=Paper=
{{Paper
|id=Vol-2706/paper6
|storemode=property
|title=A Multi-Agent System for Simulating the Spread of a Contagious Disease
|pdfUrl=https://ceur-ws.org/Vol-2706/paper7.pdf
|volume=Vol-2706
|authors=Giuseppe Antonio Nanna,Nicola Flavio Quatraro,Berardina De Carolis
|dblpUrl=https://dblp.org/rec/conf/woa/NannaQC20
}}
==A Multi-Agent System for Simulating the Spread of a Contagious Disease==
https://ceur-ws.org/Vol-2706/paper7.pdf
A Multi-Agent System for Simulating the Spread of a
Contagious Disease
Giuseppe Antonio Nanna, Nicola Flavio Quatraro and Berardina De Carolis
Department of Computer Science, University of Bari "Aldo Moro", Bari, Italy
Abstract
Recent events concerning global health risks have made truly evident the importance of advanced
strategies and tools to monitor and prevent the spread of new and unpredictable diseases. COVID-19
showed the world that there are many factors that come into play when facing a viral threat, such as
politics, social and economic aspects. Taking those into account when trying to deal with such events
can make a huge difference in the efficacy and efficiency of the responses to the viruses. In this paper,
we propose the use of a Multi-Agent system that extends the previous multi-agent-based approaches by
adding a whole new set of features to control the outbreak during the simulation in order to dynamically
verify how the government strategies can impact the disease spread.
Keywords
Simulation, Multi-agent systems, Agent-based modeling
1. Introduction
The simulation of an infectious disease spread is complex, there are multiple factors to take
into account and it is quite difficult to model all the interactions that occur between them.
Some examples of approach to this problem are the mean-field type models [1], the differential
equation models [2] and the cellular automata theory [3, 4]. But those do not consider important
aspects such as the spatial and temporal variables that describe the setting of the outbreak [5].
Agent-based modeling (ABM) is able to cover effectively all these topics since, for instance,
an agent can be easily used to model different categories of individuals constituting the social
structure of the population considered, each one with his own behavior, and his movements
in a map during time [6]. The model proposed by [5] took into account all those aspects but
lacks of features (depending on the government action and on social factors) for managing the
disease spread dynamically.
For this reason we developed 1 an ABM simulation, based on the work of [5], enriched with
some social, economical and political factors which happened to be highly relevant during the
COVID-19 outbreak.
WOA 2020: Workshop “From Objects to Agents”, September 14–16, 2020, Bologna, Italy
" g.a.nanna@inventati.org (G. A. Nanna); nicolaflavioquatraro@gmail.com (N. F. Quatraro);
berardina.decarolis@uniba.it (B. De Carolis)
0000-0002-3146-2561 (G. A. Nanna); 0000-0002-2689-137X (B. De Carolis)
© 2020 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
CEUR Workshop Proceedings (CEUR-WS.org)
Proceedings
http://ceur-ws.org
ISSN 1613-0073
1
The simulation was developed during the lockdown in the midst of the COVID-19 outbreak as a project work
for the course on Multi-Agent Systems held by Prof. Berardina De Carolis
119
Giuseppe Antonio Nanna et al. 119–134
The human population, modelled as agents, behaves and interacts in a randomly generated
urban setting, where the places with higher risk of contagion are considered. We included
households, hospitals, public places, the transportation system, businesses and mass gatherings.
In our simulation humans and businesses dynamically change their behaviour depending
on the measures and the restrictions enacted by the local government aimed at slowing down
the spread of the disease. In order to simulate a more human behaviour, we also admitted the
possibility of reckless actions.
The effectiveness of the government strategies can also be evaluated by monitoring the
response of the healthcare system, which can get overwhelmed with tragic consequences on
the population.
1.1. Related works
Starting from the early 20th century, even if the first contributions in mathematical modelling
of spread of disease were developed by Daniel Bernoulli in 1760 [7], different approaches have
been proposed to tackle the complex problem of simulation and prediction of outbreaks such as:
the ordinary differential equation model, the discrete differential equation model, the impulsive
differential equation model, the differential equation model with time delay, the finite equation
theory, the matrix theory, the bifurcation theory, the K-order monotone system theory, the
central manifold theory, the Lasalle invariant principle, etc. . . [8] The models proposed through
time can be organized as follows [9]:
Deterministic
In a deterministic mathematical model every individual belongs to a different category,
associated with a specific stage of the disease. The model is thus simulated through
differential equations because the transition between disease stages can mathematically
be represented as derivatives and it’s differentiable with respect to time. So, the whole
outbreak process can be considered as deterministic, meaning that every step in the
simulation can be calculated considering exclusively the previous simulation’s step [9].
Stochastic
Stochastic models simulate the possible outcomes of the outbreak considering probability
distributions depending on different random variation of variables with respect to time.
