Theoretical Epidemiology of
Infectious Diseases
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Anderson RM, May RM (1991) Infectious Diseases of Humans: Dynamics andControl. Oxford Univ. Press
Diekmann O, Heesterbeek JAP (2000) Mathematical Epidemiology of Infectious
Diseases: Model Building, Analysis, and Interpretation. Wiley.
Ebert D, Herre EA (1996) The evolution of parasitic diseases. Parasitology
Today, 12: 96-101.
Ewald PW (1994) Evolution of Infectious Disease. Oxford Univ. Press
Giesecke J (2002) Modern Infectious Disease Epidemiology. Arnold.
Mascie-Taylor CGN (1993) The Anthropology of Disease. Oxford Univ. Press
Rothman KJ (2012) Epidemiology: An Introduction 2nd Ed. Oxford Univ. Press.
Vynnycky E, White RG (2010) An Introduction to Infectious Disease Modelling.
Oxford Univ. Press
Wolfe ND, Dunavan CP, Diamond J (2007) Origins of major human infectious
diseases. Nature, 447: 279-283.
13 April 2020
Minato Nakazawa

1What is human infectious diseases?
●"Infectious diseases" from ecological perspective– Among the symbiosis (mutualism, commensalism,

parasitism), a kind of parasitism– The life and reproduction of parasites depend on host's
life (differently by macro-/micro-)– Host-parasite co-evolution
Antimalarial genes in malaria endemic area
– Thalassemia in Eastern Mediterranean– Sickle cell anemia in Sub-Saharan Africa●
Hypoferremic adaptation hypothesis: relatively lower ironconcentration in serum than in liver found in malaria-endemic area●

13 April 2020
Minato Nakazawa

History of human infectious diseases

Source: Mascie-Taylor CGN (1993)

13 April 2020
Minato Nakazawa

The origin of human infectious diseases●

5 Stages from animal pathogen to specialized pathogen of humans (Wolfe et al. 2007)(http://www.nature.com/nature/journal/v447/n7142/full/nature05775.html)

13 April 2020
Minato Nakazawa

Descriptive epidemiology of infectious diseases●

Epidemic curves (TIME)–

Bar chart of (or lines connecting)the numbers of newly infected (ordied) patients by time after the
onset of outbreak

Fitted by mathematical models toestimate parameters●
Epidemiologic maps (PLACE)–

Cholera outbreak map of London
by John Snow
– Recently using GIS
Sex/Age distribution (PERSON)
Seroepidemiology– Antibody titers' distribution
shows endemicity (experienceof infection)–●●

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Minato Nakazawa

Prevalence and Incidence
Infected

Recovered

Died

Majority●●●●

Available data is usually limited to prevalence (cross-sectionally, how much proportion
among the population is infected) or incidence (newly infected number among the observed population)– number of asymptomatic patients needs active detection screening
Diseases with high virulence are underestimated by cross-sectional study
Detection of asymptomatic cases is important for diseases with long latent period
Distribution of infection frequency can be obtained from retrospective study, but longitudinal cohort study is preferable.
13 April 2020
Minato Nakazawa

Basic elements which affect the transmissionof infectious diseases
Host condition: population (size, density, age-structure), gene(resistant, susceptible), nutritional status, socio-cultural
factors (network, behavior)●
Environmental condition: temperature, humidity and vector
animals (in the case of vector-borne infection)●
Parasite condition: host-specificity, lifespan, transmission
type, etc.
●
Interaction: route of infection, evolution to optimal virulence
based on the interaction between infectiousness and virulence(Ebert and Herre, 1996), virulence decrease in directtransmission (like JC virus) vs no change in vector-borne
transmission (Ewald, 1994)●

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Minato Nakazawa

Route of infection
Route of transmission

Characteristics

Contact

Requires direct/indirect contact* Indirect = infected fomite, blood or body fluid* Direct = skin or sexual contact
Ingestion of contaminated food (outbreaks may be large
and dispersed, depending on distribution of food)

Food- or water-borne
Airborne (droplet, droplet
nuclei, micro-droplet)

Inhalation of contaminated air* Droplet = large droplets by cough* Droplet nuclei = Dried particle from droplets* Micro-droplets = small suspended droplets

Vector-borne

Dependent on biology of the vector (mosquito, tick, snail,etc), as well as the infectivity of the organism
Similar to contact infection; however, the contact may occur
in utero during pregnancy or at the time of delivery

