# An agent-based epidemics simulation to compare and explain screening and
vaccination prioritisation strategies

Carole Adam (Univ. Grenoble-Alpes  LIG  Grenoble  France)
and Hélène Arduin (UMR IDEES  CNRS  Rouen  France<EMAIL_ADDRESS>
###### Abstract

This paper describes an agent-based model of epidemics dynamics. This model is
willingly simplified, as its goal is not to predict the evolution of the
epidemics, but to explain the underlying mechanisms in an interactive way.
This model allows to compare screening prioritisation strategies, as well as
vaccination priority strategies, on a virtual population. The model is
implemented in Netlogo in different simulators, published online to let people
experiment with them. This paper reports on the model design, implementation,
and experimentations. In particular we have compared screening strategies to
evaluate the epidemics vs control it by quarantining infectious people; and we
have compared vaccinating older people with more risk factors, vs younger
people with more social contacts.
Note: This paper is an extended version of a conference paper presented at
ISCRAM 2022 [1].

###### keywords:

Agent-based modelling and simulation, epidemics modelling, screening,
vaccination, contacts, scientific mediation

##  1 Introduction

The COVID-19 epidemics has now been lasting for over 2 years since the first
cases in late 2019. The only control strategy for the first year was general
lockdowns, but was hard to maintain longterm for economical and mental health
reasons. In a second phase, when tests became available, the new strategy was
to start large screening campaigns and to isolate (detected) sick individuals.
Vaccines have then become available in December 2020, and have allowed to lift
most constraining sanitary measures.

However, with the epidemics lasting longer than expected and its end being
hard to predict, people are tiring out, sanitary measures are not always well
accepted, trust goes down [33]. Fake news circulate with deadly consequences
[27], such as refusing or hesitating to get the vaccine [12, 22]. We believe
that it is very important to inform the population and explain the mechanisms
of the epidemics and the reasons behind all measures [28]. Indeed,
understanding constraints will improve their acceptability.

We claim that an interactive simulator is a good tool to explain mechanisms by
letting users play a role and learn by exploring what-if scenarios. We have
therefore designed an agent-based model that allows to simulate various
screening and vaccination strategies on a virtual population, and to compare
these strategies in order to discover insight about their optimal parameters.
It is simple and interactive, and users from the general population can play
with it in order to understand the complex mechanisms behind the epidemics and
the reasons for the various sanitary measures. This work is part of a larger
initiative aiming at answering questions from the general public about the
COVID-19 epidemics, through interactive simulators along with explaining texts
written by researchers from various disciplines [11].

##  2 Challenges of screening

This section introduces some useful background about screening, quality
features of tests, and possible prioritisation strategies for allocating a
limited number of tests.

###  2.1 Lockdowns and screening

When lifting the lockdown after the first COVID-19 wave in spring 2020, the
main goals of many countries around the world were to get back to a less
restricted way of living while still maintaining the epidemic under control to
avoid a ”second wave”. Indeed, due to the low circulation of the virus during
lockdown, herd immunity was still insufficient to prevent a rebound and new
wave. For instance, it was estimated111by Pasteur Institute:
https://www.pasteur.fr/fr/espace-presse/documents-presse/modelisation-indique-
qu-entre-3-7-francais-ont-ete-infectes that only 3 to 7 % of the French
population had been exposed to the virus (and was therefore immunised) when
exiting the first French lockdown in May 2020. And as time has since proved,
not only a second wave, but several more epidemics waves appeared, pushing
some countries to enforce other lockdowns.

But the general lockdown is hard to maintain on the longterm for both
psychological and economic reasons [3], and is hard to lift without creating a
new wave since herd immunity does not develop during lockdown. One solution is
to selectively isolate only sick individuals. However, this strategy is hard
to implement efficiently. Indeed, the COVID-19 incubation time is long (a week
on average, but sometimes up to 20 days), so infected people have time to
infect their contacts before they are detected and quarantined. Besides, the
share of asymptomatic cases was still mostly unknown, but estimated to be
around 30% [35], meaning many infected people could unknowingly spread the
virus among their contacts.

This implies that governments could not rely entirely on symptomatic displays
to isolate infected people, but needed to test their population broadly by
running large scale screening campaigns. This is precisely the strategy
recommended by the World Health Organisation (WHO), as early as the 16 March
2020222https://www.who.int/dg/speeches/detail/who-director-general-s-opening-
remarks-at-the-media-briefing-on-covid-19---16-march-2020 : to test any
suspicious case to confirm potentially infected individuals; to trace their
contacts in order to identify chains of contamination; and isolate only
(potentially) infectious people. But it took time to develop reliable tests
and start this strategy.

###  2.2 Quality of tests

There exists different types of tests to detect the SARS-COV-2 virus
responsible for COVID-19, in particular PCR (polymerase chain reaction) tests,
serological tests, antigenic tests, and auto-tests that one can realise at
home. These tests have different levels of quality, depending on 2 factors:

  * •

Sensitivity of a test indicates the probability that the test is positive when
the tested person is really sick. A 100% sensitive test applied to a sick
individual will always return positive; therefore a negative test gives
absolute certainty that the tested individual is indeed not sick. In other
words, there are no false negatives with a 100% sensitive test; so sensitivity
is the proportion of true negatives.

  * •

Specificity of a test indicates the probability that the test is negative when
the tested person is really not sick. A 100% specific test applied to a non
sick individual will always return negative; therefore a positive test gives
absolute certainty that the tested individual is indeed sick. In other words,
there are no false positives with a 100% specific test, so specificity is the
proportion of true positives.

However, it is impossible to design tests that are perfect on both criteria
(or even on a single one). Screening tests always have an error margin. In
particular, screening tests cannot be both highly specific and highly
sensitive, so a compromise must be found between two opposites:

  * •

Very sensitive tests are more likely to be positive with sick individuals:
this reduces the rate of false negatives, so prevents missing infected people
who keep moving around instead of being quarantined;

  * •

Very specific tests are less likely to be positive when the individual is not
sick: this reduces the rate of false positives, to prevent from quarantining
healthy people.

The first screening tests designed for COVID-19 were relatively specific (in
the range of 95 to 98% of true positives) but still little sensitive
(sometimes up to 30 to 40% of false negatives, sick but not detected by the
test). As a result, it was sometimes necessary to do a second test to confirm
a negative test result.

