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.