IEEE Workshop on Nonlinear Circuit Networks
December 3-4, 2021

Examination of the Effect of Restriction on
Non-Vaccinated People with COVID-19
Naohide Hashimoto, Yoko Uwate and Yoshifumi Nishio
Dept. of Electrical and Electronic Engineering of Tokushima University
2-1 Minami-Josanjima, Tokushima-shi, Tokushima-ken 770-8506, Japan
Email: {hashimoto, uwate, nishio}@ee.tokushima-u.ac.jp

Abstract ― COVID-19 is causing a global pandemic. Vaccines have already been developed and are being promotedin many countries. In the UK, most of the lockdown regulations were lifted in July this year because of the widespreaduse of vaccines. Many regulations have been lifted in Japan
since October. As deregulation progresses, it is necessary toconsider efficient measures to spread infection, assumingthat a pandemic will occur again. Therefore, in this study,
we examined the effect of restricting movement only to those
who have not been vaccinated.

determined agents to stop movement when estimating the effect of movement restriction. We believe that more effects
can be achieved by arbitrarily deciding which agent to stopmoving. Therefore, in this study, MAS was performed withthe aim of comparing changes in the infection status between
the case where the movement of random agents was regulated and the case where the movement was regulated by selecting an agent who had not been vaccinated.

Ⅰ. INTRODUCTION

Ⅱ. MULTI – AGENTS - SIMULATION (MAS)The pandemic by COVID-19 is spreading worldwide. Thebasic reproduction number of this virus was estimated to be 1.42.5 [1]. In other words, one infected people infects an averageof 1.4-2.5 people. This strength of infectivity has triggered aglobal pandemic. The incubation period that characterizes thisvirus was estimated to be 5.1 days [2].
Before the vaccine was developed, many areas took somesteps to prevent the spread of the virus. Such measures include
the use of masks, social distance, border blockages, outing restrictions, and temporary suspension of universities and businesses. Simulations have shown that these measures have someeffect [3].

Vaccines that are effective in preventing COVID-19 infection have already been developed. Governments are working
to popularize this vaccine. With the spread of vaccines, thenumber of newly infected people is declining. As a result, inJapan, restrictions on the movement of people will be withdrawn, and the market where people gather will reopen. Under such circumstances, it is important to predict the spreadof infection when the movement of people in the vaccine environment resumes.
There are two methods for predicting the spread of virus
infection. It is a method using a mathematical model and asimulation method using multiple agents (Multi-AgentsSimulation: MAS). When a mathematical model is used, it isrelatively easy to calculate and is effective for predicting amacro range. MAS, on the other hand, is useful for predicting local ranges.
In recent years, there have been many studies on COVID19 infection prediction using mathematical models. However, there are not many predictions using MAS. MAS considering vaccines is even less. Many studies also randomly

MAS is a method that controls the movements of multiple
agents individually and simulates the interaction of each agent.
It is possible to specify attributes such as age and status for theagent. Since it is possible to control the movement of individualagents, it is possible to obtain detailed information that cannot
be analyzed by mathematical models. Therefore, it is used forsocial experiments on computers. In this study, MAS is effectivein distinguishing the behavior of vaccinated and non-vaccinatedagents.

Ⅲ. ANALYTICAL MODEL
In this study, we used an extension of the SEIR model, which
is often used for infectious disease analysis. The SEIR model isa mathematical model that divides the entire population into S(Susceptible People), E (Exposed People), I (Infected People),and R (Recovered / Removed People) groups and estimates thetime change of each group. be. In this study, in addition to theabove four groups, three groups, I'(Not Symptomatic InfectedPeople), M (Minor Illness People), and G (Grave Illness People),
were added. Figure 1 shows the transition diagram of eachgroup.
Upon contact with I or E, S becomes infected and changes toE. E becomes ill over time and changes to infected people I withsymptoms and infected people I' without symptoms. After alapse of time, I changes to M or G and is quarantined. M and G
change to R or G over time.

- 26 -Table 2. Coefficients of the modelFig. 1. State transition diagram

Ⅳ. SIMULATION
The vaccine prevalence in Japan on October 25 was
78.1% for the first vaccination and 74.3% for the second
vaccination [4]. Based on this data, simulations were performed in four patterns in an environment where vaccinatedpeople exist.
Sim.1: No vaccine. No movement restrictions.
Sim.2: With vaccine. No movement restrictions.
Sim.3: With vaccine. There are movement restrictions. 10%of random agents are inactive.
Sim.4: With vaccine. There are movement restrictions. 10%
unvaccinated agents cease activity.
Table 1 shows the behavior rules of each agent.