Those models rely on the probabilistic variations of the disease model variables such as
risk of exposure, disease and other illness related events [9].
Some of the most used mathematical model for the simulation of an outbreak are the so
called Compartment (or State) Models; those are model in which there’s a division in categories
between every individual [6].
A clear and simple example of this class of models is the Susceptible-Infected-Recovered (SIR)
one [10] in which the whole population can be organized in those three different states. Every
individual who gets infected moves from the state Susceptible to the Infected one, and during a
fixed amount of time he can infect other Susceptible individuals. After this period, he moves to
the Recovered state and, if the immune hypothesis is valid, he can not be infected again [6].
This kind of model has evolved through time getting more complex in relation to the disease
considered and the setting in which the simulation holds; for instance, some models take
120
Giuseppe Antonio Nanna et al. 119–134
in account the possibility of vaccination and pharmaceutical treatment of the population or,
eventually, the measures of quarantine and isolation [6].
More complex models are, for example, the SEQIJR (Susceptible-Exposed-Quarantine-Infective-
Isolation-Recovered) model, the SEIRP (Susceptible-Exposed-Infectious-Recovered-Persevered)
model and the SLIRDS (Susceptible-Latent-Infected-Recovered-Dead-Susceptible) model [8].
Once the mathematical model is set, an often considered approach to represent it is the
Equation-Based Modeling (EBM) in which the relationships among the variables and the states
of the simulation are modelled through equations differentiable with respect to time [11]. The
SIR model can be formulated with the following equations [12]:
𝑑𝑆
= −𝛼𝑆𝐼
𝑑𝑡
𝑑𝐼
= 𝛼𝑆𝐼 − 𝛽𝐼
𝑑𝑡
𝑑𝑅
= 𝛽𝐼
𝑑𝑡
𝑆+𝐼 −𝑅=𝑀
where, 𝛼 is the global transmission rate, 𝛽 is the recovery (or death) rate, 𝑀 is the total number
of the whole population, 𝑆 = 𝑆(𝑡), 𝐼 = 𝐼(𝑡) and 𝑅 = 𝑅(𝑡) are, respectively, the number
of susceptible individuals, the number of infected individuals and the number of recovered
individuals at time 𝑡 [6].
Usually EBM systems are effective to simulate scenarios in which the outbreak can be observed
as a mathematical, self-centered event. When this approach fails, other perspectives must be
considered. In the ABM, the outbreak is the result of each individual’s behaviour and actions that
take place in the simulation. This approach allows a better understanding and representation
of system’s variables such as heterogeneity across individuals, geographical localization and
distribution, different forms of interaction between individuals and so on [6]. But, inevitably, it
has higher computational and cognitive costs.
These are some other examples of the recent approaches to epidemic spread modelling [6]:
• Agent-Based Modeling and Simulation of Influenza:
In this simulation of influenza [13], the setting is a common Chinese city with a dy-
namic contact network where every place belongs to one of four categories: workplace,
household, place of entertainment and school. Every individual in the simulation lives
in a sub-location called mixing group and interacts with other individuals in the same
household and mixing group. The interaction types are defined normal, if it occurs in a
mixing group, or random, if it occurs between different mixing groups. Every individuals
can travel from his house to his assigned location and viceversa. The model has been
tested on a city composed by 30000 citizens, 80% of them have been vaccinated, who
live in 10252 households. A simulation package QAST verifies the impact of different
restriction strategies on the simulation of infectious diseases. The experiment showed
that restriction policies can counterattack the outbreak and that agent-based models can
represent better models than the mathematical one in studying large-scale population
simulations [6].
121
Giuseppe Antonio Nanna et al. 119–134
• Agent-Based Simulation on Avian Influenza in Vietnam:
Using a SIR compartment model [12], combined a EBM and a ABM approach to evaluate
the existing restriction measures through a simulation based on the data of the avian
influenza contagion. Such model takes into account a well-mixed and homogeneous
poultry population where random contacts between infectious and susceptible individuals
occur and where the basic reproduction number 𝑅0 of the disease is a mathematically
calculated parameter, based on the daily reported individuals’ death. The experiments
showed, in order to control the outbreak, a strategic campaign of culling, bio-security
restriction and large-scale vaccination must been considered [6].