Perinatal

13 April 2020
Minato Nakazawa

8

TYPES OF TRANSMISSION●●

Host population constitutes reservoir for the pathogen– Primary habitat for pathogen– Pathogen can survive and spread via other hosts thanhuman
Highly virulent pathogen cannot survive and spreadbecause of early death of host– Variety of transmission pathway evolution●
Direct, person-to-person (communicable,
contagious): measles (host is only human) viable only
for 2-3 hours in droplets●
Via transmitting animal (vector): malaria (frominfected human with 5 types Plasmodium
gametocytes to Anopheles mosquitoes, thensporozoites in salivary gland moves to anotherhuman by the next biting). Most vectors arearthropods●
Zoonoses can spread animal reservoirs to humans– Vector-borne: Equine encephalitis, plague– Directly from animal to human: Toxoplasmosis(from cat), ebola virus (from bat), flu (hosts are
human, birds, and pigs), rabies (hosts are all
warm-blooded animals)●
CFR (Number of death due to that disease
divided by the number of diagnosed patients)of rabies is 100% if untreated (human is deadend host), but the virus can survive within otheranimals than humans
4/14/20

Transmission

Route

ExamplesDirectAirborne

Anthrax （炭疽） , chicken pox,
common cold, influenza,
measles, mumps, rubella,tuberculosis, whooping coughDirectcontact

Athlete’s foot （水虫） ,impetigo （とびひ） , warts （いぼ）Fecal-oral

Cholera, hepatitis A,
rotavirus, salmonella(=typhoid fever)Maternalfetal

Hepatitis B, syphilis

SexualChlamydia, gonorrhea,
hepatitis B, herpes, syphilis,
HPVIntermediate
host

Tapeworm (from eating
inadequately cooked pork)

Vectorborne

Bubonic plague (by fleas),malaria (by Anopheles
mosquitoes), typhus (by lice),
West Nile encephalitis (byCulex mosquitoes), yellow
fever (by Culex mosquitoes),dengue fever (by Aedes
mosquitoes)
9

IndirectDifferent frequency distributions between the diseases with vectorborne and direct transmission by virulence (case fatality rates)

Source: Ewald (1994) [pp.38, Figure 3.1]
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Minato Nakazawa

The evolution of optimal virulence

13 April 2020
Minato Nakazawa

Source: Ebert & Herre (1996)

What makes pandemic?
●●

Definition of pandemic– An epidemic of unusually high occurrence of disease.
– An epidemic occurring worldwide or over a very wide area, crossing
boundaries of several countries and usually affecting a large number ofpeople (Dictionary of epidemiology)– An influenza pandemic occurs when a new influenza virus appears
against which the human population has no immunity, resulting inseveral, simultaneous epidemics worldwide with enormous numbers ofdeaths and illness (WHO, before pandemic H1N1 flu in 2009)– An influenza pandemic occurs when a new influenza virus appears
against which the human population has no immunity, resulting in several,simultaneous epidemics worldwide (WHO, after pandemic H1N1 flu in2009)
Change of definition of pandemic flu by WHO was to answer to the critics
that the pandemic declaration for H1N1 flu in 2009 was motivated by the ties
between WHO and pharmaceutical industry (though WHO denied such ties)

4/14/20

12HERD IMMUNITY AND BASIC REPRODUCTION
NUMBER (R0), effective reproduction number (Rt)●●

The relative proportions of immune
DiseasePrimary mode ofR0
and susceptible persons in atransmission
population can determine whether TIME
t
t+1
t+2
the infection will take hold in the
Measles
Airborne
15
community or die out quickly
Pertussis
Airborne droplet
15
When substantial proportion is(whoopingimmune (herd immunity situation),cough)
an infected person will be less likely R =4
Diphtheria Saliva
6
to spread the pathogen
Smallpox
Social contact
6
R0 (basic reproduction number) is
the average number of secondary
Polio
Fecal-oral
6
cases that occur from a single
RubellaAirborne droplet
6index case in a susceptible
Mumps
Airborne droplet
5
population– If R0 < 1, the outbreak will die
HIV/AIDS Sexual contact
3
R =4
out unless fueled by external reSARS
Airborne droplet
3
R =1
infections
Ebola
Bodily fluids
2
Rt (effective reproduction number)1918 flu
Airborne droplet
2is the value of reproduction number
Susceptiblethat takes into account the mix ofTransmission
2009 flu
Airborne droplet
1.5
immunity and social interaction at
COVID-19
Airborne droplet
1.4-3?
No transmission
Immuneany point in time as an outbreakprogresses
Note: If average R0 is same, control efficacy may largely differ by variance.
0

●

0

t

●

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13

The nature of R0 and Rt
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The reproduction number reflects the
biologic potential of the infectious agent
and the social intercourse that leads tosituations in which transmission mightoccur– If directly transmitted disease patient is
too sick to move, there will be few
contact with susceptible host, results in
low reproductive number
R0 varies by population (due to behavioral
difference by age and so on)
Even if R0 is low, some social networks
within a population may form a subset with
rapid spread of infection. (eg. a few“superspreaders” such as needle-sharers
transmitting a blood-borne infection cansuffice to spark an outbreak)Superspreading is not always an attributeof person, sometimes a condition of the
field setting (in the case of COVID-19).

