Measles, mumps and rubella
seropositivity ratios according to vaccination
groups
Age / vaccination groups: (I) Individuals born before
1969. (II) Individuals vaccinated between 1969 and 1977.
(III) Individuals vaccinated between 1978 and 1987. (IV)
Individuals vaccinated between 1988 and 1990. (V)
Individuals vaccinated between 1991 and 1995. (VI)
Individuals vaccinated between 1996 and 1998. (VII)
Individuals vaccinated between 1999 and 2002. (VIII)
Individuals vaccinated in 2003. (IX) Individuals
vaccinated between 2004 and 2005. (X) Individuals
vaccinated between 2006 and 2010 (XI) Individuals
vaccinated after 2011. The lowest seropositivity ratio
(78.48%) was observed in the anti-measles antibody
titres (IgG) in the group ‘Vaccinated between 1978 and
1987’.
In case of measles, mumps and rubella
cumulative results, the seropositivity ratios were
89.97%, 91.60% and 92.58%, respectively, as
shown in Figure 3. Due to previously detailed
SEEMEDJ 2021, VOL 5, NO. 1 Imported Infections Versus Herd Immunity Gaps
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cluster-specific inadequacy of humoral antibody
levels, the cumulative anti-measles
seropositivity ratios also failed to reach the herd
immunity threshold (HIT Measles = 92–95%).
Measles Mumps Rubella
Overall seropositivity ratio
Overall seronegativity ratio
𝑆𝑒𝑟𝑜𝑝𝑜𝑠𝑖𝑡𝑣𝑖𝑡𝑦 𝑟𝑎𝑡𝑖𝑜 = 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑎𝑚𝑝𝑙𝑒𝑠 −
𝛴 (𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 + 𝑒𝑞𝑢𝑖𝑣𝑜𝑐𝑎𝑙 𝑠𝑎𝑚𝑝𝑙𝑒𝑠)
𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑎𝑚𝑝𝑙𝑒𝑠
∗ 100
HIT Measles = 92–95% HIT Mumps = 85–90% HIT Rubella = 83–86%
Figure 3. Overall seropositivity and seronegativity ratios
N measles = 3,919; N mumps, rubella = 2,132. In case of measles, mumps and rubella cumulative results, the
seropositivity ratios were 89.97%, 91.60% and 92.58%, respectively. The overall ratio of seropositive samples was the
lowest in the ‘measles’ group, where it remained under the threshold value. Seropositivity ratios were calculated as
follows:
Using the seronegativity ratio of 89.97% (≈ 90%)
obtained by the cumulative data representation
of anti-measles (IgG) antibody levels, the model
of possible outcomes of a measles outbreak in a
hospital as a function of the vaccination
coverage rate was investigated. The results of
the VBA-based SEIR model of the 2017 epidemic
in Hungary are summarized in Table 1. Three
parameters – population of the sample, ratio of
immunized individuals and reproduction rate of
the virus – were set to different values. The
effect of these adjustments was investigated
and changes in the number of measles cases
and timescale of the epidemic were observed.
Table 1. SEIR model results for the 2017 measles epidemic in Makó, Hungary
10%
90%
8%
92%
7%
93%
Population of the
sample (N)
Ratio of immunised
(%)
Total number of
measles cases
Duration of epidemic
𝑹𝟎 = 𝟏𝟖
1000 90 73 6 months
400 90 29 4 months
400 80 78 3 months
150 80 29 2.5 months
𝑹𝟎 = 𝟏𝟐
1000 90 2 6 days
400 90 2 6 days
400 80 70 4 months
150 80 26 3 months
Empirical values
? 90 29 2 months
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At R_0=18 and N = 1000, assuming 90% effective
vaccination, 100 susceptible individuals can be
found in the population. The model estimates a
total number of infected persons at 74 and the
duration of the epidemic at half a year, which is
more than double of the real values. By setting
the population at N = 400, 30 infected individuals
and 4 months were given by the model. This way
the number of infected persons corresponds to
the actual clinical data, but the duration is still
longer compared to empirical findings.
Timescale of the epidemic can be compressed
by increasing the proportion of susceptible
people. If the vaccination coverage rate is
changed from 90% to 80%, the duration of the
epidemic is reduced to 3 months, but the total
number of infected individuals becomes higher.
Based on this anomaly, it can be presumed that
the total number of involved population might
be even lower than 400. Unfortunately, the
results of the contact tracing procedure were
not available for a better approximation.
An acceptable correspondence between the
model calculations and the clinical data was
observed by assuming N = 150 and 80% of
vaccination coverage as input parameters.