###  2.3 Screening objectives

Time was needed to develop reliable quality tests and increase testing
capacity. As a result, testing kits were rare at the start of the epidemics,
forcing governments to prioritise who should be tested first to optimise the
impact of the testing campaign. Even nowadays, when testing kits are widely
available, and as new variants of the virus circulate very fast, the number of
daily tests has exploded, posing a new issue of financing those tests. Some
countries therefore again choose to restrict tests to some categories of
people, for instance, the elderly who are more at risk of serious forms, or
people with symptoms. Other countries require non vaccinated people to pay for
the tests, also in order to limit the number of tests performed.

Screening tests actually pursue two main (partly contradictory) goals.

  * •

The first one is to control the epidemics, by spotting infected people and
isolating them to break contamination chains.

  * •

The second one is to know the epidemic, _i.e._ evaluate as precisely as
possible the total number of people infected at a given time, and deduce the
actual case fatality rate.

These goals involve different screening strategies: in order to best control
the epidemics, one should test in priority people who are more likely to carry
the virus, but this leads to an over-estimation of the global circulation; to
best know the epidemics, one should randomly test a representative sample of
the global population, but this will lead to a large number of negative tests,
failing to isolate many infected people. The best screening strategy is
therefore not intuitive.

###  2.4 Screening prioritisation strategies

Under the constraint that testing kits are in limited supply, governments want
to prioritise wisely who should be tested, in order to reach both goals with
the minimum amount of tests. For instance, France started testing late and
slowly333https://www.usinenouvelle.com/article/en-retard-la-france-monte-en-
puissance-pour-les-tests-de-diagnostic-du-covid-19.N945261 : it took some time
to design reliable tests, and the small number of such available tests was
thus limited to healthcare workers and people at risk. Nowadays, tests are
widely available and are the most cost-effective mitigating measure [30], but
some countries start restricting them again in order to limit the financial
cost for society, for instance, by reserving them to elderly people, or by
asking non-vaccinated individuals to pay for the tests.

The various possible targeting strategies have different impacts on both goals
stated above:

  * •

Random targeting consists in choosing randomly people who should be tested.
This is a more representative sample of the population, and provides better
knowledge of the current state of the epidemics. But when the incidence of the
virus is very small (as it was after the first lockdown), the proportion of
people infected is very low, so most tests will return negative. There is
therefore a risk of ”wasting” many tests, _i.e._ the chances of finding
infected people to isolate them and control the epidemics are low.

  * •

A solution is to target suspicious cases (the symptomatic ones), but this
strategy is insufficient to control the epidemics since it ignores all the
(also contagious) asymptomatic cases. Besides, the sample is not
representative of the general population, and the high proportion of positive
tests in the sample might lead to overestimate the global circulation of the
virus.

  * •

Another strategy consists in targeting people who work outside of home, since
they are more likely to get infected and/or infect others. For instance, at
the beginning of the epidemic, healthcare workers were tested in priority,
since they were the most exposed to the virus; in order to reopen schools,
there was also a focus on testing teachers, school workers, and now all the
children from the same class as an infected pupil. This strategy focuses on
controlling the epidemics while allowing for economic activity, but it ignores
contaminations that happen outside of work (shopping, leisure…).

  * •

Finally a last interesting strategy consists in targeting high-risk people.
Their profile is now better known, in particular elderly people or people with
comorbidities [23]. The goal of this strategy is to detect infection soon and
treat them early to prevent serious complications. But the results would then
not be representative of the global circulation of the epidemic in the general
population.

The choice is not intuitive, and we claim that simulation can help compare
different strategies in order to draw interesting insight. Indeed, simulation
allows to run the exact same scenario with only the parameters of the
screening campaign varying, which is impossible in reality, and to compare
estimations with the ”real” epidemic curve, which can be known only in a
simulation.

##  3 Challenges of vaccination

Vaccines became available in December 2020, and many different ones are now
available. This section provides some useful background related to our model.

###  3.1 Vaccination

The goal of vaccination is to provide people with some level of immunity
against the virus, that will protect them from infection, and ultimately to
create collective immunity at the level of the population to stop further
propagation of the virus. The impact of the vaccination campaign can be
measured on different indicators: the height of the epidemic peak (how many
people are sick at the same time at the peak), the duration of the epidemics
wave (how long it takes before nobody is sick anymore), the total number of
people who got sick, the total number of serious cases, the number of people
in hospitals, or the number of deaths. The efficiency of a vaccine can be
defined on different terms [19], such as reducing the risk of infection, the
severity of the disease, or the duration of infectivity. A vaccine can have
different levels of efficiency on these different aspects. It was initially
hard to know exactly which factor was impacted by the vaccine: its effect on
infection was tested by trials before release, but it was not clear if it was
also effective on transmission [26], on asymptomatic forms [8] or on the risk
of serious forms. Governments sometimes made simplified statements to
encourage people to get the
vaccine444https://www.liberation.fr/checknews/transmission-du-covid-19-les-
autorites-ont-elles-menti-sur-lefficacite-du-vaccin-pour-justifier-les-pass-
sanitaire-et-vaccinal-20221014_JEAR5KU73RFNTPRDWQCLHSNZQE/ . The efficiency of
the vaccine has also decreased against the new variants of the virus [7].

###  3.2 Individual vulnerability

Literature has shown that infections and serious forms are more frequent in
people with risk factors, in particular those aged above 60 [31] and/or having
comorbidities (often associated with age) such as diabetes or chronic
illnesses [14, 6, 15].

Literature also shows that younger people have more contacts in average than
older people. For instance [21] studied influenza in Japan and showed
difference in contact patterns based on age, gender, as well as during the
week vs holiday. [5] also study the role of contacts with people of different
age groups; they conclude that the case growth rate increases when there is
more contacts with elderly people, but decreases with contacts among the same
age group.

###  3.3 Vaccine prioritisation strategies

The first vaccine against COVID-19 was released in December 2020. Developed
countries invested a lot of money to secure enough doses for their population,
but the production and injection of millions of doses takes time. Furthermore,
the immunity conferred by the vaccine only lasts for a few months [13], so it
is necessary to inject boosters regularly. As a result, governments are faced
with a choice about who should be vaccinated first:

  * •

Vaccinating in priority people with comorbidities (elderly people or people
with other health factors increasing their vulnerability), in order to protect
them from serious forms of the illness;

  * •

Vaccinating in priority people with more contacts (such as health workers who
are in contact with many sick or vulnerable people, teachers, or younger
people who have more social contacts), in order to reduce the global
transmission of the virus.

  * •

Randomly vaccinating the entire population, without any order of priority.