• Multiagent-Based Simulation of the HIV/AIDS Spatial and Temporal Transmission among
Injection Drug Users:
In the work [14] a model to simulate the HIV/AIDS transmission model between injecting
drug users (IDUs) has been developed. It relies on the multivalent system and geographic
information systems (GIS) in an urban setting during a ten years period using the Repast
(REcursive Porous Agent Simulation Toolkit) Simphony 1.2 platform. Every individual
interacts with other ones through randomly generated social networks, he is described
by parameters like gender, education, age and geographic location, and he belongs to
one of five different categories: IDU person, HIV-IDU person, HIV person, AIDS person
and healthy person. Every day, an individual interacts with five to eight, out of twenty
friends. Every individual can affect his friends by encouraging them, if he is healthy, to
stop taking drugs or, if he is an IDU, to keep or begin using drugs. The experiment’s
setting is Kunming, the capital of Yunnan Province, southwest of China. Results showed
that individual social influence, the percentage of needle sharing individuals and the
starting number of HIV individuals have a major role in the HIV/AIDS outbreak [6].
2. Simulation
The proposed simulation 2 is written in Java and is based on JADE, a software framework for
the development of intelligent agents 3 .
During the simulation, it is possible to monitor the contagion curves in real-time (figure 1)
and to affect the outcome of the simulation by imposing rules and restrictions such as the social
distancing (figure 2).
2.1. Agent Based Model
Every individual of the simulated population is modelled through an agent. Every Individual,
during daytime, simulate the human behaviour with a list of tasks, which can occur at a certain
location of the map, such as staying at home or at work, or can involve a path in the map, such
as moving from the supermarket location to home [5].
Thus, each agent periodically performs several possible actions based on his needs:
• going to the supermarket
2
Simulation repository: https://github.com/h3r0n/sysag_cds
3
JADE website: https://jade.tilab.com/
122
Giuseppe Antonio Nanna et al. 119–134
Figure 1: Real-time animated visualization of contagion curves
Figure 2: Government GUI
• going to the park
• going to a public event
• going to the hospital if ill
• going outside for a walk
After each action the simulated individual will return to his own house. Since the household
transmissibility of diseases like COVID-19 is epidemiologically relevant and it cannot be ignored
[15], residences (randomly assigned at the beginning of the simulation) can be shared by agents.
123
Giuseppe Antonio Nanna et al. 119–134
Every agent has some needs to satisfy during its daytime and through its movements it
may get in contact with other groups of people who can infect it or that can be infected by it
[5]. Some agents simulate workers: in addition to the already specified actions, they will also
periodically go to their randomly assigned workplace.
A worldwide study conducted on April 2020 [16] analysed the erroneous conspiracy theory
developed by many people during the COVID-19 pandemic: "Those who were more conspira-
torial were more likely to report that the government’s response was too strong, illogical and
that the government hid information to people" [16]. "Some of these beliefs were potentially
harmful and some could have led to public rejection of public health measures to suppress the
spread of the virus" [16].
For those reasons a number of people who completely ignore the restrictions imposed by the
government have been included in the simulation.
2.2. World Model
There are a multitude of factors that can hugely affect the outcome of an outbreak. Different
social networks and geographical settings determine a different spreading dynamics and different
types of epidemiology [5].
For this reason, in the simulation, agents’ activities and tasks take place in geographical
locations inside a simplified model of an urban setting in which individuals may interact with
each other, this includes engaging in activities related to the daily commuting through the urban
transportation network [5]. When an individual leaves a group, he travels through space and
time to another destinations to accomplish a different task, which often implies interacting and
joining another group of individuals [5]. This approach allows a more realistic simulation of the
daily routine of each individual, and, therefore, a more accurate simulation of the population
dynamics [5].
The world in which the agents act is modelled as a graph in which the nodes are buildings
and the edges are the roads. The graph is randomly generated at the beginning of the simulation.
Each component of the geographical world is characterized by a set of coordinates in the graph
and by a density factor which describes the average distance allowed in that place, which affects
the probability of the contagion.
Roads are used to model a simplified version of the urban transportation network. Therefore, in
order to move from a location to another, an individual has to calculate the shortest path to his
destination, which is composed by a list of roads the individual must pass through [5].
During the COVID-19 outbreak, the lockdown status imposed the suspension of a great per-
centage of the commercial and productive activities, which caused a dramatic crisis worldwide
[17].
The presence of activities, companies, institutions can affect the spread of the disease and have
been used [17] to predict the risk of contagion. Because of their importance on the spread dy-
namics, businesses were included in the simulation in order to support the local administrations
in formulating the best approaches to reduce or restart the local activities during lockdown
restrictions [17].
Each business is associated with a specific building, it can be the workplace of one or several
workers and can be closed or reopened by the Government. We distinguish different kinds of
124
Giuseppe Antonio Nanna et al. 119–134
business:
• supermarket
• park, which represents recreation and entertainment places
• hospital
• non strictly necessary business
• necessary business
The last two categories are needed to differentiate the businesses which are absolutely necessary
for the well-being of the population, such as food factories, from those that can eventually be
closed to control the outbreak.
