NCSP'22
RISP International Workshop on Nonlinear circuits,Commuinications and Signal Processing 2022
February 28 - March 1

Effect of Social Distancing on COVID-19 Infection
Using a Multi-Agent Simulation
Masaki Saito , Yoko Uwate, and Yoshifumi Nishio
Tokushima University
2-1 Minami Jousanjima-cho, Tokushima, 770-8506, Japan
E-mail: saito, uwate, nishio@ee.tokushima-u.ac.jp

Abstract
As everyone knows, COVID-19 has spread all over theworld, and cumulative infected number is still increasing
day by day. Therefore, interventions to limit the spreadof COVID-19 should be considered for each event. Effective interventions to minimize COVID-19 transmission varyfor each event, according to a quantitative framework called
event R. Of those events, the example of school is the most
likely to be infected, but the intervention of distancing cut the
number of new infections in half.
Therefore, we use a multi-agent simulation to simulate
COVID-19 transmission with no measures and with social
distancing. In order to simulate under the same conditions
as in the event R calculation, our simulation is performed under the following conditions: a single infected person entersthe classroom with the first multiple uninfected people and acertain time passes. After that, the person enters the classroom with the same number of new uninfected people, andthe process is repeated 8 times.
The simulation results show that there is a relationship between social distancing and the spread of infection, but therate of decrease is not constant.

termine whether their settings are linear or saturating, andwhether people are strongly mixed or bubbling. Figure 2 also
adapted from Paul Tuppera, Himani Bouryb, Madi Yerlanova,and Caroline Colijn shows the values of event R for no measures and each intervention. In Fig. 2, the setting of highschools is saturating and mixing, and the results show thatdifferent events have different effective interventions.
The high schools that is most likely to be susceptible to infection in these four settings are focused on. Then, event R ishalved by halving number of contacts in event R considering
the social distancing. In addition, the calculations are madeunder the following conditions in high schools: a single infected person contacts the first multiple uninfected people fora certain time. After that, the same number of new uninfected
people are contacted. This is repeated 8 times, making thetotal time one week.

1. Introduction
The interventions to limit the spread of COVID-19 should
be considered for each event such as public transport, birthday parties, and high schools because the spread has not
yet converged around the world. Here, there is a quantitative framework to determine which interventions are likely tohave the most effect in which events. The concept of event
R is the expected number of new infected people due to thepresence of a single infected person at an event[1].
Figure 1 adapted from Paul Tuppera, Himani Bouryb, Madi
Yerlanova, and Caroline Colijn shows three types of interventions for reducing event R. They are measures to reducetransmission such as face masks, barriers, and hand hygiene,social distancing, and social bubbles.
Then, in workplaces and businesses, it is necessary to de-301

Figure 1: The three types of intervention

in which agents are given the states S (susceptible), I (infectious), and Re (recovered), and their states change in turn.
The SIR model is also applied to the early spread of SARSCoV-2 and fits the reported COVID-19 cases in Italy.
In this study, Our simulation using a MAS is performed
for the case with no measures and social distancing. Recovery and death are not considered in this one-week simulation
because the infectious period is approximately 8 days[3].
4. Simulation and Conditions

Figure 2: Four different kinds of events. They are (Left) linear (low transmission probability), (Right) saturating (hightransmission probability), (Upper) static (same contacts forwhole event), and (Lower) Mixing (high turnover of contacts)

Our simulation is performed with no measures and withpracticing social distancing. The conditions of the simulation
are shown below.

Therefore, we use a multi-agent simulation to simulate thenumber of COVID-19 infections in a high school without
measures and with social distancing. Then, Examine whether
the number of new infections is reduced by half by practicing
social distancing, as in the event R calculation. In addition,
examine the effect of infection reduction on changes in theproportion of people practicing social distancing.
2. Multi-Agent Simulation• The simulation is repeated 8 times with one initially infected person, 20 uninfected people, and a 400 square
meter (20m × 20m) classroom.
• The agent’s initial position and direction of movement
are determined randomly.
• All of the agents are between the ages of 15 and 18, andall of the infections are infectious and asymptomatic,
and there is no quarantine of the infections.
• The initial infected person is in the same classroom as a
total of 160 uninfected people, and is in a situation where
he or she can contact those uninfected people because
the initial infected person is always infectious for oneweek.

