Visiting 3S Researchers #02 Dr. Hiroshi Nishiura
Mathematical Modelling to Analyze COVID-19 Pandemic and the Fight Against Infectious Diseases on the Frontline
─ Ambitions to Model Infectious Disease Spread Accounting for Behavioral Changes as a Mathematical Function ─

3S is the abbreviation for “Seiwa Scholars Society,” which consists of the past and current Inamori Research Grant recipients. The 3S has evolved since 1997 with the hope that the interactions among the various specialties of the 3S members can lead to the further development of the research of their own. In the series “Visiting 3S Researchers,” we interview researchers in 3S who are very active in a variety of fields. The second interview is with Dr. Hiroshi Nishiura (2017 Inamori Research Grant Recipient) from Kyoto University.

The epidemic of the newly emerged coronavirus disease in China from the end of 2019 has spread rapidly around the world. The cumulative number of infected individuals continues to increase in Japan. Professor Hiroshi Nishiura of Kyoto University analyzes the transmission dynamics of the coronavirus using a computer simulation and mathematical models. He proposed to the government the fundamental countermeasures for the prevention of transmission, namely “80% reduction in contact” and “Avoid Three Cs (confined spaces, crowded places and close-contact settings).” We interviewed Dr. Nishiura, who uses mathematics to fight against the invisible enemy of infectious diseases that affect all human beings, and asked about the forefront of COVID-19 countermeasures and the goals of his research.

Research on the Frontline of the COVID-19 Control

── Dr. Nishiura, you are known as “Uncle 80%” due to a countermeasure to prevent the transmission of COVID-19 by “80% reduction in contact”. You also proposed “Avoiding Three Cs,” which you derived from your mathematical analyses. They have been widely accepted throughout the country. While you moved from Hokkaido University to Kyoto University in August 2020, have you continued to be involved in the public health control of the Japanese government?

Dr. Nishiura (title omitted below) As a formal position, I participate in the advisory board of the Ministry of Health, Labor and Welfare (MHLW) for COVID-19 control every week. There, we analyze the epidemic dynamics on a daily basis using the latest dataset, and offer scientific advices to the government via Advisory Council on Countermeasures against Novel Influenza and Other Diseases. I am a part of the team that specializes in risk assessment. In order to suppress the transmission and minimize associated damages, the team members continue to discuss online day and night, regardless of weekends and holidays.

── “Go to Travel” and “Go to Eat” campaigns, which were promoted as economic stimulus measures under the corona disaster, was suspended in January.

Nishiura I think the objective analysis by the Advisory Board acted as one of the reasons for their decision to suspend the campaign. In the early stages of an unknown infectious disease such as this COVID-19, we do not know how the transmission is propagated and what kind of people are likely to be infected or become seriously ill. I think it was a certain achievement that Japan was able to avoid the explosive growth of cases at an early stage by designing its own countermeasures by analyzing cluster data using mathematical models. Mathematical models were able to point the direction for the fight against this invisible (not directly observable) virus. On the other hand, as you already know, avoiding contact avoidance and other social distancing measures have had a significant impact on people’s socioeconomic activities. I realize difficulties in balancing socioeconomic activities and infectious disease control every day.

── Prior to COVID-19, did you have opportunities to give feedbacks to the government with respect to the results of your research on mathematical modeling of infectious diseases?

Nishiura Yes, I did. At the MHLW, I have presented the results of mathematical analysis of HIV (Human Immunodeficiency Virus) infections, flu and rubella. As for the rubella control, our results revealed that supplementary vaccinations for adult males in their 30s and 40s are effective in controlling the spread of rubella, and the MHLW developed the implementation plan. However, the ongoing COVID-19 pandemic is the first time that I have had to make recommendations for countermeasures in a very short period of time, while continuing to analyze the data and update the situation awareness on a daily basis.

Does ”Factor X” Really Exist among Japanese?

── In the early stages of the epidemic, you estimated that if no countermeasures were taken, about 850,000 people in Japan could become seriously ill, and 420,000 of them could die of the infection.*1 I feel that these figures had a great impact on the public and raised awareness of the danger of coronavirus. On the other hand, the numbers of COVID-19 infections and deaths in Japan have remained small compared to Europe and the U.S.A. It has been suggested that there may be some physiological factor or the so-called “Factor X” that suppresses the risk of infection. What do you think about Factor X?