Events of large-scale group infection [18] have been considered, they occur in circumstances
in which a huge number of individuals are located in the same place, leading to a massive increase
in chances to be exposed to the infection,in a short period of time. It has been estimated that
71.7% of the confirmed COVID-19 cases in Korea [18] are related to such events, which usually
occur in places like factories, dormitories, schools, companies or places in which individuals
are constrained in a limited physical space.
Parks represent all recreation and entertainment places and can also be casually selected as
the setting of public events, attended by a large percentage of the population and may be the
source of large-scale group infections.
During a pandemic the healthcare system has an higher risk to collapse because of difficulties
in triaging, allocation, and a shortage of high-level care beds [19].
Thus, hospitals in the simulation have a limited number of beds, which implies that if the
outbreak gets out of control and all the beds get occupied, those disease-ill individual with
strong symptoms are much more likely to die due to the lack of proper care.
This allows to further evaluate the success of the Government’s strategies to control the spread
of the disease.
2.3. Government Model
Social distancing can be defined as "a deliberate effort instituted to stop or slow down the
spread of a highly infectious or contagious diseases" [20]. In order control an outbreak, every
individual must then reduce the interactions with the rest of the population,which leads in
closing partially or wholly social activities specially business and transport because they may
enhance social interaction and disease spread [20].
In order to control the epidemic of COVID-19, more than 10 million people in Wuhan were
restricted to their home by the Chinese government. By reducing the contact rate of latent
individuals, interventions such as quarantine and isolation have effectively reduced the potential
peak number of COVID-19 infections and delayed the time of peak infection [21, 22].
At any time during the simulation, the user can pose as the local government and can issue
and lift restrictions and social distancing measures with a simple GUI (figure 2). Several ways
to try to control and eventually stop the outbreak are provided:
• close the non strictly necessary businesses
• close the parks
125
Giuseppe Antonio Nanna et al. 119–134
• forbid public events
• make the use of PPE mandatory (never, everywhere or just indoors)
• close the buildings with a low average distance between individuals
• reduce the maximum movement range to go for a walk
• reduce the maximum travel distance of every individual
The government can enact those restrictions by issuing a “decree”. After this event, all the
agents simulating individuals and businesses get notified and eventually modify their behaviour.
2.4. Infection Model
Our model, based on [5], will consider a SEIR epidemic spread model where every individual
(agent) of the simulation can be in one of four different states:
Susceptible
individuals who can contract the disease
Exposed
individuals who have contracted the disease and are not contagious
Infected
individuals who have contracted the disease and are contagious
Recovered
individuals who are healed from the disease and that cannot contract it anymore
The progress of the infection in an individual is then represented through the unidirectional
translation between those states, starting from the Susceptible one and ending in the Recovered
one, assuming that once an individual is Recovered he becomes immune to the disease.
Once the individual becomes Exposed, there is a latency period before he becomes Infected.
This can be represented with a simple formula [5]:
𝐼𝑝𝑖 = 𝑡𝑖 + 𝑥𝐿𝑃
Where 𝑡𝑖 represents the moment in time where the contagion occurs and 𝑥𝐿𝑃 is the number of
days necessary to become infected.
After reaching the Infected state, there is another latency period before the individual heals
completely, becoming Recovered:
𝑅𝑝𝑖 = 𝐼𝑝𝑖 + 𝑥𝐼𝑃
Where 𝐼𝑝𝑖 represents the moment in time where the individual becomes Infected and 𝑥𝐼𝑃 is
the number of days necessary to become Recovered. The translation between Susceptible to
Exposed occurs when an Infected individual infects a Susceptible one. The way this happens
depends on two conditions:
• The two individual must meet in the same place
• The contagion must occur
126
Giuseppe Antonio Nanna et al. 119–134
The meeting represents a violation of social distancing and is modeled as a probabilistic event.
It occurs when the following formula is true:
𝑟𝑎𝑛𝑑𝑜𝑚𝑣𝑎𝑙𝑢𝑒 < 𝑚𝑎𝑥(𝑖𝑛𝑓 𝑒𝑐𝑡𝑖𝑜𝑢𝑠𝐷𝑖𝑠𝑡, 𝑠𝑢𝑠𝑐𝑒𝑝𝑡𝑖𝑏𝑙𝑒𝐷𝑖𝑠𝑡)
where 𝑖𝑛𝑓 𝑒𝑐𝑡𝑖𝑜𝑢𝑠𝐷𝑖𝑠𝑡 and 𝑠𝑢𝑠𝑐𝑒𝑝𝑡𝑖𝑏𝑙𝑒𝐷𝑖𝑠𝑡 are the probabilities (respectively associated to
the infectious individual and the susceptible one) of getting close with anyone. Those values
are randomly generated every time an individual reaches any geographical location. The values
cannot be lower than the density value associated to the location and cannot be higher than the
maximum density allowed by the Government (unless the individual is ignoring the decrees
issued by the Government).