• If an infection enters within a radius of 1m around an unThe multi-agent simulation (Hereinafter referred to as
infected person, the uninfected person becomes infected,MAS) is based on the idea that programs do exhibit behavand the time required for virus transmission is 15 miniors entirely described by the program instructions. It is posutes. This is based on the definition of intensive contact
sible to simulate an artificial world inhabited by interacting
in Japan.
processes, by relating an individual to a program. We cansimulate by transposing the population of a real bio system• For all agents, behavior and contact outside the classto its artificial counterpart in which particular hypotheses canroom is not considered.
be explored by repeating experiments. Each organism of thepopulation is represented as an agent whose behavior is pro• In order to obtain results under the same conditions as
grammed with all the required details[2].
the event R calculation, the time of our 8 repeated simuThe simulation of the number of people infected with inlations is set to one week. Weekends are not taken into
fectious diseases is sometimes performed using a mathemataccount, and the time for one simulation is set at 8 hours.
ical model based on differential equations. In addition, overall parameters such as infection rate and mortality rate are
In the simulation of social distance, a repulsion force thatdefined, in the simulation using a mathematical model. Howis inversely proportional to the distance between the agents
ever, in the simulation using a MAS, it is possible to conshould be applied if another agent enters within a radius ofsider more details than in the simulation using a mathematical
2m around an agent. The repulsion force effects the speed andmodel because several parameters are given to each agent.
direction of movement of the agents, and the agents always
try to keep their distance from each other.
In this study, the proportion of the number of new infec3. Modeltions to the 20 uninfected people is obtained. The data obOur one-week simulation using a MAS of the number of tained from 8 repeated simulations are averaged, and thisnew infections uses the SIR model. The SIR model is a model simulation is performed 10 times. Then, the average of the302data from these 10 times is obtained. In addition, our simulaThe results obtained from 11 different simulations aretions are performed with no measures and with the number of shown in Fig. 4. The value of 0% for the proportion of peoagents practicing social distancing set to 10 different values, ple practicing social distancing is the result of the simulationfrom 10 to 100% of the number of uninfected people. How- with no measures.
ever, in the simulation with social distancing, one initially infected person practices social distancing in all situations. For
example, the total number of agents practicing social distancing is 11 if 50% of the agents practice social distancing.
5. Results
An image of the result of one of our 8 repeated simulations (with no measures) is shown in Fig. 3. The scatter plot
above shows the agents, and the movement of the agents andthe infection situation can be recognized as a video by outputting 32 images continuously. The red points are the infected agents and the blue points are the uninfected agents.
The graph below shows the number of infected and uninfected people at the same time as the scatter plot above. Inthis graph, the horizontal axis is time and the vertical axis is
the number of infected people, and the red area rises as thenumber of infected people increases. In the case of the simulation shown in Fig. 3, one initially infected person eventually
generates 14 new infections.

Figure 4: Results of simulations that performed with no measures and with the number of agents practicing social distancing set to 10 different values, from 10 to 100% of the numberof uninfected people

In Fig. 4, the number of new infections decreased as theproportion of people practicing social distancing is increased.
However, the number of new infections is not reduced byhalf compared to the simulation with no measures as in theevent R calculation. The social distancing is represented byhalving the number of people in contact in the event R calculation, whereas the agents in a MAS move randomly andalways try to keep a distance of 2m each other. Even if thecontacts between initially infected person and uninfected people is halved in a MAS, the new infections contact each otherin one simulation. Therefore, the number of new infections
decreases by only about 30% when people practice social distancing of 2m because of secondary infections in the simulation using a MAS.
In addition, the simulation results for the case with no measures and the case with 10% of the people practicing social
distancing show that there is a difference of about 10% between these two values. The value of this difference is larger
than the difference of the other values. Then, one initially
infected person practices social distancing in all simulations
with social distancing. Therefore, this confirms that the effectFigure 3: An image of the result of one of our 8 repeated of practicing social distancing on the spread of infection byinfectious people is significant.
simulations (with no measures)303

6. Conclusions
The purpose of this study was twofold. To confirm whether
the number of new COVID-19 infections with social distancing is reduced by half compared with no measures. To analyze the effect of the number of people practicing social distance on the spread of infection.
Then, our simulations were performed using a MAS, withno measures and with the number of agents practicing social
distancing set to 10 different values ranging from 0 to 100%of the number of agents.
As a result, in the simulation with social distancing, thenumber of new infections is not reduced by half comparedto the simulation with no measures. However, the number of
new infections decrease as the proportion of people practicing
social distancing is increased.
References[1] Paul Tuppera, Himani Bouryb, Madi Yerlanova, and Caroline Colijn: Event-specific interventions to minimize
COVID-19 transmission, Proceedings of the National
Academy of Sciences of the United States of America,
117(50), pp.32038-32044, 2020.
[2] Alexis Drogoul and Jacques Ferber: Multi-Agent Simulation as a Tool for Modeling Societies: Application toSocial Differentiation in Ant Colonies, MAAMAW 1992.
Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence), vol 830, pp.2, July 2005.
[3] Jose M. Carcione, Juan E. Santos, Claudio Bagaini,and Jing Ba: A Simulation of a COVID-19 Epidemic
Based on a Deterministic SEIR Model, Frontiers in Public Health, Volume 8, Article 230, pp.4-12, May 2020.
[4] Marco D’Arienzo and Angela Coniglio: Assessmentof the SARS-CoV-2 basic reproduction number, R0,
based on the early phase of COVID-19 outbreak in Italy,Contents lists available at ScienceDirect Biosafety andHealth, Volume 2, Issue 2, pp.57-59, June 2020.
[5] Shaobo He, Yuexi Peng, and Kehui Sun: SEIR modelingof the COVID-19 and its dynamics, Nonlinear Dynamics An International Journal of Nonlinear Dynamics andChaos in Engineering Systems, 101, pp.1667-1680, June2020.

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