The results – 30 infections in a two-month period
– are close to the official values. For a better
comparison, modelling with R_0=12 was also
performed. The less contagious the virus, the
fewer cases are found. Using this lower
reproduction rate, only isolated cases can occur
at 90% of vaccination coverage (which is a value
that resembles the HIT). By decreasing the
vaccination rate, the number of cases increases
and the timescale is shortened, similarly to
previous test examples.
Discussion
MMR vaccination in Hungary
In Hungary, MMR vaccine is mandatory. A single-
dose, live-virus combined measles-mumps-
rubella (MMR) vaccine is used to vaccinate
infants of ≥15 months of age. A reminder vaccine
is given to sixth year primary school students (~11
years of age). PRIORIX (GSK), PRIORIX-TETRA
(GSK), ProQuad (MERCK) and the M-M-
RVAXPRO (MSD Pharma) vaccines are currently
used in Hungary for vaccination of children (at 15
months and 11 years of age) and for adults (62).
The vaccines contain live attenuated viruses (26).
Regarding insufficient cumulative anti-measles
seropositivity levels, we would like to emphasize
that potential gaps in the population-level
humoral immunity (IgG) are attributable to early
vaccination periods and are not a general
phenomenon relative to the current
immunization practices. The susceptibility of
certain cohorts is likely attributable to the
thermal instability of the historical Leningrad-16
vaccine, inefficient seroconversion owing to
vaccination at a premature age (e.g. 9 months of
age) and the questionable efficiency of the
inoculum itself (9, 11, 25, 29, 30, 31). The 2017
measles outbreak in Makó was provoked by
imported cases. Some of our bordering
countries are still endemic for measles (27–30).
Supplementary Figure 1 shows the European
measles cases in the time period relative to the
epidemics in Makó and Szeged. COVID-19 is
increasing the risk of measles outbreaks.
According to CDC Global Measles Outbreak
reports of January 2021, 41 countries may
postpone their measles campaigns for 2020 or
2021 due to the COVID-19 pandemic. This
increases the risk of bigger outbreaks around
the world (31).
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Supplementary Figure 1. European measles cases in the time period relative to the epidemics in
Makó and Szeged (ecdc.europa.eu)
Between December 2016 and November 2017, numerous measles cases occurred in Europe, most of which were
reported by Romania, one of Hungary’s neighbouring countries. Source of data: https://www.ecdc.europa.eu/
2017 measles epidemic in Hungary
In 2017, according to the data of the national
authorities, a total of 76 persons were infected
with measles (corrected to 73 laboratory
confirmed cases by ECDC Surveillance reports).
The outbreak in the hospital of the small town of
Makó involved 29 individuals and lasted from
January 2017 to March 2017 (32,33). In order to
demonstrate the spread of virus in a well-
immunized population, where despite good
vaccination coverage, latent immunization gaps
(unprotected, seronegative cohorts) are present,
we used an open-source epidemiological report
of the Hungarian National Public Health and
Medical Officer Service (ANTSZ) (17 March 2017):
‘At the peak of the Hungarian measles
epidemics during the spring of 2017, 52 cases
with measles-specific symptoms were reported.
Of these, 15 laboratory confirmed cases
(National Reference Laboratory for Measles and
Rubella, National Public Health Institute,
Budapest, Hungary) were registered by 16
March. Of these patients, 12 were health care
workers (HCWs) and two were hospitalized
patients. One of them was a foreigner, while the
86
245
86
7
3
137
5
1
13
296
647
389
36
3
19
3.891
0
2
4
0
18
1
43
29
2.257
1
6
157
30
226
8.638 5755
0 2000 4000 6000 8000 10000 12000 14000 16000
Austria
Belgium
Bulgaria
Croatia
Cyprus
Czech Republic
Denmark
Estonia
Finland
France
Germany
Greece
Hungary
Iceland
Ireland
Italy
Latvia
Lithuania
Luxembourg
Malta
Netherlands
Norway
Poland
Portugal
Romania
Slovakia
Slovenia
Spain
Sweden
United Kingdom
Total
Measles cases by notification rate (ECDC)
(December 2016 - November 2017; cumulated results)
Laboratory confirmed case Cases
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other one was a patient living in the vicinity of a
HCW. The epidemic affected two health care
institutions, the Hospital of Makó and the clinics
of the University of Szeged. The first measles
case was imported in mid-February 2017 to the
Hospital of Makó. The epidemic affected the
hospital staff and their contacts. By 17 March, a
measles infection was confirmed in case of a
patient who was presumed to be the original
importer of the virus, in case of 11 HCWs and in
case of one of the HCW’s contacts. At the time
of this report, additional 11 cases (of which seven
HCWs and three patients’ contacts) were still
under investigation. At the clinics of the
University of Szeged, two persons – a HCW and
a patient – fell ill with measles. Another 11
persons (six patients and five HCWs) were also
suspected at the time of the report. Following
the appearance of the abovementioned
measles cases, in Csongrád County, a total of
391 people were vaccinated against measles,
mumps and rubella (MMR). As the first cases of
this period had been revealed, the National Chief
Physician ordered strict monitoring and
reporting of suspected measles virus infections.