Similarly, the Contagion event follows a probabilistic distribution and occurs if the following
formula is true:
𝑟𝑎𝑛𝑑𝑜𝑚𝑣𝑎𝑙𝑢𝑒 < 𝑃 (𝑖𝑛𝑓 𝑒𝑐𝑡𝑖𝑜𝑢𝑠𝑃 𝑃 𝐸, 𝑠𝑢𝑠𝑐𝑒𝑝𝑡𝑖𝑏𝑙𝑒𝑃 𝑃 𝐸)
where 𝑃 is a function depending on whether or not the infectious individual and the susceptible
one are wearing personal protection equipment (PPE) like a mask, as according to the World
Health Organization Writing Group, wearing a mask can prevent respiratory infectious diseases
[23], [24].
This claim has been proven by several studies [24]:
• "In a large systematic review of physical interventions to control spread of infectious
diseases, Jefferson et al. concluded from 67 studies that wearing masks is effective as one
of the important barriers to transmission of respiratory viruses, and evidences indicate
N95 respirators were non-inferior to surgical masks" [25], [24].
• "Other studies also found evidence that wearing masks can significantly reduce the risk
of SARS and influenza-related diseases" [26, 27, 28], [24].
• "Aldila et al. constructed MERS determinant mathematical model and found that compared
with auxiliary nursing and government publicity, wearing masks is the optimal choice
for reducing the number of infections" [29], [24].
• "Barasheed et al. systematically analyzed the utilization and effectiveness of masks by
integrating 12,710 samples from more than 50 countries in the world, and found that
wearing masks in crowded places could reduce the risk of respiratory infections by 20%"
[30], [24].
• "A study in Hong Kong found that the odds ratio (OR) value of wearing masks in public
places was only 0.36, which was lower than that of living room disinfection (OR = 0.41) and
frequent hand washing (OR = 0.58), indicating that wearing masks effectively restricted
the community spread of SARS-CoV in Hong Kong" [31], [24].
Each individual only wears a mask if compulsory as long as he doesn’t ignore the Govern-
ment’s dispositions.
127
Giuseppe Antonio Nanna et al. 119–134
Cases 1600
1400
1200
1000 Total infectious
Recovered
Deaths
800 Available beds
Total exposed
Current infectious
600
400
200
0 5 10 15 20 25 30 35 40
Days
Figure 3: Scenario 1: No precautions - High number of infectious
700
Cases
600
500
Total infectious
400 Recovered
Deaths
Available beds
300 Total exposed
Current infectious
200
100
0
0 20 40 60 80 100 120 140 160 180 200
Days
Figure 4: Scenario 2: Precautions - High number of infectious
3. Simulated Scenarios
We chose to simulate 6 different scenarios in order to verify the capabilities of the created model.
In each one 1500 people are simulated, of which 20% ignore the Government’s restriction and
50% are workers. The map consists of 3600 buildings with 500 businesses. Hospitals have a
combined capacity of 100 beds.
128
Giuseppe Antonio Nanna et al. 119–134
Cases 1600
1400
1200
1000 Total infectious
Recovered
Deaths
800 Available beds
Total exposed
Current infectious
600
400
200
0
0 10 20 30 40 50
Days
Figure 5: Scenario 3: No precautions - Low number of infectious
Cases
100
80
60
40 Total infectious
Recovered
Deaths
Available beds
Total exposed
20 Current infectious
0
0 10 20 30 40 50 60 70 80
Days
Figure 6: Scenario 4: Precautions - Low number of infectious
• Scenario 1: No precautions - High number of infectious
This scenario simulates a community of 1500 people facing a large wave of contagion
(10% of the population is infectious at the beginning, everyone else is susceptible) without
adopting any social distancing policy.
In this scenario, as shown in figure 3, the whole population contracts the disease in a
single week and the healthcare system gets overwhelmed a few days later. As a result a
129
Giuseppe Antonio Nanna et al. 119–134
1600
Cases
Total infectious
1400
Recovered
Deaths
Available beds
1200
Total exposed
Current infectious
1000
800
600
400
200
0
0 20 40 60 80 100 120
Days
Figure 7: Scenario 5: Premature Reopening
Cases
900
800
700
600
Total infectious
Recovered
500 Deaths
Available beds
Total exposed
400
Current infectious
300
200
100
0
0 20 40 60 80 100 120
Days
Figure 8: Scenario 6: adopting progressively stricter social distancing measures
relevant number of individuals dies due to the lack of proper care.
• Scenario 2: Precautions - High number of infectious
The starting conditions of this scenario are the same of the previous one, except it
simulates the adoption of restrictive social distancing policies.
The outcome (shown in figure 4) is vastly different as the disease spreads much slower.