4/14/20

●
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While Rt>1, epidemic continues
Eventually Rt becomes 1 or below, because theproportion of susceptible people decreases orcontrol measures are implemented
If Rt=1 (endemic equilibrium), the prevalence of
infection remains level over time as new
susceptibles are added to the population tobalance those who acquire immunity– Rt = 1 = R0 x ps, where ps is the proportion of the
population susceptible to infection atequilibrium, thus R0 = 1/ps
Basic strategy to reduce transmission is isolation of
infected persons.
Related strategy is quarantine to restrict contacts
among people who are not yet ill but alreadycontacted with infected persons(For bioterrorism by smallpox, ring-vaccination is tobe conducted to reduce Rt)
In Japan, restriction of behavior to fill the conditions
for superspreading events was taken to reduce Rt
as a countermeasure against COVID-19 outbreak.
14

Example of SARS, and if
vaccine would be available?
●●●

The strategy of isolation and quarantine worked well against SARS
– SARS nearly became pandemic in 2003, rapidly spread from China to 37 countries (infected morethan 8000 people, CFR was almost 10%).
– Canadian officials quarantined more than 23000 people who had been in contact with SARS cases,
about 100 persons for every identified case of SARS. Movement of those under quarantine wasrestricted until 10 days after the last contact– SARS was emerging disease in 2003 and thus no vaccine existed
If vaccine would be available, Rt depends on vaccine efficacy (Ve) and coverage (Vc)
– Rt = R0 (1 – Ve x Vc) ↔ Rt/R0 = 1 - Ve x Vc ↔ Vc = (1 - Rt/R0)/Ve– Rt < 1 ↔ Vc > (1 – 1/R0)/Ve– When R0 is large, to succeed in curtailing the epidemic, high efficacy and coverage are needed (If
R0 is 10 and Ve is 95%, Vc has to be larger than 95% needed to reduce R t below 1; (1 – 1/10)/0.95 =
0.947… ≈ 0.95)– In the case of measles, R0 is 15. Even if Ve is 100%, Vc has to be larger than 93% to reduce R t
below 1; (1 – 1/15)/1 = 0.933… ≈ 0.93
– If R0 is 2 and Ve is 95%, Vc needs to be larger than 53% to reduce R t below 1; (1 –1/2) /0.95 =0.526… ≈ 0.53.
The same relationship may stand for not only vaccination but also naturally acquired immunity after
infection. Vaccine efficacy corresponds to the proportion of immunized by single infection andcoverage corresponds to the proportion of people ever infected and recovered (herd immunity
threshold)4/14/20

15

Terms for individual infection history
Incubation period
Latent or pre-infectious period

Clinical symptoms

Infectious period

First infection
Onset
Second infection

Two general types of infection network topology(1) Random link network(2) Scale free network* equal infection probability for each* host preferences* distribution of infection frequency* distribution obeying power law
is unimodal* superspreader exists

13 April 2020
Minato Nakazawa

16Simplest mathematical model (SI)
S

b

I

g

immune / deathdS= - b SI
dt
dI
= b SI - g I
dt
Kermack-McKendrick model (1927)
for plague outbreak in Bombay from
December 17, 1905 to July 21,
1906.

13 April 2020
Minato Nakazawa

SIR model for flu epidemic
dS/dt = ˗ βSI + δR●
dI/dt = βSI ˗ γI●
dR/dt = γI ˗ δR●
Note: None of S, I, and R canbe less than 0. It should beconsidered in numericalsimulation.
●
Estimating params
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800
600
infected

400
200– β: {I(1)-I(0)}/S(0)Example: The data in English boys
boarding school in 1978●

– δ: negligible (loss of immunity)
http://minato.sip21c.org/tiid/flu-sir-2020.R
13 April 2020
Minato Nakazawa

0– γ: 1/{mean days of recovery}
0

2

4

6

8

time (days)