Thus, another 15 suspected cases were
registered in several other counties. At the time
of the report, laboratory testing was still ongoing
(12)’.
The second group of imported cases was
detected at the end of July 2017 in Nyíregyháza,
Szabolcs-Szatmár-Bereg County, Hungary (11).
Six unvaccinated Romanian children were
hospitalised with clinical symptoms of measles.
These cases were later laboratory confirmed
(National Reference Laboratory for Measles and
Rubella, National Public Health Institute,
Budapest, Hungary). The subsequent disease
spread among two additional HCWs (also
laboratory confirmed) supports the
susceptibility of certain clusters in the Hungarian
population (11).
Epidemiological model- a didactic representation
In this section, we explain the spreading
mechanism of infectious diseases for those who
are not familiar with the computational
background of modelling. To understand the
basics of epidemic models, a simplified
mathematical interpretation can be used. The
spread of a disease can be described by S-
shaped sigmoid mathematical functions, similar
to the well-known pH titration curve, or
haemoglobin saturation curves. As infectious
diseases spread from human to human, the
number of susceptible persons is decreasing
over time and it influences the propagation of
the pathogenic agent. In the beginning of the
outbreak, the damping effect of recovered
patients is minimal; the curve is very close to
exponential and the number of new cases
increases rapidly. At a certain time, a kind of
equilibrium follows, daily recoveries can balance
new infections and the curve reaches its
inflection point. Afterwards, in the saturation
phase, the epidemic slows down and at the end,
no new cases are found and the vast majority of
the population has recovered (Figure 4). The
curves represented in Figure 4 are a graphic
interpretation of a commonly used method for
epidemic modelling – the compartment model.
In this model, the population is divided into
compartments – well-defined categories based
on their epidemiological properties. In a
compartment, all individuals behave exactly the
same, e.g. they are all infected, all vaccinated, all
exposed, etc. The simplest among these
compartment models is the SIR model, where
the letters of the acronym stand for susceptible,
infectious and recovered.
.
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0 30 60 90 120 150 180
0
200
400
600
800
1000
P
o
p
u
la
ti
o
n
Time (days)
Susceptible
Recovered
Infected
94%
6%
8%
Figure 4. SIR model curves of a hypothetical
epidemic
As the disease spreads, the number of susceptible
individuals decreases. First they get infected (I), but
later on they will progress to the recovered
compartment (R). Approximately 6% of the population
managed to avoid contact with infected individuals.
The peak of infections could be observed almost three
months after the first case was recorded, affecting 8%
of the population at the same time.
The progression of an individual in this model is
easy to follow, each member of the population
progresses from susceptible to infectious to
recovered.
𝑆
𝛽
⇒ 𝐼
𝛾
⇒ 𝑅 (1)
Transition between compartments is described
probability of transmitting the disease between
a susceptible and an infectious person. In other
individuals to whom an infectious person can
pass the disease per day (18,39,40) For example,
if the infection rate is 0.2, it will take five days on
average to infect someone. If we assume that
the patient is contagious for 10 days, two new
infections are expected in this case.
The overall efficacy of the epidemic can be
described by the number of these secondary
infections originated from the primary infection,
our first patient. This important parameter is the
basic reproduction number (R0). Each virus has
its own average R0 value – 12-18 for measles
and 3.3-5.7 for COVID-19, according to the
literature.
transition into the recovered compartment. For
instance, if this rate is 0.1, the contagious period
will last for 10 days.
From a mathematical perspective, the
transitions can be described by the following
differential equations, where S, I and R are the
number of individuals in the corresponding
compartments, while N is the whole population.
dS
dt
= −
βIS
N
(2)
dI
dt
=
βIS
N
− γI(3)
dR
dt
= γI(4)
Mathematical methods (such as the Runge-
Kutta method) are available for solving similar
equations, but there is a simpler option. Using
the built-in features of Microsoft Excel (or any
equivalent spreadsheet application), it is
possible to make calculations using an iterative
method. Instead of solving the equations, the
computer performs calculations that follow the
daily changes in different compartments.
R0 have to be defined. Based
on the definition of the transition rates, it can be
seen that the recovery rate can be determined
by the number of contagious days (T_cont).