Similar to screening, the optimal strategy is not intuitive since different
strategies improve different indicators. One might reduce the number of
serious forms but leave many younger people exposed, or reduce the total
number of contaminations to prevent saturation of the healthcare system but
take the risk of more serious forms among vulnerable people. Therefore, once
again simulation could help in testing strategies by varying their parameters
in isolation.

##  4 Agent-based simulation of epidemics

###  4.1 Goal of this work

One can see from the background above that finding the best (screening or
vaccination) strategy on all accounts is not easy by using only intuition. We
claim that simulation can help by allowing us to compare different strategies
and to measure their effects. In particular, simulation will allow us to run
the exact same scenario several times, with only selected parameters
(prioritisation strategy, etc) varying, which is impossible in reality. In
this section we discuss existing simulations of the COVID-19 epidemics,
mitigating interventions in general, and screening and vaccination in
particular. The main measures against COVID-19 have been quarantine, contact
tracing, screening, and isolation; there is no consensus on best practices,
and countries differ in their approach, but a survey of medical publications
[18] shows their efficiency, in particular when combined together. It is hard,
however, to compare their efficiency in real life since their individual
impact cannot be isolated, but simulation can help comparing them ”in silico”.

###  4.2 Advantages of simulation

Computer simulation has many benefits in the context of the crisis management
in general, and the current epidemics in particular. Indeed, only simulation
allows to compare different intervention strategies, all other things being
equal. In the real world, we can only compare between different countries
applying different strategies, but they also differ on other regards: climate,
culture, etc, that all might influence virus spread, so it is impossible to
isolate the precise impact of the strategy being evaluated. But in the
simulated world, we control all parameters, and repeat the exact same
experiment with only the strategy changing, in order to evaluate its impact
independently of all other factors.

Besides, in this work, we are interested in evaluating screening strategies
and their efficiency to assess and control virus spread. In the real world,
there is no way to access the actual number of infected people (unless we
could simultaneously test the entire country), so it is impossible to evaluate
how good the curve estimated from the tests is compared to the ”real” curve.
On the contrary, in a simulation we know the epidemiological status of all
agents, so we can access the _real_ (simulated) epidemic curve, and compare it
with estimations obtained from various screening strategies. Simulation is
therefore a great tool to assess screening strategies on a virtual population.

###  4.3 Approaches to epidemics simulation

As a result, a lot of models of the COVID-19 epidemics have been published in
the last 2 years. Current epidemic models mainly fall in two approaches.

Compartmental models divide the population in a number of epidemiological
classes. The simplest ones (often shortened as SIR models) use only 3
compartments: Susceptible (not yet infected so not immune), Infected (and
contagious), Recovered (and immune). The hypothesis is that recovered
individuals are then immune and cannot get infected again, which has proven
wrong for COVID-19. Compartmental models of COVID-19 have often integrated
more compartments, such as Asymptomatic or Hospitalised, in order to more
precisely represent the dynamics. These models then rely on the mathematical
resolution of differential equations to give a macroscopic view of the
epidemic dynamics. It is therefore quite fast and scalable.

Agent-based models model each individual as an autonomous agent, in order to
give a microscopic view of the situation. Agents are heterogeneous,
initialised with different values of their attributes, such as age, gender,
comorbidities, or social behaviour. This allows to model the influence of
individual decisions on the virus spread, such as a refusal to get vaccinated,
or not respecting social distancing. These models are more complex to
initialise as they require behaviour data that is hard to get, and are less
scalable since they require to compute the behaviour of each individual agent.
However, they are more precise, in particular to study why a specific
individual got infected.

Both approaches have their benefits and drawbacks depending on the goal and
scale of the simulator. Our goal being to explain the complex mechanisms
behind the epidemics rather than predicting its spread at the scale of the
country, we chose an agent-based approach. We survey various existing agent-
based models in the next paragraphs.

###  4.4 Simulations of interventions

A very early report (March 2020) about the results of an epidemiological
modelling informed the first policy-making in the UK and other countries [16],
leading to general lockdown. At that time, in the absence of a vaccine, they
assessed other non-pharmaceutical interventions to reduce contacts in the
population and therefore virus transmission, with 2 main possible strategies:
mitigation aiming only at slowing down the epidemic spread, vs suppression
aiming at completely stopping it. Their results showed that optimal mitigation
policies might reduce the pressure on healthcare system by two thirds and
deaths by half, but might still result in hundreds of thousands of deaths and
overwhelmed healthcare systems. Therefore they suggest that where possible,
countries should aim at suppressing the epidemics rather than just mitigating
it, which would require a combination of several very constraining measures
(quarantines, distancing, school closures) despite their negative side
effects. Besides, they predict that such measures would need to be maintained
indefinitely (or until a vaccine is found) to prevent a rebound as soon as
they are relaxed. Not knowing if such suppression can be maintained on the
long-term, or how to reduce their social and economic costs, they also suggest
intermittent measures: closely monitoring the epidemic progression to
temporarily relax measures, but re-instantiate them when needed. This is
similar to what happened around the world in the past 2 years.

Other countries have also developed simulators to help policymakers. For
instance, COMOKIT [17] is a framework composed of several realistic
spatialised agent-based models of the epidemics and of various interventions,
aiming at informing public health decisions made by the Vietnamese government.
These models have also been applied to towns in other countries, such as Nice
in France [10]. The models run on the GAMA platform. They can be fed from
various data sources, provided by the Vietnamese government (census data,
epidemiological data) or by private actors (Facebook data, mobile phone data).
They have been used to quickly compare potential strategies (lockdown at
different scales, quarantines), as well as to suggest optimal timing or
combination of multiple strategies. The models offer a precise representation
of the population and of contamination in closed spaces (shops, schools)
although they neglect the role of transportation. They are very complex models
aimed at guiding policymakers, rather than informing the general public.

Covasim [24] is an agent-based model of the epidemics that can be tailored to
various local contexts (_e.g._ age distribution, daily contacts, epidemic
progression in number of reported cases and deaths) and has been actually used
in a number of countries. It allows to test several types of interventions:
physical (_e.g._ lockdown), diagnostic (_e.g._ screening or contact tracing),
or pharmaceutical (_e.g._ vaccination). However, it is targeted at researchers
and policy makers rather than the general public, and as such is much more
complex than our intended simulator. Moreover, testing strategies are
expressed in terms of probabilities of testing people with or without
symptoms, in/out of quarantine, or over a certain age; it does not include
other interesting strategies such as random sampling or prioritising essential
workers.