Nishiura There were a lot of controversies after the announcement of estimated impact, partly because the figure of 420,000 people was perceived as substantial. That figure was obtained from an epidemic model using estimates of the transmission potential and case fatality risks in China, Germany, France, Spain, and other countries where the outbreak had already begun. At present, we think that the reason for the low number of COVID-19 deaths in Japan is not because of the physiological Factor X, but mainly because of the small number of infections. The cases were maintained to be small due to environmental conditions, stochastic fluctuations and initial countermeasures that were successful in the early stages of the outbreak. We think that early stage interventions enabled the transmission to be suppressed, in other words, the number of infectious cases kept low, and in the end, the epidemic was delayed to start.

seminar at Hoppaido Univ

Dr. Nishiura’s seminar at Hokkaido University (August, 2019・Provided by Dr. Nishiura)

── In order to control infectious diseases, I think that, besides your research on mathematical models, academic knowledge from a wide range of fields such as economics and sociology, not to mention medicine, is necessary. With what fields of researchers do you want to deepen your interaction in the future?

Nishiura I think that is highly likely. In other countries than Japan, such as Korea, Taiwan, and several others in Southeast Asia, the spread of the disease in the first half of this year was not as severe as it was in Japan. Also, if you look at the details, even in the U.S., there are differences in infection rates at the regional level, such as states. A detailed analysis of these regions revealed that there were four major factors that lead to COVID-19 transmission: population density, temperature, human mobility and contact rate, and compliance with wearing face masks, hand washing and social distancing.*2, 3 We put the four factors into functions, and made a predictive mathematical model, analyzing the time series correlation with the effective reproduction number*4 which is an objective indicator of secondary infection. The results from our model were consistent with the actual infection situation in every geographic location.

Looking at epidemiological situations in large cities such as Tokyo, Osaka, and New York, it was obvious that the spread of the virus is more severe in densely populated areas. This is because the more an area is populated, the higher the chance of encountering indoor contact will be. Analyzing epidemiological situations in Southeast Asia has also shown that the lower the temperature, the easier it is for the virus to spread. While they were recognized as excellent in epidemic control, it was a mystery why the number of infected people did not increase as much in rural areas in Thailand and Vietnam, where efforts to control infection were not as intensive as in Japan. Nevertheless, when the temperature fell in the winter season in their mountainous areas, the infection rate started to increase.

Since the coronavirus moves as people move, it has been shown that the rate of human movement determines the trend of the infection. In China, in fact, the government has been able to control the infection by forcibly restricting the movement. In the U.S.A., the Trump administration’s policies delayed the whole society from wearing face masks or addressing physical distance, which resulted in the spread of the infection. In other words, looking at the international situation, it is extremely dangerous to conclude that Japan is a special country just by looking at the numbers of cases and deaths in the early stages of the pandemic. Besides, I think it is worthwhile to continuously carry out scientific analysis towards elucidating Factor X, including physiological factors.

The Impact of Mathematical Modelling on HIV Prevention

── In the special article “What mathematics can do for fighting against COVID-19” in the September 2020 issue (No. 707) of “Sugaku Seminar,” you included population heterogeneity such as age and gender as factors in your calculations. Does racial heterogeneity also affect the infection rate and the severity rate?

Nishiura In general, analysis of infectious disease data involves looking at data such as sex, age, racial background, and occupation as basic process to see if they are associated with the risk of infection. In the case of COVID-19, mathematical models clearly show that gender and age are very much related to mortality risk. The severe acute respiratory syndrome (SARS), which caused an epidemic from 2002-03 and caused by a closely associated coronavirus, was also more severe in men. It is suggested that sex hormones play a role in the mechanism of the severe manifestations. Also, as you may know, the mortality rate increases with age.

However, there seemed to be little difference in the severity rate or the mortality rate between races. For example, The Diamond Princess,*5 which attracted huge attention in February 2020, was filled with wealthy elderly retirees from many countries, like China, the U.S.A., Europe, the Middle East, Africa, etc. But no significant difference was found in the rate of serious illness or death based on nationality or race. In the U.S.A., blacks and Hispanics continue to have the highest mortality rates per population, but this is probably not due to physiological factors of severe manifestation, but rather, because they live in densely populated areas where the risk of infection is high, or because they work in the service industry where indoor contact is unavoidable.

