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European Journal of Applied Sciences – Vol. 10, No. 1

Publication Date: February 25, 2022

DOI:10.14738/aivp.101.11507. Ohnishi, T. (2022). By What Extent the Japanese Has Been Surprised by COVID-19 Information?: Emotional Contagion and its

Mathematical Model. European Journal of Applied Sciences, 10(1). 39-56.

Services for Science and Education – United Kingdom

By What Extent the Japanese Has Been Surprised by COVID-19

Information?: Emotional Contagion and its Mathematical Model

Teruaki Ohnishi

Institute of Science and Technology for Society, Urayasu, Chiba, Japan

ABSTRACT

A strong field of negative information as the case realized by COVID-19 must greatly

enhance the public feelings such as the fear, the disgust and a sense of crisis against

it. The information environment regarding COVID-19 and the public reactions to it,

which had appeared from the early 2020 to September 2021 in Japan, were first

reviewed. The proposition of a mathematical model was followed, where the

negative and strong field of information as the issue of COVID-19 was assumed to

make the public surprised and their emotions changed negatively via the

mechanism of emotional contagion. The frequency of the public access to SNS and

Internet under the atmosphere of COVID-19 was considered as a manifestation of

the public for seeking reliable information and as an index of the public reaction

originated from the negative emotion. By using the time-varying data of the

information field of COVID-19, the extent of the public surprise that was considered

as the emotional contagion from the field was derived. That extent became clear to

have varied heterogeneously with time, having been subjected by the state of

information field which have varied with three phases as the initial, transient and

quasi-stable ones. It was found that, only in the quasi-stable state of the field, the

number of public access to SNS and Internet can mimic the social reality of the issue

concerned. Physical and mathematical models, where the psychological

phenomena as the emotional contagion are positively included, were pointed out to

be central ingredients to understand the behavior of the public in the society more

comprehensively than it is today.

Keywords: COVID-19; mathematical model; emotion; emotional contagion; SNS; surprise;

information field; news media; Japanese

INTRODUCTION

All the news media such as newspapers and the television make information environment

around us. Since people live in such an environment [1,2], they are aware of negative or positive

atmospheres of the environment so that they become to be of the same color as the

environment though it may be temporary. The sense of people on a certain subject is, thus,

determined depending on the quality and the strength of the information environment so that

the time variation of the collective sense of people can be said to link with the variation of the

information environment through the mechanism of emotional contagion [3-5].

Although the emotional contagion is defined as the propagation of emotion between people [6],

we here like to include in it also the propagation and the induction of emotion from the

environment to people. A well-known example for the emotional contagion is music, where the

environment stimulates public feelings to induce the same sense as itself [7,8]. In the

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European Journal of Applied Sciences (EJAS) Vol. 10, Issue 1, February-2022

Services for Science and Education – United Kingdom

psychological region some approaches have been done for the quantification of the contagion

of various emotions [9,10]. In recent years digital emotional contagion [11] is widely noticed to

result in many researches [12-14], where messages brought by digital media or the propagation

of emotion between SNS users lead to a specific direction of collective sense.

Also in the region of social physics, a methodology to positively take the emotion into account

as a variable has been accepted where the action and the way of thinking of people are treated

in terms of the emotion [15-22]. In these approaches the emotion is usually introduced as a

function of other variables or treated as a parameter normalized within [0, 1], for instance.

Those physical researches are situated at the downstream of information flow from the media

to the end, and therefore they are not the ones on the upstream side of the flow where the

emotional contagion becomes an issue between the news media and people.

One of the important factors for the effective propagation of information on the upstream is the

obtrusiveness of information. In the communication theory it results in whether the

information has an agenda setting function or not [23-26], that is, whether it has a particular

content topical for people or not. The agenda setting function is weak for an issue which has

been reported for a long time when it is compared to a novel issue. For the case of the former

issue people have a lot of memory about it so that it lacks of freshness and novelty even if it is

new information. It causes feelings of habituation and boredom in people. For the case of an

obsolete issue, therefore, much information is required for changing people’s mind as

compared to a new issue.

The agenda setting effect on a new issue, or in other words the recognition of the significance

of the issue becomes maximum around 8-12 weeks after the exposure of information, and

decreases after 12-25 weeks [27]. For the assessment of this effect it must evaluate the strength

of the impact of exposure which has not been studied quantitatively, although in the past the

extent of the exposure has been quantitatively counted by the number of articles in newspapers

or the broadcasted time on the television. For the strength of agenda setting effect, it is also

pointed out the importance of the treatment of information by statistically taking into account

the prominence of the issue such as the size of title [23] for instance, but any researches have

also been done quantitatively. Watt, Mazza and Snyder [23] show, in relating the information

environment to people, that the following four factors become important for people’s cognition

of information; (1) memory of information, (2) habituation to the issue, (3) delay of people’s

reaction or the so-called attitudinal inertia and (4) selective attention toward a specific

information.

In the case when a specific emotion propagates through the society from the news media to the

end and the people’s view of values is influenced by that emotion [28], we can simply depict its

aspect as in Fig.1. Emotional resonance by music corresponds to the process 4) in this figure,

and the propagation of rumor with emotion and the influence of emotion in various social

activations correspond respectively to 5.1) and 5.2). The study by Wheaton, Prikhidko and

Messner [29] is a research of emotional contagion regarding COVID-19 on such an upstream

side by a psychological approach. Researches including modeling on this side have been forced

to be phenomenological mainly because of the lack of reliable numerical data. In this paper the

processes 3) and 4) on the upstream side in Fig.1 is mathematically modeled by using the data

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Ohnishi, T. (2022). By What Extent the Japanese Has Been Surprised by COVID-19 Information?: Emotional Contagion and its Mathematical Model.

European Journal of Applied Sciences, 10(1). 39-56.

URL: http://dx.doi.org/10.14738/aivp.101.11507

of COVID-19 in Japan to exemplify the emotion which has been treated only implicitly in

physical sciences.

In Section 2 the statistics are shown for the information environment on COVID-19 in Japan up

to the end of September 2021. In Section 3 the social atmosphere and the time variation of

people’s emotion regarding COVID-19 are shown. A simple mathematical model and its

example calculation are given in Section 4. By using this model, the emotional contagion factor

is derived in Section 5, which is our index to indicate by what extent people’s emotion is affected

by the contagion from the COVID-19 information. Conclusion is given in Section 6.

Fig.1. Schematic diagram for the relation between the public and emotion

INFORMATION ENVIRONMENT OF COVID-19 AND JAPANESE REACTION ON SNS

In this paper we set 1 January 2020 as t=1 and use a unit of time ∆t=1 [day] from t=1 to 30

September 2021 (t=639). In 2020 the news media to which the Japanese access for getting news

once or more per week are (1) the television (of which 74.5% of the Japanese make use), (2)

Web sites (54.7%), (3) newspapers (46.1%), and (4) the SNS (36.8%) [30]. We divide the

information released by the television and newspapers as the primary one for which they cover

events to get their originality, and the secondary information released from the remaining

media except for them. In what follows we quantitatively investigate how the primary

information on COVID-19 has been released with time after January 2020 in Japan.

Fig.2(a) shows the time variation of the number of patients infected by COVID-19 per day [31],

d(t), and its moving average over the past one week D(t). Here the quantity D(t) is defined as

(1)

( ) ( )

6

0

D t N f d t t t

t o å × - ¢ ¢=

¢