###  4.5 Simulations of testing

Various models have specifically studied different screening strategies. For
instance, [29] modelled several scenarios regarding the measures needed for a
safe re-opening of US colleges. They modelled 5000 students, of whom 10 were
infected at the start of the semester, and tested several epidemic scenarios
(with reproductive numbers values between 1.5 and 3.5, a 0.05% fatality rate,
and a 30% probability of showing symptoms when infected). They varied the
following parameters of screening: frequency (every 1, 2, 3, or 7 days),
sensitivity of tests (between 70 and 99%), specificity of tests (98 to 99.7%),
and cost (10 to 50 dollars per test). They conclude that it is best to screen
frequently (every 2 days) in addition to strict observance of sanitary
measures to keep the reproduction number under 2.5. In order to limit costs,
they also show that even a rapid, less expensive but poorly sensitive test
(around 70%) is sufficient to control the number of infected students, who are
isolated in a dedicated dormitory (within an 8h delay). Of course this
strategy is not applicable at the scale of a country (not enough medical staff
to test the entire population every 2 days). The population of a college
campus is also not representative of the general population, and in particular
is younger so less exposed to serious forms.

[4] focus on the economic benefits of testing. They provide an SIR model of
the US population with 5 age groups, working in various economic sectors.
Their study shows that the economic benefits of rapid screening programs far
exceed their costs, with a ratio between 4 and 15 (excluding the monetised
value of lives saved) depending on the parameters of the screening. However,
an interesting aspect of their study is that they consider a variable
adherence to quarantine measures, depending on the probability to be a false
positive: They conclude that tests used must be highly specific, or combined
with a confirmatory test, in order to both reduce the cost of having healthy
workers in quarantine, and decrease the number of people who break quarantine
because they (wrongly) believe they are a false positive.

To conclude, models that include testing as an intervention generally focus on
controlling the epidemics: testing is part of the testing, tracing, isolating
strategy recommended by WHO. On the contrary, we want to compare testing
strategies with respect to 2 different objectives: not only controlling the
epidemics by appropriately isolating infected individuals, but also precisely
estimating the current state of the epidemics (number of cases), which is
useful to evaluate the impact of current measures and the necessity to adapt
them.

###  4.6 Simulations of vaccination

Finally, other models focus on the impact of a vaccination campaign. This is
relevant as vaccination poses a similar problem of prioritisation for the
allocation of a limited number of doses, but also an additional problem of
compliance, or trust: some people might not want to get vaccinated, for
various reasons [20].

For instance, [25] modelled a nation-wide vaccination campaign in the USA.
They varied parameters such as vaccine efficacy or population compliance, and
tested 6 scenarios combining a vaccination campaign with other interventions
(distancing, etc). Their results show that the vaccine significantly reduces
infections, even with very low population compliance. However, they also show
interesting counter-intuitive results: when compliance is very high, and since
the older population is vaccinated first, the delay is longer for younger and
more connected individuals to access the vaccine; as a result, the virus
spreads more than if the compliance was lower. This also proves that the
vaccine alone is not sufficient, and should be combined with other
interventions to reduce the spread of the epidemics.

Other studies are concerned with prioritising the vaccines. [34] simulate
different prioritisation strategies with a limited supply of vaccines, in a US
urban region of 2.8 million residents. They show a limited impact of
vaccination on reducing viral spread, mainly due to exponential contaminations
before the start of vaccination, meaning that lots of adults were already
immunised. Consequently, they suggest that vaccines should be distributed as
fast as possible among all eligible adults after vaccinating the most
vulnerable, to improve the speed of the vaccination campaign, rather than
strictly respecting a priority schedule. The study of [36] compares age-
related vaccination strategies in 3 countries; the authors find that
vaccinating younger people first allows to reduce the number of infections,
while vaccinating elderly people first reduces the number of deaths.

The results of both these studies are consistent with the findings of [25].
Besides, these studies also show the interest of simulation to reveal
unexpected and unintended consequences of potential sanitary policies, that
cannot be tested in real life.

###  4.7 Summary

Not many models specifically focus on comparing various screening strategies
to both evaluate and control an epidemic. This can be explained by the now
wide availability of testing kits in developed countries, that allow to
massively test the entire population. Nevertheless, such work is still
important to explore screening strategies in countries where tests are not yet
widely available, or to reduce the cost of screening, or for potential future
epidemics. Such a model can also be extended to comparing the allocation of
other limited resources, such as the vaccine doses.

In this paper, we present a model for comparing strategies of priority for the
allocation of testing kits and of vaccine doses. Our model does not aim at
predicting the exact evolution of the epidemics for deciders, but rather at
explaining the mechanisms to the general public. It does so by letting users
interact with the simulated population and take on the role of public health
deciders to select the parameters of a screening strategy or a vaccination
campaign. The originality of our work is to target the general public and
focus on explaining a complex phenomenon, unlike most models that are targeted
at governments to help them make decisions.

##  5 Our model for screening strategies

As explained above, our agent-based model is quite simple since it is targeted
at the general population, and its goal is not to predict the evolution of the
epidemics, but to explain its mechanisms.

###  5.1 Characteristics of the population

We have modelled a population of 2000 individuals, distributed in several age
categories. This influences their sensitivity to the virus (older people have
more risk to be symptomatic) as well as their mobility. For instance, 50% of
people aged 20 to 65 have work outside their home (’essential’ workers)
whereas the rest stay at home (remote work, furloughed workers, family carers,
etc.). People aged less than 20 and over 65 are considered homebound (by
respectively remote schooling and retirement). Individuals in our population
can be in one of five distinct states regarding the virus, as shown in Figure
1 below:

  * •

Susceptible: they have never been infected and are therefore not immune either

  * •

In incubation: they have been infected but are not yet sick (it lasts 6 days
on average)

  * •

Asymptomatic: they are sick but display no symptom. Only a test will reveal
them (30% of patients below 65 years old, for an average of 21 days)

  * •

Symptomatic: they are sick and display symptoms. (70% of patients below 65
years old, and 100% of older patients, for an average of 21 days)

  * •

Recovered: they are immune and cannot get infected again (this was a
hypothesis of our model, at a time when this was unknown [32]; we now know
that reinfection after recovery or vaccine has a lower risk but is still
possible [9]

Figure 1: Evolution of epidemiological status of agents

When they move in the simulation world, individuals can come into contact with
one another. Infected people (in incubation, asymptomatic and symptomatic) are
all contagious and can therefore transmit the virus to susceptible people they
are in contact with. Individuals working from home do not move but they can be
in contact with people passing by their home (deliveries, postal services,
etc.). However, they have less contacts on average than people who have to
work outside of home.

