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Multi-agent modeling of the spread of diseases
using the example of coronavirus disease
COVID-19
Mariia Pyvovar
department of Information Technology of
Design
National Aerospace University «KhAI»
Kharkiv, Ukraine
0000-0002-2136-233X
Olha Pohudina
department of Information Technology of
Design
National Aerospace University «KhAI»
Kharkiv, Ukraine
0000-0001-5689-2552
Dmitriy Kritskiy
department of Information Technology of
Design
National Aerospace University «KhAI»
Kharkiv, Ukraine
0000-0003-4919-0194
Abstract – Throughout the history of humanity, large-scale
epidemics and pandemics have repeatedly erupted. Athenian
ulcer, several plague and cholera pandemics, Spanish flu, Avian
influenza, Swine influenza, HIV/AIDS - millions of people have
died due to lack of medicines and medical knowledge. In the 21st
century, it would seem that world medicine is ready and capable
of preventing many diseases, but by the beginning of 2020, a new
pandemic of the coronavirus disease COVID-19 caused by the
SARS-CoV-2 virus broke out. The paper provided a brief
systematic overview of modeling methods in epidemiology. A
modified SEIRD simulation model of epidemic spread is
presented. The proposed model was implemented in the AnyLogic
system.
Keywords: epidemic; simulation modeling; multi-agent
modeling; model; AnyLogic; COVID-19.
I. INTRODUCTION
The virus emerged and began to spread among humans in
December 2019 in Wuhan, Hubei Province, China. The
authorities took the strictest measures to prevent the spread of
the disease when the number of patients began to increase
sharply, but already on January 20, the South Korean authorities
made an official statement about the first confirmed case of
coronavirus in the country.
The spread of the coronavirus has led to massive quarantines
and large economic losses in all countries of the world. As of
May 24, 2021, more than 167 million cases of infection were
registered in the world, of which more than 148,580,000 people
recovered, and more than 3,460,000 people died [1]. A
campaign to vaccinate the population has begun, but invented
injectables are in short supply. Many people distrust vaccines
because of the potential side effects.
The sudden onset of the epidemic led to massive negative
consequences, as medical industries in almost all countries of
the world were not ready for the spread of the disease. Mistrust
in the possibility of a sharp increase in the number of patients in
the world is due to the suppression of data and the lack of a
qualitative forecast of the expected morbidity. Therefore,
predicting the dynamics of a possible increase in the spread of
the virus as a result of building a simulation model allows
specialists and virologists to draw up a plan of work to combat
the epidemic in advance.
II. MAIN PART
A. Analysis of Process Modeling Capabilities
Artificial intelligence is a field of science that deals with the
creation of computer systems that simulate the human solution
to problematic behavior in order to understand human
intelligence [2]. Modeling is an effective method for studying
complex systems.
When using simulation, the system being investigated is
replaced by a model that describes the real system with sufficient
accuracy. Experiments are carried out with the created model in
order to obtain information about the object under study and to
determine in what state the system will be in the future [3].
Simulation modeling can be divided into four main
approaches [4]:
• system dynamics;
• dynamic systems;
• discrete-event modeling;
• multi-agent modeling.
At the heart of multi-agent modeling is an attempt to
understand the logic of decision-making by an individual
consumer, formalize it and combine it into a single model that
aggregates the individual choice of hundreds and thousands of
independently acting consumers.
Agent-based modeling makes it possible to identify how
significant consequences arise from small and seemingly
insignificant factors that determine the behavior and interaction
of each of the agents. This type of modeling is based on the
description of bottom-up processes: the model is based on a set
of basic parameters that characterize agents and the algorithm
for making individual decisions. The generalized behavior of the
system is born from these individual decisions, as well as
interactions between agents [5]. An agent is a certain entity with
activity, autonomous behavior, which can make decisions in
accordance with a certain set of rules, interact with the
environment and change independently [6].
B. Analysis of Methods and Models of Epidemic Behavior
There are a large number of methods that simulate the
dynamics of epidemics. Among them:
• static forecasting methods;
• forecasting based on machine learning;
• forecasting based on filtering;
• math modeling:
• mixed techniques [7].
The first popular mathematical model that is still used today
to model epidemics in large cities was the SIR model, created
by Scottish epidemiologists Kermak A. and Mackendrick W. in
the 1920s. The SIR (“Susceptible – Infected – Recovered”)
model, which identifies groups of people and simulates the
transmission of diseases between them, provides a basic
qualitative understanding of the dynamics of the spread of
infectious diseases.