── I see. It is shocking to hear that “Factor X” may not exist, but I understand that by using a mathematical model, we can make an objective analysis based on empirical data, not based on vague impressions.

Nishiura In my experience, one of the epoch-making achievements was the calculation of infected and undiagnosed HIV patients in Japan based on a mathematical model, which led to the national AIDS policy. It takes an average of 10 years to develop AIDS from the HIV infection. During that time, it remains silent. This is why it is extremely important for people to be aware that they might be infected and get themselves tested in order to prevent the spread of the disease. Using a mathematical model called “backcalculation” to estimate the number of infected people under the surface, we can quantitatively estimate that there are about 30,000 HIV-infected people in Japan at present, and about 80% of them have already been diagnosed. As a result, we realized that it is important to implement targeted interventions to get the remaining 20% diagnosed, and proposed this to the government. Before conducting the study, I thought that the calculation would be quite mathematically difficult. But as I thought about it, I realized that it could be described with even a single estimation formula, and was really delighted that we were able to come up with a figure that would lead to an actual reduction in the number of patients.

x t = s = 1 t λ t s x = t s + 1 t 1 1 α x y = 1 s 1 1 ρ y

Equation for estimating (undiagnosed) HIV-positives at a calendar time t (xt ) from three rates:HIV incidence (λ), HIV diagnosis (α), and AIDS onset (ρ)*6
Incorporating Behavioral Changes into the Model Function

── What is your current research goal?

Nishiura COVID-19 infections have peaks and drops in outbreaks every few months. Not to mention the impact of strong countermeasures against the pandemic, but I think this is probably because behavior changes are occurring as a result of media coverage or changes in people’s awareness. I began to think about creating a mathematical model of the interrelationship between media announcements and infection rates.

In Sapporo city, Kanto region or Osaka prefecture, the second wave peaked between the end of July and the first week of August. I analyzed the timing in detail, and the result suggested that even though the Japanese government did not request people to refrain from certain activities, many people “read the room” (i.e. feel the atmosphere) and voluntarily reduced their mobility, which weakened the exponential rate of infection.

Daily number of PCR positives in Osaka prefecture (Formulated by the Inamori Foundation based on data posted on the Osaka Prefecture’s COVID-19 Taskforce website)

Nishiura As you have probably felt firsthand, when the public’s mood toward coronavirus becomes “this looks bad,” the number of people drinking at night suddenly decreases. Then, the contact rate decreases, and the infection rate is also reduced a little later. In my experience, COVID-19 is the first infectious disease in which infection can be clearly controlled by reducing the contact rate. Of course, this phenomenon can only be seen while the number of infected people is low, but as the epidemic grows, people’s mobility changes, and as a result, the infection rate also decreases. If we can make a mathematical model of the mechanism of this interaction, we may be able to design effective measures to control infectious diseases by giving effectively-timed announcements that encourage people to change their behavior.

── So, you are aiming to integrate even the behavioral changes of people into the function of the mathematical model.

Nishiura Yes, I believe this is a very interesting and meaningful challenge from a mathematical point of view, as well as being of practical value to the society. Vaccines against COVID-19 have now been developed and vaccination has started in many countries. However, it will take a long time before the vaccine is available to all the people in Japan. I am certain that the epidemic will occur a few times before vaccine roll-out. Therefore, as one of the effective measures to help buy time, I hope to be able to implement a customized method of infection control through early announcements.

Imagining the ” Human Story” Beyond the Figures

── What do you think you would be doing if you had not chosen this profession?

Nishiura Definitely a jewelry appraiser. I am from Osaka, and since I was an elementary school student, I liked to see the jewelry appraisers’ small temporary booth-like stores near Namba station of Nankai Electric Railway. It was the time of the bubble economy, and there were all these beautifully-dressed women lined up in front of those stores with their pieces of jewelry. The appraisers would look at the jewels and tell their valuation to the ladies. Each time they would do so, I could see how disappointed or happy the ladies were, which gave me a sense of human drama through jewelry. I feel that it is really wonderful to be able to witness human drama in such a way through your professional skills and work that can’ t be performed by others. My current job involves dealing with inorganic data in the form of numbers, and the results I derive will affect the lives of many people. Having started working with bureaucrats and politicians who are in the center of the country, I sometimes get a little tired of the “too much human drama” of the situation, haha, but I find it as interesting as being a jewelry appraiser.