In order to reduce the spread of the virus, people who tested positive are put
into quarantine and are completely isolated: they cannot transmit the virus
any further.

###  5.2 Testing strategies

In our model, we simulate tests with both a sensitivity and specificity of
90%. It would be interesting to vary these 2 parameters in future work, to
study their impact on the evaluation of the epidemic curve. Our goal is to
find out how we can best use the tests available each day to reach the two
main objectives of a massive testing campaign: to monitor the epidemic
(optimise fit between estimated and ”real” curve) and to control it (minimise
the epidemic peak). The screening campaign has the following attributes:

  * •

The number of tests available each day. The testing strategy of the French
government plans for 5 to 700.000 tests per week, which corresponds to about 2
to 3 tests per day for our 2000 agents;

  * •

The triggering time for testing, defined in terms of a threshold X for the
proportion of symptomatic people: when more than X% of the population is
symptomatic, the testing campaign starts;

  * •

The target population being tested, among: random sampling; symptomatic
people; elderly / at-risk people; or people working outside of home.

###  5.3 Interactive simulator

Figure 2: Interface of the online simulator

Our simulator is implemented in Netlogo and playable online555Covprehension
question 17: https://covprehension.org/en/2020/05/12/q17.html. Fig 2
illustrates its online interface. The user plays the role of a public health
decider with several goals:

  * •

To minimize the total number of tests used;

  * •

To minimize the spread of the epidemic, _i.e._ the total number of people
infected;

  * •

To minimize the number of people quarantined for no reason, _i.e._ the number
of false positive tests;

  * •

To estimate as closely as possible the “true” curve in order to precisely
monitor the epidemic over time;

To reach these goals, the user can modify the parameters of the testing
campaign as defined above:

  * •

The number of tests available each day (_i.e._ time necessary to test the
entire target population);

  * •

The starting date of the testing campaign: immediately from the start of the
epidemic, or later on;

  * •

The target population: in-person workers, elderly, random, symptomatic.

These goals are obviously not always compatible, and actions can have opposite
effects on different goals, improving one at the cost of failing another. For
instance, to best know the status of the epidemics, one could test every
citizen but would fail to minimise the number of tests used; or one could
randomly test people to get a representative picture of the situation, but
would then “waste” many (negative) tests that fail to spot and isolate
infected people. Managing the situation thus requires finding some compromise.
We expect that playing with the simulator will help people understand the
stakes behind the sanitary measures, and make them less subject to blindly
believing disinformation. This will require future experiments of our
simulator with users to test its actual impact.

In the following section we describe the experiments that we ran by manually
varying the different parameters (target population, number of tests per day,
and starting date), and we compare how well they estimate the ”real” curve,
which the simulation allows to know.

##  6 Screening experiments

###  6.1 Inference of the epidemic curve

There are several ways to compute the estimated curve from the results of
screening tests. The number of confirmed cases communicated every day by the
authorities of different countries is a combination of test results and
expertise of health professionals. But like any statistical estimation, these
figures have error margins and potential biases. We believe that the general
public should be aware that the “true” number of infected people is unknown
and can only be approximated. It is one goal of our simulator to allow them to
observe these variations and errors.

Indeed in our simulator we know the status of all of the agents, so we do know
this ”true” number of infected agents over time, which is impossible in
reality. We can therefore compare the curve estimated using tests, with the “
_true_ ” curve, in order to verify the correctness of the estimations obtained
with different strategies. This is a great advantage of agent-based
simulation, which will allow us to evaluate how well different computation
methods do fit this real curve. We have actually tested two simplified
estimation methods, described below: proportionality, and predictive values.

####  6.1.1 Proportionality rule

First, we could intuitively use a simple cross multiplication: the number of
positive tests among the total number of tests provides an estimation of the
proportion of cases in the general population, by a proportionality rule. For
instance, if we test 700000 people and that 1000 of them are infected, this is
a proportion of 0.14%, so we deduce that out of the 70 millions residents of
France, 100000 are infected. But this simple proportionality rule does not
work well in epidemiology, especially when the number of people tested is low,
or when the prevalence of the epidemic (_i.e._ the total number of cases at a
given time) is too low, as is the case at the beginning and at the end of an
epidemic, or when tests are not entirely reliable.

####  6.1.2 Predictive values

Another method for estimating the total number of infected people is to
compute the predictive values of the test, which depend on three elements: the
prevalence of the epidemic, the rate of false positives (which is equal to
$1-specificity$, with specificity being the probability that a positive
individual receives a positive test), and the rate of false negatives (equal
to $1-sensitivity$, since sensitivity is the probability that a negative
individual receives a negative test) obtained with the test. The positive and
negative predictive values are not intrinsic to the test (unlike true positive
rate and true negative rate), and do not concern a single individual but a
population, so they also depend on the prevalence of the epidemics in this
population (_i.e._ the probability that an individual is positive).

The positive predictive value (PPV) is also called precision. Its complement
is the false discovery rate, _i.e._ the rate of false positives among the
total of positive tests.

$PPV=\frac{sensi*preval}{sensi*prev+(1-specif)*(1-preval)}$ (1)

The negative predictive value (rate of true negatives in total negative tests)
is the complement of the false omission rate (rate of false negatives upon
total negative tests).

$NPV=\frac{specif*(1-preval)}{specif*(1-preval)+(1-sensi)*preval}$ (2)

The following paragraphs describe our experiments on a simulated population of
2000 agents, exploring different scenarios by varying the different parameters
of the screening campaign.

###  6.2 Comparison of estimated cases for the different samples of population

In this scenario we choose a daily number of tests equivalent to that of the
French government (_i.e._ 3 tests for 2000 individuals) and start testing as
soon as the first case appears (which has not been the case in France).

We compare the curves representing the number of cases estimated by the
proportionality rule (in red), the number of cases estimated by computing the
predictive values (in blue), and the “true” number of cases (in black), for
each sampling strategy (testing priority among: random, elderly / at-risk,
workers, symptomatic). Figures 3 summarises the results.

(a) Random sample

(b) Symptomatic sample

(c) Elderly sample

(d) Workers sample

Figure 3: Experiment 1: 3 tests/2000, immediate start, different samples

Firstly, we note that the blue and red curves (estimated cases) vary a lot
more than the black curves (“true” cases). Indeed, they depend on the number
of positive tests each day, which varies greatly depending on who is tested.
In general, we choose to “smooth” this estimation by computing the mean result
of tests over several days (here, a mean over 7 days), but there is always a
larger variability depending on who is tested each week. For example, a lot of
negative tests may result in an estimation of a decreasing epidemic which is
not necessarily true (maybe we just tested non-infected people, which does not
mean that no one is sick anymore).