()
where β is the intensity of contact between individuals, γ is the
intensity of the transition of individuals to the state R [8].
In the SEIR model, to the above groups of individuals
modeled in the SIR model, another was added: “Exposed” is the
people whose disease is in the incubation period (E):
()
where В is the average birth rate of individuals in the simulated
area, µ is the average mortality rate of individuals in the
simulated area, 1/ε is the average duration of the incubation
period of the disease [9].
For quantitative modeling, it is necessary to take into
account the peculiarities of the occurrence and spread of specific
infectious diseases, therefore, later models were developed: SIS
(“Susceptible – Infected – Susceptible”); SEIRFD
(“Susceptible – Exposed – Infected – Recovered – Funeral –
Died”), SEIHFR ("Susceptible – Exposed – Infected –
Hospitalized – Funeral – Deleted”) etc. [10].
For model the development of the coronavirus epidemic, the
SEIRD model was modified, and new conditions were added:
“No Symptoms”, “Symptoms”, “Hard”, “Lite” and “Immune”.
III. SYNTHESIS OF SOFTWARE
A. Software Architecture
An epidemic-based model of the spread of the epidemic has
been improved, taking into account the movement of people
between home and work, created using the Anylogic simulation
tool using the object-oriented Java programming language.
The model contains several populations of agents, each of
which is modeled as a separate object with its own parameters,
state variables, and rules of conduct. The following agent
populations were created:
1) Family is population of agents "Family". Each agent
contains:
• members is population of family members;
• infected is variable, which indicates the presence of the
patient in the family;
• X and Y are coordinates of the location of the house image
for building the animation.
2) Main is top-level agent that is referenced by other agents.
Contains a general presentation of all agents, namely the
location of stationary objects, movement of human agents and
changes in their status in relation to the disease model (Fig. 1).
Fig. 1. The structure of agent Main
3) Transport is population of agents “Public transport”. Each
agent contains:
• intransports is passenger population;
• X and Y are the coordinates of the location of the car image
for building the animation.
4) Work is population of agents of “Enterprises”. Each agent
contains:
• colleagues is workers population;
• X and Y are the coordinates of the location of the company
image for building the animation.
5) Person is he is responsible for the population of human
agents. Each agent has identifiers of two state diagrams is
“Illness”, which is responsible for the algorithm of the epidemic
behavior model, “Location”, which is responsible for the daily
route of the person. Taking into account the data obtained from
these diagrams, several events were indicated that occur in a
certain period of time and are cyclical (Fig. 2).
Fig. 2. The structure of agent Person
The diagram “Illness” assigns the following possible
statuses to the agent according to the epidemic behavior model:
• Susceptible is the agent is healthy and may become ill;
• Exposed is the agent is infected, but is in an incubation
state, so it cannot yet transmit the virus to others;
• Infectious is the agent is infected and can infect others;
• NoSymptoms is the agent is asymptomatic but can infect
others;
• Symptoms is the appearance of symptoms of the disease, a
person self-isolates at home;
• Hard is the agent is in a serious condition;
• Lite is a person is mildly ill;
• Recovered is the person has recovered;
• Immune is the person has received immunity;
• Dead is the person died as a result of an illness.
The state diagram “location” contains the agent movement
algorithm:
• AtHome is the agent is at home, but is going to work;
• ToWork is travel by public transport to the place of work;
• AtWork is agent at work;
• ToHome is the agent goes home after work.
Several events are specified in the model:
• morning is if in the morning a person does not feel
symptoms of the disease, then he goes to work using public
transport;
• goToWork is the person arrived at the place of work;
• endOfWorkDay is at the end of the working day, the
worker goes home by bus;
• evening is a person arrives home.
B. Simulation Model
When starting the experiment for the model of the spread of
coronavirus, the user can specify new values for the parameters
"Number of families", "Number of enterprises", "Number of
public transport vehicles" (Fig. 3).
Fig. 3. Running the experiment model
The work of the model with the given data is visualized,
when all people are healthy and are at home (Fig. 4).
Agents begin to move along their usual route (“home” →
“transport” → “work” → “transport” → “home”). Some family
members stay at home and do not visit crowded places.