𝛾 =
1
𝑇𝑐𝑜𝑛𝑡
(5)
The basic reproduction number can be given as
follows:
𝑅0 =
𝛽
𝛾
(6)
Let us assume that in a certain population
measles can be transmitted from a single person
to 12 others (R_0=12) and they stay contagious for
6 days (T_cont=6). In this case:
SEEMEDJ 2021, VOL 5, NO. 1 Imported Infections Versus Herd Immunity Gaps
11 Southeastern European Medical Journal, 2021; 5(1)
𝛾 =
1
𝑇𝑐𝑜𝑛𝑡
=
1
6
(7)
𝛽 = 𝑅0𝛾 = 2 (8)
Incubation time plays an important role in the
spread of a disease. In a more sophisticated
model (SEIR model), this can also be taken into
consideration. A new compartment for the
exposed part of the population can be
generated. The susceptible person first gets
exposed and will progress to the infectious state
only after a certain time.
𝑆
𝛽
⇒𝐸
𝛼
⇒𝐼
𝛾
⇒ 𝑅 (9)
The parameter ‘α’ is a new transition rate,
which can be determined by the incubation time
(T_inc) , similarly to γ:
𝛼 =
1
𝑇𝑖𝑛𝑐
New compartments can be added to the model
anytime, such as the compartment M for
individuals with maternal immunity or the
compartment E for exposed individuals, who are
already infected, but not infectious. Based on the
characteristics of certain infectious diseases,
further models have been developed, such as
the SIS, MSIR, SEIR, SEIS, MSEIR and MSEIRS
models. The second ‘S’ in the acronym indicates
that after the infection, no permanent immunity
can be reached and the individuals step to the S
compartment again. In other models, the ratio of
hospitalization, the ratio of mild and severe
cases and epidemiological interventions can be
included, with a more complex mathematical
background.
In the examples described above some
important parameters are simply disregarded,
although it is possible to perform a more
detailed computation. Vital dynamics, the
natural dynamics of birth and death, can be
included by adding two further parameters.
It is necessary to mention that compartment
models have their well-known limitations and
shortcomings. For instance, all individuals in the
population are assumed to have an equal
probability of coming in contact with others,
although society is inhomogeneous from the
perspective of social distancing. Another
drawback is that the traditional compartment
model cannot handle uncertainty in model
parameters. Working with a smaller set of data
increases this uncertainty, making predictions
unreliable. To overcome this problem, it is usual
to calculate the SIR model over a few possible
values for each parameter. A more complex
solution is to use distribution functions instead of
single numbers and if real-time data is available
(e.g. we are in the middle of a pandemic), a
clinical dataset can be utilized to adjust these
parameters (36–38).
Regarding the SEIR model resembling the 2017
measles outbreak in Makó (Figure 4), we would
like to note that both the simplified
mathematical method and the input data were
unreliable. With more sophisticated models,
many different parameters can be taken into
consideration (37,39). Despite that fact, the
calculated values correspond in order of
magnitude to the available data on the epidemic
and support the experimental results describing
the vaccination gap.
Model curves using a lower percentage of the
population-level anti-measles protection rate
are more fitting. This finding may indicate an
even lower percentage of effectively vaccinated
population than it was found previously (~90%).
It is concluded that the importance of
seroepidemiological surveys is confirmed by the
recent outbreaks of measles, mumps and
rubella infections in several countries
(14,16,17,40–45). Considering the HIT values,
suboptimal anti-measles seropositivity ratios
were detected in certain clusters of the early
vaccination era (78.48% of sufficient anti-
measles IgG antibody titres among individuals
vaccinated between 1978 and 1987). This finding,
which is in accordance with a recent study
published by our colleagues (11) and historical
literature data (46), suggests the existence of
age-specific immunization gaps in the
Hungarian population. For mumps and rubella,
our preliminary data shows satisfactory
immunity levels. Nowadays, in our country, the
MMR vaccination coverage is ideal due to the
SEEMEDJ 2021, VOL 5, NO. 1 Imported Infections Versus Herd Immunity Gaps
12 Southeastern European Medical Journal, 2021; 5(1)
mandatory administration of safe and modern
trivalent vaccines. Nevertheless, dubious
immunization practices in some of our
neighboring countries, aggravated by the
detrimental effect of the COVID-19 pandemic
and subsequent suspension of measles
vaccination campaigns, may facilitate the
occurrence of minor importation-related MeV
outbreaks in susceptible cohorts. Using the
example of the 2017 measles outbreak in Makó,
it has been demonstrated that in possession of
key epidemiological parameters (e.g. R0 value,
estimated vaccination coverage of a given
population, number of infected and recovered
individuals, duration, etc.), a simple SEIR model
can give a good approximation regarding the
course of an infection.