10

12

14

THE REED-FROST EPIDEMIC MODEL
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Assumptions– There is random mixing, with contact between infected
people and susceptible people within the population
during each time period– There is a uniform, fixed probability that a contact
between an infected person and a susceptible person
would result in transmission– An infection is always followed by immunity– The population is isolated from other populations– These conditions remain constant with timeC(t+1) = S(t) {1 – (1 – p) C(t)}– C(t): the number of newly infected people at time t– S(t): the number of susceptible people at time t– p: the probability that within one time period an infected
person will transmit the infection to a susceptible personwith whom there is contact
Reed-Frost projection of epidemic curve for infected,
susceptible, and immune sub-populations among 100
people with one initial infected person and an effective
contact probability of 4% (high R0 in upper panel) and 1.5%
(low R0 in lower panel). The time scale is measured ingeneration times
If R0 is small, susceptible people remain after the epidemic.
4/14/20

http://minato.sip21c.org/tiid/ReedFrost.R
19

INFECTIOUS DISEASE EPIDEMIOLOGYINVESTIGATIONS●●

Several types of epidemiologic studies are unique to the investigation of infectious
diseaseFour types are worthy to mention– Contact-tracing studies: In the early stage of an epidemic, it may be possible tointerrupt person-to-person transmission enough to bring R0 below 1 by isolation,
treatment and quarantine of patients (shoe-leather approach).
– Outbreak investigation: When a local epidemic occurs, documenting outbreak andinvestigating its origin and propagation. Often detective work such as identification of
the cause of diarrhea outbreak as the church supper on the potato salad.
●(Note: AIDS is an acronym of Acquired Immuno-Deficiency Syndrome, not Acute)– Seroprevalence surveys (sero-epidemiology): Distribution of prevalence of a specificdisease is reflected in the distribution of the antibody titers against that disease agent
in the blood, since the antibody titers remain for several months after infection. It canassess the vulnerability of a population to existing infectious agents, for finding
susceptible subgroups– Vaccine trials: A randomized trial of preventive measure is called a field trial (Chapter5). It’s much more difficult than clinical trials. One of the reasons is the outcome(prevented) is rare. (eg.) Salk vaccine trial. Infection of polio virus was popular but
paralysis symptoms were rare.

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20

OUTLOOK FOR INFECTIOUS DISEASEEPIDEMIOLOGY
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In the very beginning period after the invention of antibiotics, human misunderstood that the ultimate
defense against infection from bacteria was found
For vaccines, human also misunderstood that viral illness might be tamed and possible to eradicate as
smallpox
However,– High reproductive rate of microorganisms and their ability to mutate have enabled them to evade manyof our technologically driven defenses– Widespread and unnecessary use of antibiotics produced antibiotic-resistant bacteria– Increasing urbanization and intercontinental travel added risk of communicating infectious diseases– Social and medical practices opened new routes of transmission
Infectious disease epidemiology is a frontier that has observed 2 remarkable triumphs– Eradication of smallpox– Near-elimination of poliomyelitis
The hope of eradication of other diseases: malaria is candidate but challenging– Quinine, chloroquine, artemisinine, and other chemotherapy were effective to cure patients but
resistance developed– DDT and other insecticides were effective to reduce anopheles mosquitoes but those were toxic forenvironment and mosquitoes got resistance– Development of highly effective vaccine is very difficult because life-cycle of malaria parasite is very
complex and multi-stage and P. falciparum can escape from antibody by distributing junk antigens– Previously nonhuman (simian) malaria, P. knowlesi switched the host from monkeys to human

4/14/20

21

Epidemiology of COVID-19●

Lipsitch M, Swerdlow DL, Finelli L (2020) Defining the epidemiology of
Covid-19 – Studies Needed. New England Journal of Medicine, 382:
1194-6, 26 Mar. https://www.nejm.org/doi/full/10.1056/NEJMp2002125

4/14/20

22

What is pathogen of COVID-19?
(Lai C-C et al. https://doi.org/10.1016/j.ijantimicag.2020.105924)●●

The pathogen of COVID-19 is SARS-CoV-2, which is the 7th corona virus for human host.
– Among the corona viruses for human host, 4 types cause common cold.
– Other 3 types are SARS-CoV, MERS-CoV, and currently prevailing SARS-CoV-2 (it was called as
2019-nCoV at first). The genomes of SARS-CoV and SARS-CoV-2 have similarity of 80%. A kind of
bat CoV genome showed almost complete similarity with SARS-CoV-2 genome.
●
SARS-CoV originated from bat, through other animal, then human to human●
MERS-CoV originated from camel, rarely human to human●
SARS-CoV-2 originaned from bat, probably through other animal, human to humanCharacteristics of SARS-CoV-2– Latent period (from infection to symptom) is 5 days in average (Linton et al. 2020)– Serial interval (between the occurrence of symptoms of first case and second case) is 4 days inaverage, which means infection occurs in presymptomatic period. Contact tracing is difficult(Nishiura et al., 2020)– About 80% of the infected persons are asymptomatic or showing mild symptoms (Severity pyramid).
– The risk of severe symptoms or deaths depends on the patients age. Elderly and the people with
underlying diseases show high risk, but some young patients without any underlying diseases may
also die at much higher risk than influenza.
– The periods from admission to the hospital to either getting well or death are about 20 days.
– Because of no vaccine nor effective medicine, severe cases have to be treated by respirator orECMO in ICU, otherwise die at high risk. The risk of death depends on medical standard.
4/14/20

