A SYSTEM DYNAMICS MODEL FOR ANALYSING POPULATION RISK IN
CASE OF A VOLUNTARY VACCINATION PROGRAM AGAINST
MENINGOCOCCAL MENINGITIS
Y olanda Alvarez
Martin Caicoya
Rafael Garcia
Begotia Gonzalez-Busto
Summary
Mennigococcal meningitis outbreak is a complicated public health problem.
Control measures include prompt treatment of cases, vaccination and contacts
chemoprophylaxis. The treatment of an index case cuts the spread of bacteria, the treatment
of contacts avoids the disease in those that might be infected and cuts the spread of the
disease by carriers and the vaccination lowers the risk of disease. Vaccination has a limited
value because it does not protect children less than two years, only confers partial
immunity against certain serogroups, the duration of immunity is short, it does not provide
herd immunity and revaccination has conflicting results. When the incidence is high, mass
inmunization is recommended. If the incidence is not high, in some situation where public
pressure is high, an offer of voluntary vaccination has been done. We hypothesise that in
this situation the risk of nonvaccinate might be increased. In effect, those that decide to be
vaccinated will have the same risks and benefits than those that did so under massive
vaccination. However, those that decide no to vaccinate might be an increased risk. This
is so because vaccination has avoided the disease in those that would have become cases
if no vaccination; but it does not avoid their infection: they will be spreading virulent
bacteria, and as no treatment is imposed to cut their infection, they would do so as long as
it lasts the natural history of this situation. Those contacts that are vaccinated are at low
risk but non-vaccinated contacts are at high risk because they are not to benefit from
chemoprophylaxis and they might be exposed for longer periods of times to the aborted
index case.
Introduction
Mennigococcal meningitis outbreak is a complicated public health problem. Most
of the cases and the deaths occur among children and teenagers. The industrialised
countries are not used to loose children because of infectious diseases. The presence of a
temporal or geographical cluster of meningitis produces an alarm in the society and usually
a mass hysteria (1). Media and population pressure over the Public Health Authorities
might be one of the most important components in the decision to vaccinate.
In Spain the incidence of Mennigococcal disease had a peak in 1979 with a rate of
17.9 cases per 100000 inhabitants. In the last 10 years the rates varied between 1 and 3
cases per 100000, however there are interregional differences (2). Rates similar are found
in England and Wales (3). In 1996 we experience in Spain an increment meningococcal
disease (2). This prompted vaccination in several regions (4) and a consensus conference
to evaluate and produce guidelines for the management of the problem (5).
The strategies to control meningoccal disease are aimed to reduce the risk of death
among cases and reduce the risk of disease among contacts. In order to reduces reduce the
mortality rate the diagnosis and treatment of suspected cases should be rapid as well as the
admission to hospital. Here, the public health authorities and the media have a role in the
dissemination of the information to enable the public to recognise the early symptoms of
the disease. The strategies to reduce the dissemination of the disease include good housing
and vaccination and treatment of close contacts. Most of the cases are sporadic, i.e. the
source is not known, therefore the usefulness of chemoprophylaxis in close contacts is
limited. However, serogroup C causes epidemic diseases (6). The attack rate for the people
who live in the same household as a case of meningococcal disease is increased by about
500 to 1200 times, representing a risk of 1% for household (7). For serogroup C the attack
rate may be as high as 1000/100000 in schools while it is only between 5 and 20/100000
in the community (6). The estimated secondary attack rate in American schools is
2.5/100000, while the annual incidence of meningococcal disease is 1.08/100000 for the
same age group (8). The risk of a secondary case is mainly reduced to the first week since
the case is diagnosed. Vaccination against serogroup C meningococci is recommended
whenever the risk of meningococcal disease is high enough as to render benefits. It has
been recommended to vaccinates when the rate is 10/100000 of this serogroup, considering
the denominator the population that is subject of vaccination, or the occurrence of at least
three in three months, in an organisation or a community (9).
The treatment of an index case cuts the spread of bacteria, the treatment of contacts
avoids the disease in those that might be infected and cuts the spread of the disease by
carriers and the vaccination lowers the risk of disease. Vaccination has a limited value
because it does not protect children under two years, only confers partial immunity against
certain serogroup, the duration of immunity is short, it does not provide herd immunity and
revaccination has conflicting results (8). We hypothesise that the risk of nonvaccinate
might be increased. In effect, those that decide to be vaccinated will have the same risks
and benefits than those that did so under massive vaccination. However, those that decide
no to vaccinate might be an increased risk. This is so because vaccination has avoided the
disease in those that would have become cases if no vaccination; but it does not avoid their
infection: they will be spreading virulent bacteria, and as no treatment is imposed to cut
their infection, they would do so as long as it lasts the natural history of this situation.
Those contacts that are vaccinated are at low risk but non-vaccinated contacts are at high
risk because they are not to benefit from chemoprophylaxis and they might be exposed for
longer periods of times to the aborted index case.
The experience of Galicia (Spain) might serve as reference. There, in 1996 the
incidence of meningitis went up to 14.5/100000 person-years from a previous rate in the
80' and 90' lower than 4/100000-person year's (4). The incidence of serogroup C meningitis
was calculated to be 12/100000 person-year. This situation precipitated a massive
vaccination starting in December 1996. We have estimated from the data published that
In 1996 the peak incidence for children 2 to 4 years was 4,5/100000 person-week for
serogroup C. In the first 16 weeks of 1997 the incidence of serogroup C meningitis among
non-vaccinated (5% of the population) for children 3 to 5 years was 8/100000 person-week,
an incidence that is twice that of the worst week in 1996, when there was no vaccination.