As a result hospitals don’t have to operate at over capacity and less people die.
130
Giuseppe Antonio Nanna et al. 119–134
• Scenario 3: No precautions - Low number of infectious
In this scenario 1% of the population is infectious at the beginning and no social distancing
policy is adopted. Despite the different starting conditions, the outcome (shown in figure
5) is close to the Scenario 1 due to the exponential nature of the infection transmission.
• Scenario 4: Precautions - Low number of infectious
The starting conditions of this scenario are the same of the previous one except it simulates
the same social distancing policies adopted in Scenario 2.
As shown in figure 6, the spread of the disease progresses very slowly compared to the
previous scenarios, while the number of active cases slowly decreases over time.
• Scenario 5: Premature Reopening
This scenario simulates the non gradual lifting of all restrictions at the end of the previous
scenario. The outcome (shown in figure 7) is the same of Scenario 1 and 3 with the whole
population exposed to the disease and a large number of deaths.
• Scenario 6: adopting progressively stricter social distancing measures
This scenario (shown in figure 8) is similar to Scenario 4, except the Government doesn’t
act proactively, but only gradually enacts restrictions after a spike in the number of
infectious people.
The outcome (shown in figure 8) is different because of the large share of the population
who contracts the disease, but less people die (compared to Scenario 1 and 3) because the
healthcare system doesn’t get overwhelmed.
4. Conclusions and Future Work
The proposed model is able to simulate a wide range of different situations. It allows to take into
account aspects often overlooked by other works, such as the response of local administrations,
the capacity of the health system and the presence of local businesses. These factors, as shown
in the simulated scenarios, have a not negligible importance on the spread of the disease and its
effects on the population.
Even if the proposed approach is general enough to model a generic contagion setting, the
examples are shown in the context of the COVID-19 disease. In this context, the contagion
curves observed during the COVID-19 pandemic show a strong resemblance to the more
realistic scenarios such as Scenarios 4 and 6. Especially in the case of European countries where
the adoption of social distancing measures (similar to the simulated ones) allowed the local
governments to control the spread of the virus.
The COVID-19 outbreak has given a new perspective on the variables which rule the out-
break response. The economic consequences of the quarantine, isolation and social distancing
strategies have been far more worse than expected and every government in such situations
has to make very complex choices.
Our goal with this proposed approach is to simulate the effect of such choices on the population
and the public health system in order to help making such difficult choices to preserve the
interests of the nation and of the population. Even though this simulator relies on a quite simple
mathematical formulation, it has been able to properly reproduce the normal distribution of the
disease spread curve when no restrictions were imposed while it follows a linear trend when
131
Giuseppe Antonio Nanna et al. 119–134
those restrictions come into force. Those results are then matching the expectations and the
events that occurred during the COVID-19 outbreak.
However there are many aspects of this tool which can be improved, such as:
• a wider geographical setting where people are able to travel between different communi-
ties
• a more heterogeneous social structure with more classes reflecting each individual’s age
and role
• a more diverse and complex behaviour of each agent allowed by the use of a BDI model
In the future we believe that improving those aspects, with the help of experts in the field,
can provide a valid tool that can assist the administrations, before and during an outbreak, in
choosing the most optimal strategies to safeguard public health and minimize the consequences
of restrictions on the economy at the same time.
References
[1] A. Kleczkowski, B. T. Grenfell, Mean-field-type equations for spread of epidemics: the
‘small world’ model, Physica A: Statistical Mechanics and its Applications 274 (1999) 355 –
360. doi:https://doi.org/10.1016/S0378-4371(99)00393-3.
[2] S. Fu, G. Milne, Epidemic modelling using cellular automata, in: H. Abbass, J. Wiles
(Eds.), The Australian Conference on Artificial Life ACAL 2003, volume N/A, UNSW Press,
Australia, 2003, pp. 43–57. Epidemic Modelling Using Cellular Automata ; Conference date:
01-01-2003.
[3] G. Sirakoulis, I. Karafyllidis, A. Thanailakis, A cellular automaton model for the effects of
population movement and vaccination on epidemic propagation, Ecological Modelling
133 (2000) 209 – 223. doi:https://doi.org/10.1016/S0304-3800(00)00294-5.
[4] L. Q.-X. Jin Zhen, A cellular automata model of epidemics of a heterogeneous susceptibility,
Chinese Physics B 15 (2006) 1248. doi:10.1088/1009-1963/15/6/019.
[5] L. Perez, S. Dragicevic, An agent-based approach for modeling dynamics of contagious
disease spread, International Journal of Health Geographics 8 (2009) 50. doi:10.1186/
1476-072X-8-50.