23

Severity●●

The common indicator of severity is CFR (Case Fatality Ratio/Risk). It's the number of deaths caused
by a disease divided by the number of confirmed cases of that disease.
– CFRs for SARS, MERS, Spanish flu and Asian flu were 10%, 35%, 3% and 0.5%, respectively.
– It is widely misunderstood that the CFR of seasonal flu is "less than" 0.1%. Actually, the estimatesof confirmed cases of seasonal flu in Japan is about 10 million, and the number of death due toseasonal flu is 2000 to 3000, so that CFR is 0.02-0.03%.
– The CFR of COVID-19 ranges from 1 to 10%.
●
The wide range of CFR is caused by large difference of examination ability, medical capacity,and the age distribution of the patients.
●
Like in South Korea and Germany, extensive RT-PCR examination for many people leads tolarge number of confirmed patients, subsequently smaller CFR estimates. In South Korea,
younger patients with lower fatality shared majority of positives, which made CFR lower.
●
Like in Italy and France, if the number of patients went beyond the medical capacity with rapid
increase (so-called "overshoot" in Japan, analogously with "overshoot" in ecology, which means
excess population growth beyond the carrying capacity), CFR goes higher.
In the case of COVID-19, as above mentioned, CFR depends on examination and medical capacity, sothat the meaning of CFR is difficult to interpret. Based on the data from China, where the examination
coverage was already assessed, estimated CFR ranged from 3% to 6% and the confirmed cases wereconsidered to share about 10% of all infected patients, Infection Fatality Risk/Ratio (IFR) was
suggested as 0.3-0.6%. IFR may be applicable as universal indicator of disease severity (Nishiura2020).
– The IFR of seasonal flu seems to range from 0.005 to 0.01%.

4/14/2024

Age dependency of CFR
Age-specific CFRs in Mainland China up to
11 Feb 2020.
http://weekly.chinacdc.cn/en/article/id/
e53946e2-c6c4-41e9-9a9b-fea8db1a8f51
Confirmed
cases

Deaths●

CFR(%)

0-9yr

416

0

0

10-19yr

549

1

0.2

20-29yr

3619

7

0.2

30-39yr

7600

18

0.2

40-49yr

8571

38

0.4

50-59yr

10008

130

1.3

60-69yr

8583

309

3.6

70-79yr

3918

312

8.0

80yr+

1408

208

14.8

All

44672

1023

2.3

4/14/20

Age-specific CFR of Pandemic flu 2009
– MHLW data in Japan(https://www.mhlw.go.jp/bunya/kenkou/kekkaku-kansenshou04/dl/infu10060803.pdf)
0-4yr 0.0007%
5-9yr 0.0003%
10-14yr 0.0001%
15-19yr 0.0001%
20-29yr 0.0005%
30-39yr 0.0009%
40-49yr 0.0031%
50-59yr 0.0066%
60-69yr 0.0147%
70yr+ 0.0282%– NY city H1N1pdm2009(https://doi.org/10.1371/journal.pone.001
1677)
0-17yr 0.0008-0.0012%
18-64yr 0.0081-0.0132%
65yr+ 0.0094-0.0147%
25

Other severity factors than age(Zhou F et al. 2020, Lancet, 2020Mar11)●●●

Patients discharged or died from 2 hospitals in Wuhan until 31 Jan
2020, ages higher than 18 yr: 191 (137 discharged, 54 died; meandays from onset to admission were 11 days for each)Result from the multiple logistic regression analysis, higher risk ofdeath was attributable to the following factors– Age (1.1 times by 1 age increase)– Higher SOFA score at admission (used to diagnose sepsis) (OR5.65 ， 95 ％ CI [2.61, 12.23])– Higher d-dimer than 1μg/mL (Comparing with less than
0.5μg/mL, OR18.42, 95 ％ CI [2.64, 128.55])
As another result of this paper, for discharged patients, the median
duration of virus shedding from onset was 20 days (IQR 17-24
days), but for died patients, virus shedding was observed until
death.