From this perspective, the risk of the non-vaccinated in a population which high
vaccination coverage might be twice that of non-vaccinated when the vaccination coverage
is absent or low. In the other hand, the incidence among those vaccinated (95% of the
population) went down to 0,2 /100000 person-week, with an estimated protection as
compared to the incidence among nonvaccinated in the same weeks of 97,5%.
The experience of Australia is similar. An outbreak was declared for a rate before
vaccination was 17.55/1000. After a massive vaccination and chemoprophylaxis for
serogroup C outbreak, 6 cases occurred among 483 vaccinated children and 2 among 47
non-vaccinated children, for rates of 12.92/1000and 42.55/1000. Therefore the rate among
non-vaccinated was 2.5 times that of the rate that occurred when the outbreak was declared
(10). In Asturias the vaccination campaign took place in 1997-1998. Among the 145599
vaccinated persons a case of meningoccal meningitis C occurred in the first weeks
following the vaccine campaign, and none among the 59522 non-vaccinated. Therefore,
there is no evidence that the risk is higher among non-vaccinated (11)
From this analysis it might be concluded that vaccination is able to diminish the
rate of meningococcal disease among vaccinated but it might increase its risk among non-
vaccinated. Therefore, if vaccination is offered, it might be necessary to inform the
population that the risk of disease among those that decide not to vaccinate might be
increased because of the vaccine. The purpose of this study is to examine the hypothesis
by means of a system dynamics model. The hypothesis is that the nonvaccinated population
is at higher risk in a community where the immunisation rate is high than that where the
immunisation rate is low.
Material and methods
We built a system dynamics model with Vensim with the following assumptions:
1-Cases are infectious 4 days before starting treatment.
2-Each case makes 0.05 contacts a day.
3-10% of the contacts becomes infected
4-10% of the infected becomes cases
5-Infected cases remain infected for 1 month if they had not developed the disease
and they develop immunity.
6-20% of the cases dies.
7-We introduce an exogenous infective rate of 5/100000 in time=25
8-We assume that the efficacy of the vaccine is 100% given this is not the subject
of our enquire.
8-We compare the index of cases in the two situation: when a mass vaccination is
introduced ( in our case the coverage is 85%) and when no vaccination occurs. The index
is defined as the number of cases occurred among the nonvaccinated population.
In the next figures we depict the flow structure of the model, the definition of
infection rate, and the used indexes.
<vaccinanati
on>
<contention effective
rate> vaccination
|
VACCINE
EFFICACY
ro
Immune
Susceptibles
SICKNESS
a DURATION
cure <I
éxitus
MORTALITY
RATE
Cases
Be) Deads
<immune INCUBATION
infection> PERIOD
morbidity
<resistent 4
infection>
remission
__4
Nonimmune
Susceptibles|
Carriers
INonimmunes|
——
Figure 1. Flow
nonimmune.
infection>
diagram of the model
INITIAL
VULNERABLE
POPULATION
SCOPE
vy
total
population
A
1
> total carriers <t
immunized CONTACT Carriers
Carrier RATE Nonimmunes,
PROPORTION
OF
RESISTENTS sw
ra EPIDEMY
vy y vy
resistent nonimmune. immune 4
infection infection infection
At AN 4h
<total
ATTACK population>
RATE
total
contention
ten = population>
INFECTION
Nonimmune RATE Immune
Susceptibles \ Susceptibles|
<morbidity>
total
susceptibles
J
Figure 1. Diagram of the infection rates
Vaccinated
Population
infection index
Total Infected
VACCINE
EFFICACY
incidence
index
Figure 3. Infection index
INITIAL
VULNERABLE
POPULATION
sickness index
Total Cases
Results
In figure 3 we show the result o the simulation. Among nonvaccinated cases in a
population with a 85% coverage of vaccine the rate of meningococcal disease is double
than that occurring in a population where no vaccination has been introduced. This
proportion are maintained for contact rate up to 0.5, duration of carrier state up to
10months, epidemic attack of 1 per day per 100 days.
Graph for incidece index
0.04
0.03,
0.02
0.01 ZL
0
0 10 20 ««30:=«40'—sS—sis—sia 8
Time (day)
incidece index : vaccinated
incidece index : non vaccinated
Conclusion
With the assumption taken in this model we find that the risk of those that do not
accept vaccination or are not reached by the vaccination campaign doubles when the
vaccination coverage is high. In the examination of the data from two experiences of
massive vaccination we found similar results. This renders robustness to our findings.
However, epidemics models are very complicated to reproduce. The model of diffusion
produces a number of cases way over the reality even for a very low contact rate. This is
because of the mechanics of contact and the ecology of the bacteria. Modelling the last is
complicated.
The decision to perform vaccination against meningococcal disease must be
presided by an analysis of cost/benefit . The public health authorities must decide how
much they want to spend for each year of life saved. The benefits will be higher when the
rate of disease is higher. Once vaccination is adopted as a public health measure, the
objective should be to accomplish a high coverage, not only in order to benefit the most
and in this way to control the epidemic, but also not to increase the risk of those that do not
get to be vaccinated. We think that in case the vaccination strategy is adopted, the public
health authorities should inform of all the risk and benefits of complying and not
complying with the recommendation. With most of vaccines, herd immunity protects those
not vaccinated, therefore they are at lower risk that if no vaccination campaign has taken
place. But with meningococcal vaccine the risk of non vaccinated is increased. In this
sense, an emphasis should be putted in informing the population of the risk of non
accepting vaccination when the coverage is high.
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