We also note that the blue curves (with predictive values) are better
estimators than the red curves (proportionality rule), especially at the
beginning and at the end of the epidemic when the prevalence of the virus is
low, and especially for symptomatic people, who are less representative of the
total population.

Secondly, we find that the worst estimation happens when we only test
symptomatic people (top right figure): since we only test symptomatic people,
who therefore have a high probability of being infected by COVID-19, we obtain
a high positivity rate of the tests, so we overestimate the “true” number of
cases in the general population. Given that the tests we model are diagnostic
ones, it is really not sound to extrapolate the number of cases in the general
population from the tests performed on symptomatic people. The model confirms
this. Such tests allow to control the epidemic by confirming and isolating
infected people, but they do not allow to monitor its spread in the
population.

###  6.3 Comparison of estimated cases _w.r.t._ the number of daily available
tests

In a second experiment, we set the strategy to random sampling, and the
beginning of the testing campaign as soon as the first case appears, and vary
the number of daily tests from 3 tests per 2000 people (left), to 6 tests per
2000 people (middle) and finally 9 tests per 2000 people (right). Figure 4
illustrates the resulting estimations of the epidemics curve, only with the
predictive values method since it is better than the proportionality method.

(a) 3 tests / 2000 people

(b) 6 tests / 2000 people

(c) 9 tests / 2000 people

Figure 4: Experiment 2: immediate start, random sample, varying number of
daily tests

We notice that the higher the number of tests, the better the estimation of
the number of cases in the general population. After an initial
overestimation, when there are very few cases in the population and very
little tests performed, the reconstructed curve follows rather precisely the
actual epidemic curve, in particular around the peaking time, the key moment
of the epidemic.

###  6.4 Comparison of estimated cases _w.r.t._ activation date of testing
campaign

In this final experiment, we use the random sample again, and vary the
starting date of the campaign as well as its intensity, in terms of the number
of daily tests performed. The lower intensity, 3 tests/2000 people,
corresponds to the initial strategy in France, when the number of available
kits was still quite low. The objective of this experiment is to assess how
well we can estimate the _”real”_ epidemic curve, by either starting screening
very early, or performing it at a very high intensity, or both. Figure 5 shows
the results of the 4 different combinations of parameters.

(a) Immediate start but low intensity
(3 tests/2000)

(b) Immediate start with high intensity
(9 tests/2000)

(c) Late start with low intensity
(3 tests/2000)

(d) Late start with high intensity
(9 tests/2000)

Figure 5: Experiment 3: random sample, varying starting date and intensity of
the testing campaign

We notice that with a low screening intensity of 3 tests for 2,000 people
(first column), the reconstructed curve cannot capture the epidemic peak when
screening started late (after 15% of infections, upper left).

Similarly, if the screening campaign starts late (15% people symptomatic,
bottom figures), even increasing the number of tests to 9 per 2000 people
(bottom right), we notice that the peak identification is very uncertain, and
cases are strongly overestimated after the peak. When screening starts
immediately and intensively, this overestimation only happens when the number
of cases is very low (top right). The conclusion is that if we wait too late
to activate the testing campaign, the knowledge of the epidemic is strongly
reduced, even if we ramp up the number of daily tests.

##  7 Model of vaccination

In this section we describe the updated model including vaccination.

###  7.1 Modifications to the population model

The initial model was adapted to consider the new situation when the vaccine
became available. In particular we lifted the lockdown rules that are not
enforced anymore: concretely, individuals are not considered to work from home
anymore, but instead their mobility is now affected by other factors. Namely,
all agents have 2 more attributes, randomly initialised based on their age:

  * •

Their risk factor, which represents their probability to develop a serious
form of the illness when contaminated. Since age is a known comorbidity for
COVID-19 mortality, the risk factor attribute is set randomly as proportional
with age: most younger people have less risks to develop a serious form, even
though some of them can have a high risk; and most older people have more risk
to develop serious forms.

  * •

Their number of daily contacts, that affects the number of other agents that
can contaminate them at each step. This number is initialised with a random
individual part, plus a random part reversely proportional to age (as contacts
usually decrease with age), and minus another random part proportional to the
level of risk (as we assume people who know they are at risk will voluntarily
limit their contacts from fear of being ill).

We also added new states to the epidemic model, set as boolean variables of
the agents:

  * •

serious form: when an agent is symptomatic it has a probability equal to its
risk factor (or reduced if vaccinated) to develop a serious form. Serious
forms last longer than other symptomatic forms.

  * •

vaccinated: vaccinated agents have a lower probability (set by the vaccine
efficiency parameter) to get infected, to contaminate others, and to develop a
serious form when ill.

Finally, unlike the previous model, we now consider that the immunity
conferred by either vaccination or recovery is not permanent. We added 2
parameters for these 2 durations of immunity. Agents then return to the
Susceptible state, and their vaccinated attribute becomes false, meaning they
can be infected again, and they can be considered for vaccination again.
However, we remember for each agent the number of times they got sick, and the
number of vaccine doses they received, for statistical purposes.

###  7.2 Modelling vaccination

The vaccination campaign has the following parameters:

  * •

Start of the vaccination campaign, in percentage of infected people in the
population.

  * •

Speed of the vaccination campaign, in number of daily doses available.

  * •

Target population that receives vaccine in priority, (”high risk”, ”more
contacts”, or ”random”).

  * •

Vaccine efficiency was set to 90%, meaning that vaccinated agents have a
probability reduced by 90%: to be infected when in contact with a sick person;
to develop a serious form when infected and symptomatic; and to transmit the
virus to their contacts when infected. To simplify we consider that the
vaccine efficiency is the same on all 3 values.

  * •

Duration of immunity conferred by the vaccine, after which the agent’s status
is reset to unvaccinated.

If the proportion of sick agents in the population is above the selected
threshold, the vaccination campaign can start. The target population for
vaccination at each step is computed as follows. First, only agents that are
not infected, and not currently immune (whether from vaccination or recovery)
are considered as candidates. Then, the number of daily doses (parameter)
provides the maximal number of agents that can be vaccinated at that step.
Finally, this number of agents are selected among the candidates, in
decreasing order of the value of the attribute corresponding to the selected
strategy (daily contacts or risk factor), or randomly if so selected. This
ensures that when the agents with the highest priority are already vaccinated,
the following agents in order of priority can also access vaccination.

###  7.3 Vaccination strategies

We defined three vaccination strategies in our model:

  * •

Randomly targeting non-vaccinated, non-sick agents.