4/14/20

26

Infectiousness (ability of transmission)
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Commonly used measure of infectiousness is the Reproduction Number (R), which means theaverage number of secondary infected people from the first case.
– In the beginning of epidemic, nobody has immunity. Under such situation, where everybody issusceptible, if one index case invades, R is called as Basic Reproduction Number (R0). R0
depends on the nature of pathogen, host behavior, and environment.
– After the progress of epidemic, recovered (immune) people increase. Some of the population
are vaccinated, immune people also increase. In either case, the proportion of susceptible
people decreases and thus R decreases, which is called as Effective Reproduction Number(Rt or Re). Rt depends on R0, protective measure, and the size of the population.
If R<1, the epidemic will be suppressed.
The R0 of SARS was about 3, but the variance of R0 was very large because of many cluster
infection occurred in the airplane or hospital, where superspreading event may occur. The R0 of
MERS was generally less than 1 except for nosocomial infection (https://www.who.int/csr/disease/coronavirus_infections/risk-assessment-august-2018.pdf).
The R0 of Spanish flu was estimated around 2. The R0 of seasonal flu or Influenza (A)H1N1pdm2019 ranges 1.1-1.5 (eg. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6670001/).
The R0 of COVID-19 was initially estimated as 1.4-2.5 based on the data obtained Wuhan(WHO, 23rd Jan 2020). With accumulation of data, the estimates of R0 largely varied by model ordata, at highest, 6.47 (Tang B et al. 2020). However, inter-individual difference was very large,
so-called "overdispersion" (Voltz E et al. 2020; Grantz K, Metcalf CJE 2020; Nishiura H et al.
2020).

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27

The routes of infection in SARS-CoV-2
(PV)
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●

Random link routes of infection, where
everybody have the same risk of infection (sameas flu)– Droplets: face-to-face conversation withoutmask with distance within 2m.
– Contact with contaminated material surface:touch the material surface contaminated bydroplets, saliva or something else excreted
from patients– Fecal-oral: The viral shedding occurs tofeces, so that without washing hands after
defecation, the patients touch something,which become source of contact infection
Scale free route of infection (The cause of
overdispersion of R)– Cluster infection due to suspended microdroplets, which likely occur under 3Cs env.
See, the movie provided by NHK:https://www3.nhk.or.jp/news/special/coronavi
rus/protection/?tab=3●
Closed space (poor ventilation)●
Crowded (high population density)●
Close contact with conversation

4/14/20

Random link network = everybody
have the same probability of infection.

Scale free network causes cluster
28

The fewer number of testing in Japan than
Europe/USA was caused by fewer patients●●

Presumption– Testing performance is not perfect (RT-PCR cannot detect
positive patients if the nasal/throat swab could not sample
viral RNA particles)– Early detection cannot lead to effective early treatment toprevent severity or deathThe 3 purposes of RT-PCR to confirm infection (A is cruciallyneeded, B is more effective than C when contact tracing is
successfully conducted. If the disease becomes prevailing, B
is difficult because it may excess the capacity of manpower ofhealth center)– (A) When doctor judged the necessity of confirmation fromatypical pneumonia or other results of clinical inspection,
to prepare ICU beds, respirator, and ECMO (WHOrecommends, many countries incl. Japan do)– (B) Detect positive patients (incl. asymptomatic, or with
only mild symptoms) from all closely contacted people
with patients [active case detection] to prevent spread byisolation of detected cases. (Also WHO recommends,
impossible after excess number of new patients as inEurope/USA, Singapore and Taiwan succeeded, Japan
did until mid-March and try to continue)– (C) Widely examine suspected people to detect all cases(under low prevalence situation, efficacy is low) to prevent
spread by isolation (South Korea and Germany did)

4/14/20●

Wrong doubt: The number of patients looks few due tolimited testing– Until mid-March, the change of cases by date plottedby semi-log scale, Japan and Singapore showedsharrower slopes from Europe and USA, but bothgroups showed linear relation. Linear relation insemi-log scale means exponential growth.
https://www.datacat.cc/covid/– If untested cases are hidden behind the detectedcases at a considerable probability, the slope doesn'tchange, only the intercept changes. Shallower
slope means smaller R.

29

Estimates of detected proportion andprevalence in Japan
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In the paper (2nd April 2020) linked from https://www.uni-goettingen.de/en/606540.html, Prof. Sebastian Vollmer
from University of Goettingen estimates the proportion of detected cases among total patients.
Methods– Assume that the number of reported death by COVID-19 is correct (Japan reported 56 on 31 st March)– Assume that the age-specific IFR in the paper "Estimates of the severity of coronavirus disease 2019: amodel-based analysis" in Lancet Infectious Diseases on 30 th March 2020 by Verity R et al. (The groups ofImperial College London) is universally applicable.
– Weighing by age-structure of each county from UN database, age-adjusted IFR is obtained (Japan is 1.60%).
– Divide the number of death by age-adjusted IFR, then the number of total infected people in 2 weeks before is
obtained (Japan on 17th March is 3490, which is 56/0.016).
– Divide the number of confirmed cases (878 in Japan on 17 th March) of each country by estimated total
infected people, the proportion of detected cases among total patients is estimated.
Results– It's rough estimate, the proportion of detected cases in Japan on 17 th March was about 25%, which isthird highest level following 49% of South Korea and 38% of Norway. Germany is 16%, Denmark is 13%.
Many European counties incl. Italy, France, UK and USA are all less than 5%.
– Assume that the proportion of detected cases doesn't change, divide the confirmed cases on 31 st March (inJapan, it's 1953) by that value (0.25), the estimates of total infected cases can be obtained (in Japan, it's7762). Divide it by the total population, the prevalence can be obtained (in Japan, it's 0.01%). By thismethod, the countries with the prevalence higher than 10% on 31 st March were Spain and Turkey.
According to the result of antibody test from 500 sample in a city of Germany, about 14% showed positive (MIT,https://www.technologyreview.com/2020/04/09/999015/blood-tests-show-15-of-people-are-now-immune-to-covid19-in-one-town-in-germany/). The important information is that remaining 86% is still susceptible.