Dr. NIshiura at online interview

Dr. Nishiura speaking in the online interview

── In order to control infectious diseases, I think that, besides your research on mathematical models, academic knowledge from a wide range of fields such as economics and sociology, not to mention medicine, is necessary. With what fields of researchers do you want to deepen your interaction in the future?

Nishiura The present pandemic of new coronavirus has taught us the importance of thinking beyond the scope envisioned by the word “interdisciplinary” up to now. For example, would it be a smart decision for people to continue to live in urban cities after the COVID-19? In order to make our society more resistant to infectious diseases, we will surely need the opinions of urban planning experts. Without a comprehensive, cross-sectional approach that includes not only the natural sciences but also the social sciences and humanities, we cannot overcome infectious diseases. Since I joined the network of the Inamori Foundation research grantees, the Seiwa Scholars Society, I have received contacts and information from researchers in other fields including social sciences that I got to know. I hope to use these connections to make my research even more relevant to the world.

── Thank you again for taking your time Dr. Nishiura.

*1. Estimated damage announced on April 15, 2020, at a press conference by the Novel Coronavirus Response Headquarters team at the Ministry of Health, Labor and Welfare of Japan, to which Dr. Nishiura belongs.

*2. Merow C, Urban MC (2020) Seasonality and uncertainty in global COVID-19 growth rates. Proc Natl Acad Sci U.S.A. 117:27456-27464.

*3. Smith TP, et al. (2020) Environment influences SARS-CoV-2 transmission in the absence of non-pharmaceutical interventions. medRxiv:2020.09.12.20193250.

*4. An indicator of infectious status. The average number of secondarily infected individuals directly produced by an infected individual in the current population where an infected person may already exist.

*5. A cruise ship on which a large number of passengers were infected with COVID-19 in January 2020. A long-term quarantine was imposed at the Port of Yokohama, and the measures were continuously reported by the media in many countries.

*6. Nishiura H (2019) Estimating the incidence and diagnosed proportion of HIV infections in Japan: a statistical modeling study. PeerJ 7:e6275.


By My Side Blackboard
Since his days as a researcher in Europe, he has been using a blackboard to write equations in his research. This blackboard is the one he carries around with him, disassembling it every time he moves from one university to another. He seems a little disappointed that young researchers tend to prefer whiteboards. “I love the sound and smell of writing equations on the blackboard with chalk, and the feeling of erasing with a blackboard eraser and starting again. Writing equations on a whiteboard with a pen doesn’t give me the same feeling.”
This Book The Ecological Detective: Confronting Models with Data” by Ray Hilborn.
As the ”Ecological Detective” in the title implies, this book presents the mechanisms of life as a story, drawing on mathematical and statistical models. “There are not many academic books that are accessible to everyone, but this book is so fun that you can lie down and read it. It makes me want to share the excitement of my research field with my students in such a way.”


Hiroshi Nishiura
Born in Osaka in 1977. Dr. Hiroshi Nishiura received his M.D. in Medicine from Miyazaki Medical College (presently University of Miyazaki School of Medicine) and Ph.D. from Hiroshima University Graduate School of Health Sciences. After graduation, he gained extensive research and teaching experience at Imperial College London, University of Tuebingen, University of Utrecht, Nagasaki University Institute of Tropical Medicine, and the University of Hong Kong. Dr. Nishiura served as associate professor at the University of Tokyo Graduate School of Medicine from 2013, professor at Hokkaido University Graduate School of Medicine from 2016 and has been a professor at Kyoto University Graduate School of Medicine since August 2020. His speciality is the analysis of epidemic data using mathematical models of infectious diseases. He has been working on epidemic data analysis for the Novel Coronavirus Response Headquarters team at the Ministry of Health, Labour and Welfare.

Interview date: December 15, 2020
Interview and original article by Yutaka Ogoshi (team Pascal)

*The interview was conducted online.


“Visiting 3S Researchers” series    
#01 Dr. Rie Umetsu
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