We believe that awareness may significantly
reduce the extent of an epidemic (38,47). In the
light of current disquieting epidemiological
circumstances, we suggest the introduction of
open-access mathematical and epidemiological
models into modern natural science education
of students. Today, online epidemic models are
easily available for the public (35,36). Practical
introduction to these plain calculation models
could help students understand the rationale
behind epidemiological data. We believe that a
practical demonstration of epidemiological
events can promote a better understanding of
countermeasures and also allow for an easier
adaptation to the current epidemiological
regulations.
Limitations of experimental work
The diagnostic ability of our assay was
calculated based on the results obtained by
well-established kits capable of humoral
antibody detection, rather than on neutralizing
antibody titres that could serve as an absolute
correlate of protection (48–50). It is important to
emphasize that immunity to measles is a
complex orchestration between the cellular and
humoral immunity. For this reason, only
antibody-based definitions of vaccine success
and failure may be misleading, or at least
simplistic and incomplete (51).
Limitations of mathematical modelling
Input data plays a key role in modelling of
epidemics. Even when the number of cases is
high – like in the 2020 COVID outbreak – the
confidence of fitting is poor at the beginning of
new cases vs. time graph. The first cases are
usually unexpected, quarantine and social
distancing protocols are not applied yet and if
the disease has a low prevalence in the
population, the accuracy of the diagnosis might
be low. Besides that, atypical symptoms can be
misleading for physicians. Furthermore,
statistical values, such as basic reproduction
number, incubation and recovery time, depend
on other factors, such as social distancing and
the health care system.
Acknowledgement. None.
Disclosure
Funding. This work was realized with the
financial support of the University of Pécs,
Medical School (Pécs, Hungary) and the
following grants: EFOP-3.6.1-16-2016-00004,
2019 Higher Education Excellence Program
(FIKP II PoP) and HUHR/1901/3.1.1/0032
CABCOS3. Project no. TKP2020-IKA-08 has been
implemented with the support provided from
the National Research, Development and
Innovation Fund of Hungary, financed under the
2020-4.1.1-TKP2020 funding scheme.”
Transparency declaration: We declare that we
have no commercial or potential competing
interests or any financial and personal
relationships with other people or organizations
that could inappropriately influence our
network.
References
1. Haralambieva IH, Kennedy RB,
Ovsyannikova IG, Whitaker JA, Poland GA.
Variability in Humoral Immunity to Measles
Vaccine: New Developments. Trends Mol Med
2015;21(12):789-801. doi:
10.1016/j.molmed.2015.10.005.
2. COVID-19’s Impact on Measles
Vaccination Coverage. Available from:
https://www.cdc.gov/globalhealth/measles/n
SEEMEDJ 2021, VOL 5, NO. 1 Imported Infections Versus Herd Immunity Gaps
13 Southeastern European Medical Journal, 2021; 5(1)
ews/covid-impact-on-measles-
vaccination.html
3. Suspension of vaccination due to COVID-
19 increases the risk of infectious diseases
outbreaks - UNICEF and WHO. Available from:
https://www.unicef.org/ukraine/en/press-
releases/suspension-vaccination-due-covid-
19-increases-risk-infectious-diseases-
outbreaks (press release)
4. Durrheim DN, Andrus JK, Tabassum S,
Bashour H, Githanga D, Pfaff G. A dangerous
measles future looms beyond the COVID-19
pandemic. Nat Med 2021; 27:360–361.
https://doi.org/10.1038/s41591-021-01237-5
5. WHO Western Pacific Region. WHO
Western Pacific Region: Countries and areas.
Measles-Rubella Bull. 2021;15(1):1–10.
https://iris.wpro.who.int/bitstream/handle/106
65.1/14713/Measles-Rubella-Bulletin-2021-Vol-
15-No-01.pdf
6. Torre G La, Saulle R, Unim B, Meggiolaro
A, Barbato A, Mannocci A, Spadea A. The
effectiveness of measles-mumps-rubella (MMR)
vaccination in the prevention of pediatric
hospitalizations for targeted and untargeted
infections: A retrospective cohort study. Hum
Vaccin Immunother. 2017;13(8):1879- 1883. doi:
10.1080/21645515.2017.1330733
7. Rosian-Schikuta I, Fröschl B, Habl C,
Stürzlinger H. The Measels-Mumps-Rubella
Vaccination from a health political and
economical point of view. GMS Health Technol
Assess. 2007 Nov 28;3:Doc12.
8. Plans-Rubió P. Evaluation of the
establishment of herd immunity in the
population by means of serological surveys and
vaccination coverage. Hum Vaccin Immunother.
2012; 8(2):184–8.