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To continue the type (B) testing, "Digital
Contact Tracing" may be effective●●●

Type (B) testing becomes difficult when the newly found cases (especially with unknown link) increased,because manual contact tracing requires huge time and effort of the professionals of health center,
which exceed the capacity soon.
If we can easily find the people who had close contact with the infected case, even after propagation of
epidemic, type (B) testing can more effectively detect the infected cases than type (C) testing, and thus
type (B) testing may have higher priority than type (C) testing.
There may be a solution. It's the use of big data automatically collected by smartphone apps
(https://www.cnbc.com/2020/03/27/coronavirus-surveillance-used-by-governments-to-fight-pandemic-privacy-concerns.html)

China seems to have enhanced the information collection system using GPS tracking andsurveillance camera since Beijing Olympic. The report 11 from the group of Imperial College used
the population movement data from GPS record by Baidu.
– South Korea has a strong regulation based on the law of infection control, by which the movement of
the infected cases using GPS data is visualized and opened to public.
– In Singapore, the smartphone app "TraceTogether" is recommended to install for everybody. Whenthe smartphone with the TraceTogether running comes close each other, the other's information
without location information is automatically detected using bluetooth and recorded with time in eachsmartphone. The information is kept for 21 days within each smartphone. When a person is proved
to be infected, it's possible to find all close contactees of the person during previous 21 days.
According to the paper by the groups Prof. Fraser in Science (Ferretti et al., 2020), "digital contact
tracing" using smartphone app may enable the suppression of epidemic to avoid "overshoot" without"lockdown". They also discussed ethical issue in that paper.
–●

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Why the number of cases increased more
slowly in Japan than Europe (PV)●●Infection via droplets or contact randomly occurs fromone case to 0, 1, 2, or at most 3 secondary cases, sothat the distribution of the number of secondary
infection may obey normal distribution.
– In Japan, the number may be mostly 0 or 1, sothat the part of R0 due to this route of infection
may be less than 1.
●
As cultural norm, personal space has been
wider than Europe/USA (distant bow vshandshake/kiss/hug)●
Clean piped water is available for everybody atvery cheap price.
●Handwashing with soap before school lunch isstrongly forced in elementary school. In
addition, handwashing has been strongly
recommended since January.
– In Europe/USA, the number may be mostly 1 or 2,
so that the part of R0 due to this route may be
more than 1.
●
In most European countries and USA, keeping
the more than 2m inter-individual distanceaway from each other is recommended due tothis reason.
R>1 leads to spread of epidemic.

4/14/20●●

Actually, the distribution of the number of secondary
infections from the first case may obey the mixtureof normal distribution and power distribution
representing cluster infection.
– The cluster control group under the specialists
committee of the government on 25th Feb set by
Dr. Omi and Dr. Oshitani's leadership, in which
Prof. Nishiura is responsible for analysis andmodeling, tried to decrease R less than 1 byfinding the common condition for cluster
infection and preventing it.
→ They found 3 Cs (Closed environment,
Crowded population, Close contact withconversation) and promoted campaign toprevent the 3 Cs (Nishiura et al., 3rd March 2020
at preprint server).
– This "prevention" of 3 Cs was specially featured
in Japan's strategy.
– To prevent cluster infection, banning massgathering event is conducted in most countries.
Until mid-March, probably due to low mean levelof the part of R0 due to contact/droplet infection
and the cluster control strategy, Japan could
suppress the number of infected cases.
32