[6] M. Shatnawi, S. Lazarova-Molnar, N. Zaki, Modeling and simulation of epidemic spread:
Recent advances, 2013 9th International Conference on Innovations in Information Tech-
nology, IIT 2013 (2013) 118–123. doi:10.1109/Innovations.2013.6544404.
[7] H. Hethcote, The mathematics of infectious diseases, SIAM Review 42 (2000) 599–653.
doi:10.1137/S0036144500371907.
[8] S. Bin, G. Sun, C.-C. Chen, Spread of Infectious Disease Modeling and Analysis of Dif-
ferent Factors on Spread of Infectious Disease Based on Cellular Automata, Interna-
tional Journal of Environmental Research and Public Health 16 (2019) 4683. doi:10.3390/
ijerph16234683.
[9] F. Brauer, C. Castillo-Chavez, Mathematical Models in Population Biology and Epi-
demiology, volume 40 of Texts in Applied Mathematics, Springer New York, New
York, NY, 2012. URL: http://link.springer.com/10.1007/978-1-4614-1686-9. doi:10.1007/
978-1-4614-1686-9.
132
Giuseppe Antonio Nanna et al. 119–134
[10] W. O. Kermack, A. G. McKendrick, G. T. Walker, A contribution to the mathematical theory
of epidemics, Proceedings of the Royal Society of London. Series A, Containing Papers
of a Mathematical and Physical Character 115 (1927) 700–721. doi:10.1098/rspa.1927.
0118.
[11] H. Van Dyke Parunak, R. Savit, R. L. Riolo, Agent-Based Modeling vs. Equation-Based
Modeling: A Case Study and Users’ Guide, in: G. Goos, J. Hartmanis, J. van Leeuwen, J. S.
Sichman, R. Conte, N. Gilbert (Eds.), Multi-Agent Systems and Agent-Based Simulation,
volume 1534, Springer Berlin Heidelberg, Berlin, Heidelberg, 1998, pp. 10–25. doi:10.
1007/10692956\_2.
[12] D. M. Nguyen, H. Deguchi, M. Ichikawa, Agent-based simulation on avian influenza in
Vietnam: Basic characteristics of the epidemic and efficiency evaluation of control mea-
sures, in: 2010 7th International Conference on Service Systems and Service Management,
2010, pp. 1–6. doi:10.1109/ICSSSM.2010.5530215, iSSN: 2161-1904.
[13] Zhang Fa, Zhao Qiao-xia, Li Lu, Intervention for contagious disease: Agent-based modeling
and simulation, in: 2011 2nd IEEE International Conference on Emergency Management
and Management Sciences, 2011, pp. 155–158. doi:10.1109/ICEMMS.2011.6015643.
[14] J. Xiong, J. Wang, K. Yang, S. Peng, Q. Xu, Multiagent-based simulation of the HIV/AIDS
spatial and temporal transmission among injection drug users, in: 2010 18th International
Conference on Geoinformatics, 2010, pp. 1–6. doi:10.1109/GEOINFORMATICS.2010.
5567671, iSSN: 2161-0258.
[15] Q.-L. Jing, M.-J. Liu, J. Yuan, Z.-B. Zhang, A.-R. Zhang, N. E. Dean, L. Luo, M.-M. Ma,
I. Longini, E. Kenah, Y. Lu, Y. Ma, N. Jalali, L.-Q. Fang, Z.-C. Yang, Y. Yang, Household
Secondary Attack Rate of COVID-19 and Associated Determinants, preprint, Epidemiology,
2020. doi:10.1101/2020.04.11.20056010.
[16] N. Georgiou, P. Delfabbro, R. Balzan, COVID-19-related conspiracy beliefs and their
relationship with perceived stress and pre-existing conspiracy beliefs, Personality and
Individual Differences 166 (2020) 110201. doi:10.1016/j.paid.2020.110201.
[17] V. Sangiorgio, F. Parisi, A multicriteria approach for risk assessment of Covid-19 in
urban district lockdown, Safety Science 130 (2020) 104862. doi:10.1016/j.ssci.2020.
104862.
[18] Y.-J. Kang, Lessons Learned From Cases of COVID-19 Infection in South Korea, Disaster
Medicine and Public Health Preparedness (2020) 1–8. doi:10.1017/dmp.2020.141.
[19] M. Sorbello, K. El-Boghdadly, I. Di Giacinto, R. Cataldo, C. Esposito, S. Falcetta, G. Merli,
G. Cortese, R. M. Corso, F. Bressan, S. Pintaudi, R. Greif, A. Donati, F. Petrini, The Società
Italiana di Anestesia Analgesia Rianimazione e Terapia Intensiva (SIAARTI) Airway Re-
search Group, and The European Airway Management Society, The Italian coronavirus
disease 2019 outbreak: recommendations from clinical practice, Anaesthesia 75 (2020)
724–732. doi:10.1111/anae.15049.