9. Böröcz K, Csizmadia Z, Markovics, Farkas
N, Najbauer J, Berki T, Nemeth P. Application of
a fast and cost-effective “three-in-one” MMR
ELISA as a tool for surveying anti-MMR humoral
immunity: The Hungarian experience. Epidemiol
Infect. 2020; 148: e17. doi:
10.1017/S0950268819002280
10. Böröcz K, Csizmadia Z, Markovics Á,
Mészáros V, Farkas K, Telek V, Varga V, Ouma
Maloba G, Bodó K, Najbauer J, Berki T, Németh
P. Development of a robust and standardized
immunoserological assay for detection of anti-
measles IgG antibodies in human sera. J
Immunol Methods. 2019 Jan; 464:1-8. doi:
10.1016/j.jim.2018.07.009.
11. Lengyel G, Marossy A, Ánosi N, Farkas SL,
Kele B, Nemes-Nikodém É, et al. Screening of
more than 2000 Hungarian healthcare workers’
anti-measles antibody level: results and
possible population-level consequences.
Epidemiol Infect. 2019 Sep 11;147:e7.
12. ANTSZ - Tájékoztatás a kanyarós
megbetegedésekről. Available from:
https://www.antsz.hu/felso_menu/temaink/ja
rvany/jarvany_archivum/kanyaro/tajekoztatas
kanyarosmegbetegedesekrol.html
13. Epidemiological update: Measles -
monitoring European outbreaks, 7 July 2017.
Available from:
https://www.ecdc.europa.eu/en/news-
events/epidemiological-update-measles-
monitoring-european-outbreaks-7-july-2017
14. Lambert N, Strebel P, Orenstein W,
Icenogle J, Poland GA. Rubella. Lancet. 2015;
385(9984):2297–307.
15. Moss WJ. Measles. Lancet. 2017;
390(10111):2490–502.
16. Hviid A, Rubin S, Mühlemann K. Mumps.
Lancet. 2008;371(9616):932–44.
17. Lewnard JA, Grad YH. Vaccine waning
and mumps re-emergence in the United States.
Sci Transl Med. 2018; 10(433):eaao5945.
18. Peng L, Yang W, Zhang D, Zhuge C, Hong
L. Epidemic analysis of COVID-19 in China by
dynamical modeling. 2020. arXiv:2002.06563 [q-
bio.PE]
19. Kretzschmar M. Epidemic Model - an
overview | ScienceDirect Topics. International
Encyclopedia of Public Health (Second Edition).
2017. p. 571–84.
https://www.sciencedirect.com/topics/medici
ne-and-dentistry/epidemic-model
SEEMEDJ 2021, VOL 5, NO. 1 Imported Infections Versus Herd Immunity Gaps
14 Southeastern European Medical Journal, 2021; 5(1)
20. Böröcz K, Csizmadia Z, Markovics Á,
Mészáros V, Farkas K, Telek V, Varga V, Maloba
GO, Bodó K, Najbauer J, Berki T, Németh P.
Development of a robust and standardized
immunoserological assay for detection of anti-
measles IgG antibodies in human sera. J
Immunol Methods. 2019 Jan;464:1-8. doi:
10.1016/j.jim.2018.07.009.
21. Plotkin SA. Correlates of protection
induced by vaccination. Clin Vaccine Immunol.
2010; 17(7):1055–65. Available from:
http://www.ncbi.nlm.nih.gov/pubmed/204631
05
22. Plotkin SA. Complex correlates of
protection after vaccination. Clin Infect Dis.
2013;56(10):1458–65.
23. Plotkin SA, Gilbert PB. Nomenclature for
immune correlates of protection after
vaccination. Clin Infect Dis [Internet]. 2012 Jun
[cited 2019 Aug 30];54(11):1615–7. Available from:
http://www.ncbi.nlm.nih.gov/pubmed/224372
37
24. Böröcz K, Csizmadia Z, Markovics Á,
Farkas N, Najbauer J, Berki T, et al. Application of
a fast and cost-effective “three-in-one” MMR
ELISA as a tool for surveying anti-MMR humoral
immunity: The Hungarian experience. Epidemiol
Infect. 2020;
25. Agócs MM, Markowitz LE, Straub I,
Dömök I. The 1988-1989 measles epidemic in
Hungary: assessment of vaccine failure. Int J
Epidemiol [Internet]. 1992 Oct [cited 2019 May
5];21(5):1007–13. Available from:
http://www.ncbi.nlm.nih.gov/pubmed/146883
7
26. MMWR Weekly. MMWR Publications |
MMWR [Internet]. [cited 2019 May 5]. Available
from:
https://www.cdc.gov/mmwr/publications/ind
ex.html
27. Hungary V. Vacsatc - Oltásbiztonság |
Nyitólap [Internet]. [cited 2020 Mar 31]. Available
from: http://www.oltasbiztonsag.hu/
28. Vacsatc - Oltásbiztonság | Szakmai
oldalak | Virális oltóanyagok [Internet]. [cited
2019 Dec 21]. Available from:
http://www.vacsatc.hu/?Vir%E1lis-
olt%F3anyagok&pid=37
29. International Notes Measles -- Hungary
[Internet]. Available from:
https://www.cdc.gov/mmwr/preview/mmwrh
tml/00001472.htm
30. Böröcz K, Csizmadia Z, Markovics Á,
Mészáros V, Farkas K, Telek V, et al.