Fig. 4. Getting started with the model
By default, the average value of indicators of infectiousness
and course of coronavirus is set, however, the user can change
these indicators at his discretion.
Infected people who are in the incubation period continue to
live according to the usual schedule. But after the onset of
symptoms, the sick person stays at home. The model has the
ability to adjust the conditions of isolation - at home waiting for
recovery only sick people, or the whole family together,
regardless of the number of cases.
The number of healthy, sick and recovered people changes
over time. This can be seen in the graph (Fig. 5).
Fig. 5. Graph of statistics on the course of the spread of COVID-19
Also, depending on the status of the person in relation to the
model of the course of the disease, the schematic representation
of agents can be colored in several colors. For convenience, the
decoding of the agents coloring was given directly on the
presentation of the model (Fig. 6).
C. Analysis of Simulation Results
According to the results of practical experiments were
obtained the data shown in Tables 1-4.
The modeling was carried out taking into account the
parameters of the presence (30% of all cases) / absence of
asymptomatic carriers, taking into account different conditions
of isolation: only the patient or the whole family.
TABLE I
There are no Asymptomatic Carriers.
The Whole Family is Isolated
Total
Ill and
recovered
Did not get
sick
Died
% of
infection
870
679
176
15
79,8
874
781
75
18
91,4
862
662
192
8
77,7
859
665
182
12
78,8
866
661
189
16
78,2
854
634
206
14
75,9
896
751
130
15
85,5
881
657
213
11
75,8
Fig. 6. Operation of the COVID-19 coronavirus distribution model
TABLE II
There are no Asymptomatic Carriers.
Only Patients are Isolated
Total
Ill and
recovered
Did not get
sick
Died
% of
infection
883
818
44
21
95,02
850
788
44
18
94,8
879
827
38
14
95,7
868
807
42
18
95,2
863
781
68
14
92,1
869
818
37
14
95,7
864
770
79
15
90,1
844
778
46
20
94,5
TABLE III
There are Asymptomatic Carriers.
Only Patients are Isolated
Total
Ill and
recovered
Did not get
sick
Died
% of
infection
872
858
4
10
99,55
844
828
2
14
99,76
897
888
1
8
99,9
859
847
5
5
99,4
875
863
1
11
99,89
879
866
4
9
99,55
848
835
3
10
99,65
868
848
7
12
99,2
TABLE IV.
There are Asymptomatic Carriers. The Whole Family is
Isolated
Total
Ill and
recovered
Did not get
sick
Died
% of
infection
875
850
10
15
98,86
892
867
12
13
98,66
877
851
13
13
98,52
877
851
18
8
97,88
899
882
8
9
99,11
894
872
12
10
98,66
877
851
8
18
99,01
896
874
7
15
99,22
The presence of asymptomatic cases significantly worsens
the epidemic picture of the spread of coronavirus disease;
therefore, it is extremely important to conduct a large number of
tests and follow the isolation rules.
During testing of the model with the condition of isolating
the whole family from the moment the symptoms appeared in
the first COVID-19 patient, it was obtained that only one family
had been ill. This is not possible in real life, since it is initially
extremely difficult to identify a certain infectious disease in
“patient zero”.
The obtained results show that for the isolation of the whole
family, the spread of the epidemic is much less than for the
isolation of only sick people.
IV. CONCLUSION
The paper suggests that anyone can potentially contract
COVID-19. This means that initially no one individual has full
or partial immunity, but he can find it after the illness. At the
same time, repeated cases of infection have been proven,
therefore, the possibility of obtaining / not receiving immunity
is implemented in the model.
A comparison of the obtained results of agent-based
modeling was carried out taking into account various conditions:
• depending on variations of propagation and the parameters
of the disease;
• in the presence of asymptomatic carriers (there was a
significant increase in the incidence of disease
COVID-19);
• compliance with the conditions of isolation (assuming
isolation of the whole family, where there is at least one
patient, the rate of proliferation decreases).
The used method, which based on agent-based modeling, has
allowed obtaining predictable results that can justify making
managerial decisions aimed at limiting the spread of the
epidemic.
The results obtained in some cases coincide with the results
of real waves of morbidity. Compliance depends on the number
of tests carried out in real life and, accordingly, calls people to
health facilities for proper diagnosis. In future works, it was
planned to consider the use of not only the agent-based
approach, but also neural networks.
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