  * •

Higher risk first: targeting people with the highest level of risk first, and
then in decreasing order of risk. This is the most used strategy where elderly
people or people with comorbidities are vaccinated first.

  * •

Higher contacts first: targeting people with the highest number of daily
contacts first, and then in decreasing order of daily contacts. This is partly
applied when vaccinating medical staff first since they are exposed to many
sick or vulnerable people. Our literature review discussed several simulation
showing the efficiency of this strategy.

###  7.4 Interactive simulator

Figure 6: Screenshot of the online vaccination simulator

We implemented this new model in Netlogo666The model code and simulator are
available online at: http://nausikaa.net/wp-
content/uploads/2022/10/virus2-vaccine-web-en.html.. The interface is rather
similar to the previous simulator, but we have replaced the testing parameters
with vaccination parameters. Our goal was to keep the interface simple enough,
and not lose the user with too many different parameters. The fewer parameters
there are, the easier it is to measure their individual impact. The user can
select when to start the vaccination campaign, how many vaccines are available
per day, the duration of immunity, and the target population. A number of
graphs and monitors let them observe the results of their choices. Figure 6
shows this interface. We have also added 2 buttons:

  * •

One button allows to randomly introduce a sick individual. This allows to
simulate people arriving from the outside, who can possibly bring back the
virus when the epidemics is locally controlled.

  * •

One button allows to start/stop a lockdown: all agents stop moving until the
lockdown is lifted. This allows to simulate emergency measures when the
situation gets out of control.

##  8 Vaccination experiments

We conducted a number of experiments: first to test our model, and then to
compare various parameters of the vaccination strategy.

###  8.1 Verifying the impact of attributes

##### Daily contacts.

We first tracked infections by number of daily contacts. The ”low contacts”
category are agents with less than 4 daily contacts, while ”high contacts” are
agents with over 10 daily contacts. We tracked the percentage of agents in
each category who got infected. Figure 7 shows that people with more contacts
get infected first, and earlier than people with less contacts; but after a
while, when the incidence rate is higher, even people with few contacts get
infected as the virus has propagated to the whole population of agents. When
vaccination is on, the incidence rate is lower, so the difference is even more
visible between agents with high or low number of contacts.

Figure 7: Infections by number of daily contacts: low incidence (top) or high
incidence (bottom)

##### Risk factor.

We then tracked infections and serious forms by individual risk factor. We
considered as ”high risk” agents with a risk over 0.75, and as ”low risk”
agents with a risk under 0.25. We then tracked the percentage of agents in
each category who got infected, and who developed a serious form of the
illness. Figure 8 reports the results. We can see that there are slightly more
agents infected among the ”high risk” category, but the main difference is in
the proportion of serious forms: almost none among ”low risk” agents, but many
among ”high risk” agents. This also reflects in the width of the peak: since
serious forms last longer than other infections, the peak is larger (lasts
more steps) among ”high” risk” than ”low risk” agents.

Figure 8: Infections and serious forms per risk category

###  8.2 Verifying the vaccinations targets

Figures 9 illustrate how the mean values of relevant attributes (daily
contacts, risk factor, and age) evolve over the vaccination campaign. We
averaged those three values in the group of agents that were the most recently
vaccinated (at the previous step) as well as among the agents not yet
vaccinated.

##### Risk first.

One can see that with risk-first strategy (middle), the average risk factor of
just vaccinated agents is stable at 1 (the maximum value) for an amount of
time, requested to vaccinate all higher-risk agents. It then decreases as
agents selected to receive vaccination have a lower and lower risk. In the
mean time the level of risk of agents not vaccinated yet (and therefore still
exposed to the virus) decreases. The average age also goes down as it is
linked with a higher risk.

##### Contacts first.

When selecting agents with more contacts to be vaccinated first (bottom), one
can observe that the average number of daily contacts decreases among agents
just vaccinated, and not yet vaccinated. This means that the agents having
more contacts, and more probability to get infected and/or to infect others,
are already protected by the vaccine. We can observe that in that case the
average age of vaccinated agents increases with time: since a younger age is
linked to more contacts, younger people are vaccinated first.

##### Randomly.

The baseline is provided when vaccinating agents in random order (top). In
that case we can see that the average values of attributes is oscillating
around the mean value in the global population.

Figure 9: Vaccination targeting: random (top), risk-first (middle) and
contacts-first (bottom).

###  8.3 Comparing durations of immunity

In the following experiment, we set the duration of immunity provided by the
vaccine, or by recovering from the illness, to 40 steps. We started without
vaccination, and observed 4 successive waves of the epidemics. We then started
vaccinating with the risk-first strategy, and observed 3 subsequent waves, but
much lower than the previous ones. We manually stopped the simulation, since
the stop condition that no agent is infected anymore cannot be reached with
such a short immunity duration. Figure 10 shows the epidemics dynamics with
its 7 waves, as well as the immunity of the agents: agents that are protected
after recovering, or after getting the vaccine, and agents that are
susceptible again, despite having at least one dose of the vaccine, or one
recovery.

Figure 10: Epidemics dynamics and immunity of agents: 7 waves created with a
shorter immunity duration (40 steps), vaccinating risk-first

This immunity duration of 40 steps is very short, but in a closed environment
with no agents arriving from the outside, it is required to observe such
waves. Another option to create such waves with a longer immunity duration is
to introduce new infected agents in the simulation when the population of
agents has become susceptible again. This is what happens in real life, when
people start travelling again: even when the epidemics is locally controlled,
new individuals can arrive and bring back the virus, which restarts another
epidemics wave. We have witnessed this same phenomenon over and over again
since the end of the first general lockdown. We have therefore added a button
in the interface that lets the user add new infected agents whenever wanted.
We could also extend the model to automatically randomly introduce such
visitors from time to time in the simulation loop.

###  8.4 Exhaustively comparing vaccination strategies

##### Experimental setting

In order to exhaustively compare strategies, we ran various experiments,
varying different parameters of the vaccination campaign. We have set the
vaccine efficiency to 0.9 and immunity duration to permanent (to avoid
infinite waves and ensure simulations stop). The simulation stops when no more
agent is infectious. For each configuration, we ran 20 simulations in order to
smooth randomness, and logged the average values of 5 indicators that allow to
evaluate the efficiency of the campaign:

  * •

Duration of the simulation, _i.e._ how long it took to control the epidemics

  * •

Serious: number of serious forms, _i.e._ how many agents got seriously ill

  * •

Peak: epidemic peak as the maximal number of daily new infections

  * •

Infected: total number of agents infected

  * •

Vaccines: total number of vaccines injected

The results are summarised in the tables below.