Number of agents

400 people

Number of Initially infected

20 people

Period of exposed

5.1 days

Period of Disease duration

10 days

Plobability of infection(α)

50%Probability of symptom(β)

80%Plobability of severe(γ)

5%robability of death(δ1)

1.30%

robability of death(δ2)

9.80%

Plobability of Infection prevention(Once vaccination)
Plobability of Infection prevention(Twice vaccination)
Probability of prevention of severe(Once vaccination)
Probability of prevention of severe(Twice vaccination)
Period of isolation

Table 1. Agent behavior rules

DaytimeGather at company or school

Evening:Free to move in the town

NightStay homeHolidays

Free to move in the town
Ⅴ. CONDITIONS

Table 2 shows the values of each parameter used in the simulation. In general, the infection probability α is difficult toestimate. Therefore, referring to the estimated basic reproduction number of COVID-19 [1], the parameters were adjusted sothat the number of infected people infected in one day would beabout 2.
The image of the simulation is shown in Fig. 2.

- 27 -Fig. 2. Simulation image

61%
93%
68%
96%
2days

people continue to occur for a long time. In addition, it can beseen that there is no significant change in the spread of infectionin each simulation.

15

Infected

Ⅵ. RESULT
Figure 3 shows the changes in the number of newly infected
people observed in Sim.1 and Sim.2. This is the amount of increase in M and G. I' is not symptomatic and is not observed, itis not included in the number of infected people.
From Figure 3, the peak infection is around 12 days in theabsence of vaccine. On the other hand, when more than 70% ofagents are vaccinated, there is no major peak and few infectedpeople continue to occur for a long period of time.

300

Sim.2
Sim.3
Sim.4

10Infected

5Sim.1
Sim.2

200

00

1020304050

Day100Fig. 5. Changes in the number of newly infected people(Sim.2, Sim.3, Sim.4)00

1020304050

DayFig. 3. Changes in the number of newly infected people(Sim.1, Sim.2)

Figure 4 shows the transition between illnesses in infectedagents. The peak of Sim.1 is high and the peak of Sim.2 is low.
In general, a sharp increase in the number of infected people
causes medical collapse. The results show that the spread ofvaccines is effective in reducing peak infections and preventing
the problem of medical confusion.

Next, Table 3 shows the total number of infected people andthe number of deaths.
Table 3 shows that the total number of infected people is lowest in Sim.3. Furthermore, the number of infected people in
Sim.4 is 29.4% lower than in Sim.3. This indicates that the number of infected people can be reduced by 29.4% by selecting
unvaccinated agents and implementing movement restrictions.
On the other hand, the number of deaths is the maximum
value in Sim.1 and the minimum value in Sim.2. However, due
to the extremely small number of deaths, no significant difference is shown.
Table 3. Total number of infected people and number of deaths

Infection

Infected

4030

Sim.1
Sim.2

20

Sim.1

302

5

Sim.2

177

1

Sim.3

153

4

Sim.4

1083

1000

Death

Ⅶ. DISCUSSION
1020304050

DayFig. 4. Changes in the number of disease agents(Sim.1, Sim.2)

Fig. 5 shows the transition of the number of newly infected
people observed from Sim.2 to Sim.4.
Looking at Figure 3, it is shown that from Sim1 to Sim3, there
is no sudden peak of infection, and a small number of infected

In Table 3, there was a difference in the total number of infected people, but there was no significant difference in thenumber of deaths. The cause may be that there is a large difference in mortality rate by age. It is also reported that the mortality
rate in the 70s is about 93 times higher than that in the 30s. Thistime, the ages of all agents were regarded as the same, and thesimulation was performed assuming an average mortality rate.
As a result, the mortality rate was low and the number of deaths
was small, so it is considered that there was no significant difference in the number of deaths.

- 28 -

Ⅷ. CONCULUSION
In this study, we investigated the infection prevention effectwhen selective movement regulation was implemented in amodel considering vaccines. As a result, it was found that thenumber of infected people was reduced by 29.4% when themovement regulation was implemented by selecting the nonvaccinated people as compared with the random movement regulation. In addition, it is considered that the number of deaths
can be discussed by considering the age in the simulation model.

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