Why the increase of cases accelerated
after late March (PV)
●

●

●

●

●

The global basic strategy to tackle infectious diseases is IHR2005 (International Health Regulations 2005 revision). It
includes the minimizing the restriction of trade and traffic. Complete closure of each country is ideal to prevent pandemic, but
it's impossible, because the social system largely depends on the international traffic and trades.
The first wave of COVID-19 patients influx to Japan from China was suppressed by "cluster-control". However, the number of
new patients has rapidly increased since the late March.
The second wave of COVID-19 patients (mostly asymptomatic) influx from Europe/USA was much larger than the first wave.
It caused rapid increase of newly confirmed cases without links since late March.
– According to the opinion by Prof. Oshitani, the second wave caused many hidden clusters, then each one sporadic casewas detected from each hidden cluster. Since rapid increase of sporadic cases means increase of hidden clusters, active
case detection by contact tracing and isolation becomes impossible. Remaining possibility of suppression is to decrease
the human-to-human contact by 80% (According to Prof. Nishiura, 79% based on the detailed model analysis) by
emergency declaration.
– The virus attacked Japan in the second wave has mutated from the original virus and got higher infectiousness (?).
– (My PV) If the increased cases due to the second wave was not the part of hidden cluster but the result of hidden chain of
random link due to droplets or contact route, there is a possibility that the cluster control is still effective. (It's possible tocheck by making the model including the different distribution for different route of infection and movement.)
Essential problem in cluster control strategy– Though the some workplaces with 3 Cs can be modified to prevent cluster infection (of course, guaranteeing the basic
income or other life support is necessary), but other workplaces especially lifelines, hospital, elderly care center and dayservice cannot avoid 3 Cs as their own nature. Most cluster infection after the end of March was shared by such
essentially vulnerable workplace or the places to be hidden with hesitation (in relation to so-called nightlife). 80%
reduction strategy consider those as inevitable part of 3 Cs. Break-through for this issue is expected.
– For most people, long-term "self-regulation" to avoid 3 Cs and human-to-human contacts is impossible. The government
should take huge financial support.
In early April, to prevent "overshoot", the prime minister issued emergency declaration on 7 th April (He said it being different
from lockdown), 80% reduction of human-to-human contact (based on the calculation by cluster control group) was asked forthe citizens strongly.

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How long will it continue? At least 1 year.
●●●

Until the vaccine or specific drug with high efficacy become widely available (Ultimate solution)– At least 1 year and half or 2 years, or more.
– There is no guarantee to reach this goal, because there are many infectious diseases without effective
vaccines though huge efforts were paid to do so for decades.
Until the population establish herd immunity (Bad end)
– According to the projection by Prof. Marc Lipsitch on 15th Feb, COVID-19 will infect 40-70% of the world
population in 1 year, herd immunity will be established and Rt becomes less than 1, then pandemic willend.
●
However, at least 7.5 billion x 0.4 x 0.003 = 9 million will die.
●If "overshoot", which means explosive increase of new cases and exceeds the capacity of medical
treatment, will occur in many countries, at worst, 7.5 billion x 0.7 x 0.01 = 52.5 million will die.
Until the number of newly infected cases decreases under a certain level without herd immunity (It's not
ultimate suppression)– The No.9 report from the Imperial College of London, written by Prof. Neil Ferguson and colleagues
showed the possibility to control the epidemic for 1.5-2 years under the capacity of medical treatment by
repeated suppression (combination of several behavioral changes) for 1-3 months. Their model was
individual based simulation model using actual contact frequency indicator and population density byregion, modified from a kind of flu-model, and thus overestimating the effect of school closure, but solointervention by school closure only reduces total infected cases by 2%.
– Since the community mitigation measures such as social distancing to reduce the number of death
postpone the timing of the peak of the epidemic curve, the pandemic will continue longer than 1 year.
– In addition, this strategy cannot lead to herd immunity in the total population, so that the behavioral change
to avoid explosive increase of the infection has to be continued even after suppression.

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For the safe campus life●●●

According to the announcement from Ministry of Education, Culture, Science and Technology (https://www.mext.go.jp/content/20200324-mxt_kouhou01-000004520_4.pdf, in Japanese), lectures in the
University can take various methods including remote learning via Internet.
– Remote learning is strongly recommended.
– It may last for a year, the student should prepare PC and the conditions for networking at home.
– In special cases, the students can go to the campus (except for lockdown situation). But the students haveto keep properly modified behavior listed below.
Needed behavior– To avoid infection from yourself to others (even if you have no symptom, you may have virus in your body)●Don't go out and stay home if you feel, even slightly, ill (If your symptom seems severe, you should
consult with health center or physician by phone). Wear mask always when you talk– To prevent the infection by droplets or contact●
Frequent proper handwash, social distancing to keep yourself away from others by at least 2m,
avoidance of face-to-face talk●
Any private conversation in the class is prohibited– To avoid cluster infection●
Prevent 3 Cs (Closed environment with poor ventilation, Crowded population and Close contact withconversation).
●
Keep door and window opened during the class.
●See, Notice from WHO
https://www.who.int/docs/default-source/coronaviruse/getting-workplace-ready-for-covid-19.pdf<Important thing> Even if you pay attention to avoid infection, you may have non-zero risk of infection. It's
same for anybody else. Therefore, stigmatization or discrimination of infected cases is strongly prohibited.

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