[20] G. Musinguzi, B. O. Asamoah, The Science of Social Distancing and Total Lock Down:
Does it Work? Whom does it Benefit?, Electronic Journal of General Medicine 17 (2020)
em230. doi:10.29333/ejgm/7895.
[21] C. Hou, J. Chen, Y. Zhou, L. Hua, J. Yuan, S. He, Y. Guo, S. Zhang, Q. Jia, C. Zhao, J. Zhang,
G. Xu, E. Jia, The effectiveness of quarantine of Wuhan city against the Corona Virus
Disease 2019 (COVID-19): A well-mixed SEIR model analysis, Journal of Medical Virology
133
Giuseppe Antonio Nanna et al. 119–134
92 (2020) 841–848. doi:10.1002/jmv.25827.
[22] K. Prem, Y. Liu, T. W. Russell, A. J. Kucharski, R. M. Eggo, N. Davies, M. Jit, P. Klepac,
S. Flasche, S. Clifford, C. A. B. Pearson, J. D. Munday, S. Abbott, H. Gibbs, A. Rosello, B. J.
Quilty, T. Jombart, F. Sun, C. Diamond, A. Gimma, K. van Zandvoort, S. Funk, C. I. Jarvis,
W. J. Edmunds, N. I. Bosse, J. Hellewell, The effect of control strategies to reduce social
mixing on outcomes of the COVID-19 epidemic in Wuhan, China: a modelling study, The
Lancet Public Health 5 (2020) e261–e270. doi:10.1016/S2468-2667(20)30073-6.
[23] World Health Organization Writing Group, Nonpharmaceutical Interventions for Pandemic
Influenza, National and Community Measures, Emerging Infectious Diseases 12 (2012)
88–94. doi:10.3201/eid1201.051371.
[24] J. Wang, L. Pan, S. Tang, J. S. Ji, X. Shi, Mask use during covid-19: A risk adjusted
strategy, Environmental Pollution 266 (2020) 115099. doi:https://doi.org/10.1016/
j.envpol.2020.115099.
[25] T. Jefferson, C. B. Del Mar, L. Dooley, E. Ferroni, L. A. Al-Ansary, G. A. Bawazeer, M. L. van
Driel, N. S. Nair, M. A. Jones, S. Thorning, J. M. Conly, Physical interventions to interrupt
or reduce the spread of respiratory viruses, Cochrane Database of Systematic Reviews
(2011). doi:10.1002/14651858.CD006207.pub4.
[26] T. Jefferson, C. Del Mar, L. Dooley, E. Ferroni, L. A. Al-Ansary, G. A. Bawazeer, M. L. van
Driel, R. Foxlee, A. Rivetti, Physical interventions to interrupt or reduce the spread of
respiratory viruses: systematic review, BMJ 339 (2009) b3675–b3675. doi:10.1136/bmj.
b3675.
[27] C. R. MacIntyre, S. Cauchemez, D. E. Dwyer, H. Seale, P. Cheung, G. Browne, M. Fasher,
J. Wood, Z. Gao, R. Booy, N. Ferguson, Face Mask Use and Control of Respiratory Virus
Transmission in Households, Emerging Infectious Diseases 15 (2009) 233–241. doi:10.
3201/eid1502.081166.
[28] L. Zhang, Z. Peng, J. Ou, G. Zeng, R. E. Fontaine, M. Liu, F. Cui, R. Hong, H. Zhou,
Y. Huai, S.-K. Chuang, Y.-H. Leung, Y. Feng, Y. Luo, T. Shen, B.-P. Zhu, M.-A. Widdowson,
H. Yu, Protection by Face Masks against Influenza A(H1N1)pdm09 Virus on Trans-Pacific
Passenger Aircraft, 2009, Emerging Infectious Diseases 19 (2013). doi:10.3201/eid1909.
121765.
[29] D. Aldila, H. Padma, K. Khotimah, B. Desjwiandra, H. Tasman, Analyzing the MERS disease
control strategy through an optimal control problem, International Journal of Applied
Mathematics and Computer Science 28 (2018) 169–184. doi:10.2478/amcs-2018-0013.
[30] O. Barasheed, M. Alfelali, S. Mushta, H. Bokhary, J. Alshehri, A. A. Attar, R. Booy, H. Rashid,
Uptake and effectiveness of facemask against respiratory infections at mass gatherings: a
systematic review, International Journal of Infectious Diseases 47 (2016) 105–111. doi:10.
1016/j.ijid.2016.03.023.
[31] J. T. Lau, H. Tsui, M. Lau, X. Yang, SARS Transmission, Risk Factors, and Prevention in Hong
Kong, Emerging Infectious Diseases 10 (2004) 587–592. doi:10.3201/eid1004.030628.
134