Development of a robust and standardized
immunoserological assay for detection of anti-
measles IgG antibodies in human sera. J
Immunol Methods. 2019;464.
31. Lengyel G, Ánosi N, Marossy A, Mátyus M,
Bosnyákovits T, Orosz L. Az európai és a
magyarországi kanyaróhelyzet összefoglalása
és tanulságai. Orv Hetil [Internet]. 2019 May 12
[cited 2019 Jul 31];160(20):767–73. Available from:
https://www.akademiai.com/doi/10.1556/650.
2019.31397
32. Habersaat KB, Pistol A, Stanescu A,
Hewitt C, Grbic M, Butu C, et al. Measles
outbreak in Romania: understanding factors
related to suboptimal vaccination uptake. Eur J
Public Health [Internet]. 2020 Oct 1 [cited 2021
Mar 5];30(5):986–92. Available from:
https://academic.oup.com/eurpub/article/30
/5/986/5847956
33. Dascalu S. Measles Epidemics in
Romania: Lessons for Public Health and Future
Policy [Internet]. Vol. 7, Frontiers in Public Health.
Frontiers Media S.A.; 2019 [cited 2021 Mar 5]. p.
98. Available from:
/pmc/articles/PMC6496956/
34. The Lancet. Measles, war, and health-
care reforms in Ukraine. Vol. 392, The Lancet.
Lancet Publishing Group; 2018. p. 711.
35. Wadman M. Measles epidemic in Ukraine
drove troubling European year [Internet]. Vol.
363, Science. American Association for the
Advancement of Science; 2019 [cited 2021 Mar
5]. p. 677–8. Available from:
http://stm.sciencemag.org/content/scitransm
ed/10/433/eaao5945.full
SEEMEDJ 2021, VOL 5, NO. 1 Imported Infections Versus Herd Immunity Gaps
15 Southeastern European Medical Journal, 2021; 5(1)
36. Global Measles Outbreaks [Internet].
[cited 2021 Jan 31]. Available from:
https://www.cdc.gov/globalhealth/measles/
data/global-measles-outbreaks.html
37. ECDC. Epidemiological update: Measles -
monitoring European outbreaks, 7 July 2017
[Internet]. [cited 2020 Mar 31]. Available from:
https://www.ecdc.europa.eu/en/news-
events/epidemiological-update-measles-
monitoring-european-outbreaks-7-july-2017
38. ANTSZ. ANTSZ - Public information on
measles epidemics [Internet]. [cited 2020 Mar 31].
Available from:
https://www.antsz.hu/felso_menu/temaink/ja
rvany/jarvany_archivum/kanyaro/tajekoztatas
kanyarosmegbetegedesekrol.html
39. Stella R. Quah WC. International
Encyclopedia of Public Health - Second Edition-
Google Books [Internet]. Elsevier. 2017 [cited
2020 Apr 4]. Available from:
https://books.google.hu/books?hl=hu&lr=&id=
WAnpCgAAQBAJ&oi=fnd&pg=PP1&dq=Measure
ment+and+Modeling:+Infectious+Disease+Modeli
ng+Mirjam+Kretzschmar,+in+International+Encycl
opedia+of+Public+Health+(Second+Edition),+2017
&ots=k662f-7bGN&sig=CQ-q-
rJ9YMRIG9BDwTm
40. Epidemic Calculator [Internet]. [cited
2020 Apr 4]. Available from:
https://gabgoh.github.io/COVID/index.html
41. Buckman SR, Glick R, Lansing KJ,
Petrosky-Nadeau N, Seitelman LM, Francisco S.
Replicating and Projecting the Path of COVID-19
with a Model-Implied Reproduction Number.
2020;2020–44.
42. Röst G, Wu J. SEIR EPIDEMIOLOGICAL
MODEL WITH VARYING INFECTIVITY AND
INFINITE DELAY [Internet]. Vol. 5, AND
ENGINEERING. 2008 [cited 2020 Apr 4]. Available
from: http://www.mbejournal.org/
43. Li M, Wang M, Xue S, Ma J. The influence
of awareness on epidemic spreading on random
networks. J Theor Biol. 2020 Feb 7;486:110090.
doi: 10.1016/j.jtbi.2019.110090.