##### Varying the strategy

In this first experiment, we set the vaccination to start at a threshold of 5%
infected agents, with 30 daily vaccines. We then varied the strategy among the
3 possible targets. Table 1 shows the resulting indicators averaged over 20
runs per strategy.

Strategy | Duration | Serious | Peak | Infected | Vaccines
---|---|---|---|---|---
Random | 122,8 | 333,25 | 47,65 | 1156,4 | 936,9
Contacts | 132,15 | 401,55 | 52,55 | 1231,05 | 1011,45
Risk | 122,3 | 192,45 | 50,4 | 1163,55 | 914,3
Table 1: Comparing 3 strategies in terms of 5 indicators

##### Vaccinating high risk first

In the next experiment, we set the strategy and varied its timing, _i.e._ the
start and intensity (number of daily doses) of the vaccination campaign. Table
2 shows the results for the ”risk first” strategy. We can observe that
vaccinating the most vulnerable people very early (before any agent is
infected, so a preventive campaign) is very effective against serious forms.
With the start at time 0 and 30 daily doses, the number of serious cases is as
low as 19.7 in average over 2000 agents. This is due to the much lower number
of infections.

When starting later, the number of serious forms is much higher since many
people would have been infected before the vaccination starts. This can be
seen through the higher values of the total number of infections, and the
subsequently lower number of vaccines injected (since recovered agents are
already immune and not considered for vaccination).

Start | Speed | Duration | Serious | Peak | Infected | Vaccines
---|---|---|---|---|---|---
0 | 10 | 132,55 | 232,55 | 56,3 | 1501,55 | 695,6
0 | 20 | 135 | 60,75 | 30,3 | 755,2 | 1408,15
0 | 30 | 125,3 | 19,7 | 14,35 | 315,85 | 1769
10 | 10 | 127,2 | 472,35 | 75,8 | 1808,85 | 308,5
10 | 20 | 124,35 | 339,45 | 71 | 1594,85 | 581,55
10 | 30 | 126,6 | 275,45 | 61,15 | 1398,25 | 793,25
20 | 10 | 128,45 | 513,5 | 74,25 | 1828,6 | 274,25
20 | 20 | 125,05 | 414,45 | 75,85 | 1674,4 | 473,4
20 | 30 | 124,2 | 344,35 | 71,65 | 1530,25 | 644,7
Table 2: Risk-first vaccination, impact of early/late start and speed of
vaccination on epidemic peak and serious forms

##### Contacts first.

The results for the ”more contacts first” strategy show that the number of
serious forms is much higher with that strategy. It also shows again that when
starting vaccination very early and fast, the epidemics can be contained to a
very low level (with an epidemic peak of only 8.8 new daily infections). The
difference in total number of infections is flagrant when starting immediately
and increasing the speed: this shows how fast the epidemic can spread, so that
going from 10 to 30 daily doses (for a population of 2000) makes an enormous
difference. This difference is less flagrant when starting too late, since
agents are already infected, as shown by the much lower number of vaccine
doses used.

Start | Speed | Duration | Serious | Peak | Infected | Vaccines
---|---|---|---|---|---|---
0 | 10 | 143,9 | 500,4 | 51,5 | 1502,35 | 778,1
0 | 20 | 145,6 | 167,1 | 17,7 | 505,5 | 1627,6
0 | 30 | 122 | 57 | 8,8 | 176,8 | 1877,25
10 | 10 | 134,8 | 619 | 75 | 1837,5 | 339,95
10 | 20 | 133,45 | 519,4 | 67,85 | 1590 | 637,65
10 | 30 | 128,15 | 443,65 | 58,25 | 1362,35 | 867,95
20 | 10 | 131,55 | 633,55 | 78,65 | 1874,25 | 275,55
20 | 20 | 128,75 | 560,85 | 71,4 | 1687,15 | 512,45
20 | 30 | 128,15 | 470,25 | 65,4 | 1463,3 | 646,7
Table 3: Contacts-first vaccination, impact of early/late start and speed of
vaccination on epidemic peak and serious forms

##  9 Discussion and conclusion

###  9.1 Summary of contributions

In this work, we have provided a simple model of the propagation of COVID-19
in a population. In a first version, we have integrated different screening
strategies to both control and evaluate the epidemic curve. The model is based
on figures available for France but is easily adaptable to other countries. It
is willingly simplified, in order to provide an interactive simulator to
explain to the general public the mechanisms of the epidemics and how the
count of infected people is estimated every day. Besides, we have also used
our simulator to compare different computation methods to estimate the
epidemic curve, and different screening parameters. In other work [1], we have
used an optimisation algorithm to prove the required properties of a
successful screening campaign, which happen to have been successfully used by
South Korea at the start of the epidemics.

In a second version of our model, we have integrated several vaccination
strategies to either limit the total number of cases by targeting people with
more contacts, or limit the number of serious forms by targeting people with
risk factors. Consistently with other works, we find that vaccinating younger
people very early on can provide a better herd immunity to limit the total
number of cases. However, we also show that when starting vaccination later or
when the immunity duration is shorter, it is important to rather vaccinate
older people who have more risks factors, in order to reduce the number of
serious forms.

Both simulators are available online, in French and English, so that people
can play with them. The source code is also available. We believe that
providing the population with scientific facts and explanations is key to
protect them from fake news and to improve the acceptability of sanitary
measures (_e.g._ necessity of regular self-tests for children at school,
usefulness of vaccination, etc).

###  9.2 Limitations and future work

In the interest of simplicity of use, we have limited the number of parameters
and outputs in each simulator. As a result, we have not tested the combination
of sanitary measures (screening + quarantine, vaccination). Another limitation
concerns trust: we assumed here that agents eligible to vaccination will
receive the vaccine in order of priority. In fact, this is not necessarily
true, some people might not want to receive the vaccine because they do not
trust it. In other work, we are interested in how trust evolves and influences
the speed of the vaccination campaign [2].

Our simulator has been made available online but we have not yet surveyed the
users to assess its impact. Future experiments need to be setup with users of
different profiles to prove our claim that changing role (playing the role of
a health decider), actually interacting with the parameters to test what-if
scenarios, and getting feedback about one’s choices, can provide a welcome
feeling of control and a better understanding and acceptance of a difficult
situation.

We would like to thank to the CovPrehension
collective777https://covprehension.net for their insight and help about design
and testing of the screening model, as well as publication and translation of
the original blog post.

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