44. Lipsitch M, Cohen T, Cooper B, Robins
JM, Ma S, James L, et al. Transmission dynamics
and control of severe acute respiratory
syndrome. Science (80- ). 2003 Jun
20;300(5627):1966–70.
45. Ujiie M. Rubella Resurgence in Japan
2018–2019. J Travel Med [Internet]. 2019 Sep 2
[cited 2021 Feb 1];26(6). Available from:
https://academic.oup.com/jtm/article/doi/10.
1093/jtm/taz047/5523888
46. WHO | New measles surveillance data
from WHO. WHO [Internet]. 2019 [cited 2019 Aug
22]; Available from:
https://www.who.int/immunization/newsroom
/new-measles-data-august-2019/en/
47. Wadman M. Measles epidemic in Ukraine
drove troubling European year. Science (80- )
[Internet]. 2019 Feb 15 [cited 2019 May
16];363(6428):677–8. Available from:
http://www.sciencemag.org/lookup/doi/10.11
26/science.363.6428.677
48. The Lancet. Measles, war, and health-
care reforms in Ukraine. Lancet [Internet]. 2018
Sep 1 [cited 2019 May 16];392(10149):711.
Available from:
http://www.ncbi.nlm.nih.gov/pubmed/3019181
2
49. Ukraine: Measles Outbreak - Jan 2019 |
ReliefWeb [Internet]. [cited 2019 Aug 22].
Available from:
https://reliefweb.int/disaster/ep-2019-
000017-ukr
50. Balbi AM, Van Sant AA, Bean EW, Jacoby
JL. Mumps: Resurgence of a once-dormant
disease. J Am Acad Physician Assist [Internet].
2018 May 1 [cited 2021 Feb 1];31(5):19–22.
Available from:
https://pubmed.ncbi.nlm.nih.gov/29642091/
51. Takahashi S, Sato K, Kusaka Y, Hagihara
A. Public preventive awareness and preventive
behaviors during a major influenza epidemic in
Fukui, Japan. J Infect Public Health. 2017 Sep
1;10(5):637–43.
52. Liu Y, Liu Z, Deng X, Hu Y, Wang Z, Lu P,
et al. Waning immunity of one-dose measles-
SEEMEDJ 2021, VOL 5, NO. 1 Imported Infections Versus Herd Immunity Gaps
16 Southeastern European Medical Journal, 2021; 5(1)
mumps-rubella vaccine to mumps in children
from kindergarten to early school age: a
prospective study. Expert Rev Vaccines
[Internet]. 2018 May 4 [cited 2019 May
16];17(5):445–52. Available from:
http://www.ncbi.nlm.nih.gov/pubmed/294783
47
53. Bankamp B, Hickman C, Icenogle JP, Rota
PA. Successes and challenges for preventing
measles, mumps and rubella by vaccination.
Curr Opin Virol [Internet]. 2019 Feb [cited 2019
May 15];34:110–6. Available from:
http://www.ncbi.nlm.nih.gov/pubmed/308524
25
54. Kontio M, Jokinen S, Paunio M, Peltola H,
Davidkin I. Waning antibody levels and avidity:
Implications for MMR vaccine-induced
protection. J Infect Dis. 2012;206(10):1542–8.
55. Ovsyannikova IG, Dhiman N, Jacobson
RM, Vierkant RA, Poland GA. Frequency of
measles virus-specific CD4+ and CD8+ T cells in
subjects seronegative or highly seropositive for
measles vaccine. Clin Diagn Lab Immunol
[Internet]. 2003 May [cited 2019 Aug 2];10(3):411–
6. Available from:
http://www.ncbi.nlm.nih.gov/pubmed/127386
40
1 Author contribution. Acquisition of data: Böröcz K,
Markovics Á, Csizmadia Z
Administrative, technical or logistic support: Böröcz K,
Csizmadia Z
Analysis and interpretation of data: Böröcz K,
Markovics Á, Najbauer J, Németh P
Conception and design: Böröcz K, Markovics Á,
Csizmadia Z, Berki T, Németh P
Critical revision of the article for important intellectual
content: Böröcz K, Najbauer J, Berki T, Németh P
Drafting of the article: Böröcz K, Markovics Á,
Csizmadia Z, Najbauer J
Final approval of the article: Najbauer J, Németh P.
Guarantor of the study: Berki T,
Obtaining funding: Berki T, Németh P
Provision of study materials or patients: Böröcz K,
Statistical expertise (statistical analysis of data):
Markovics Á,
http://www.ncbi.nlm.nih.gov/pubmed/12738640
http://www.ncbi.nlm.nih.gov/pubmed/12738640