Epidemiology (8)Chapter 6. Infectious
Disease Epidemiology
Minato NAKAZAWA, Ph.D.
<minato-nakazawa@umin.net>

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What is human infectious disease?
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Symbiosis: Interactive relation between different species– Mutualism: Both species get benefits– Commensalism: One side gets benefits, the other gets no benefit but no damage– Parasitism: One side (parasite) gets benefits (nutriment) from the other (host), which gets damaged.
Features of parasites– Tend to reproduce more quickly than hosts– Tend to evolve rapidly in response to host defenses●
Defense = innate immune system (nonspecific inflammatory reaction → recruits a variety of blood cells suchas mast cells, phagocytes, neutrophils, ...) + adaptive immune system (cytotoxic T cells and antibodies from
specialized B cell lymphocytes and helper T cells, which record antigenic pattern, enable faster response in thenext invasion of the same antigen: antigenic memory = immunity ← after the natural infection and vaccination)●
Emerging infectious diseases: by changing social conditions, contact of human host with newly met pathogens
occurs, when human has no immunity against such pathogens– Not quite new: common European diseases (smallpox, measles, typhus, cholera) brought to the New Worldin Middle Ages were emerging, catastrophic diseases for the native Americans who had no defense against
such diseases, conversely syphilis (common for native Americans) caused catastrophic damage inEuropeans– Infectious parasite is typically much smaller than host
– Agents infecting human host include:●
Microorganisms (pathogen = micro parasite): Virus, bacteria, fungi, protozoa, ...
●Larger animals (parasite = macro parasite): Helminths, …
Public health burden from infectious disease began to diminish after the acceptance of germ-theory and the arrival of
greatly improved sanitation and hygiene. Figure 6-1 shows steady decline in mortality in the US over 20 th C. Spike in
1919 was due to pandemic H1N1 influenza (so-called Spanish flu), which brought same damage with Black death(bubonic plague) in Europe in 14th C. Since mid-20th C, antibiotics contributed to the mortality decline.
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What makes pandemic?
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Definition of pandemic– An epidemic of unusually high occurrence of disease (Chapter 4)– 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)

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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
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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)
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IndirectHERD IMMUNITY AND BASIC REPRODUCTION
NUMBER (R0), effective reproduction number (Rt)
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The relative proportions of immune
and susceptible persons in a
population can determine whether
the infection will take hold in thecommunity or die out quickly
When substantial proportion isimmune (herd immunity situation),
an infected person will be less likely
to spread the pathogen
R0 (basic reproduction number) is
the average number of secondary
cases that occur from a single index
case in a susceptible population– If R < 1, the outbreak will die out
0unless fueled by external reinfections
Rt (effective reproduction number) is
the value of reproduction numberthat takes into account the mix of
immunity and social interaction at
any point in time as an outbreakprogresses

TIME

t

t+1

DiseasePrimary mode oftransmission

R0

Measles

Airborne

15

Pertussis(whoopingcough)

Airborne droplet

15

Diphtheria

Saliva6

Smallpox

Social contact

6

Polio

Fecal-oral

6

RubellaAirborne droplet

6

Mumps

Airborne droplet

5

HIV/AIDS

Sexual contact

3

SARS

Airborne droplet

3

Ebola

Bodily fluids

2

1918 flu

Airborne droplet

2

t+2

R0=4

R0=4
Rt=1

Susceptible

Transmission

2009 flu

Airborne droplet

1.5

ImmuneNo transmission

COVID-19

Airborne droplet

1.4-3?

Note: If average R0 is same, control efficacy may largely differ by variance.
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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 reproduction 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).

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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 to balance
those who acquire immunity– Rt = 1 = R0 x ps, where ps is the proportion of the
population susceptible to infection at equilibrium,
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 R t asa countermeasure against COVID-19 outbreak.
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Estimating R0 from data
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Using SIR model, let the populations in eachcompartment at time t S(t), I(t), and R(t). Let thetransmission coefficient (proportionate to the probabilityof transmission per contact) β, and the rate ofrecovery/isolation γ,– dS(t)/dt = –βS(t)I(t)– dI(t)/dt = βS(t)I(t) – γI(t)– dR(t) = γI(t)The total population at time t is denoted as
N(t)=S(t)+I(t)+R(t), and then N(t) is constant becausedN(t)/dt=0
In the beginning, S(0)+R(0)=N
Since dI(t)/dt = (βS(0) – γ)I(t),infected population exponentially increases in the
beginning, and then I(t)=I(0)exp{(βS(0)–γ)t}Using the coefficient of exponential growth, R0 can be
simply estimated as βS(0)/γ = R0. This Exponential
Growth method is the most simple ("EG" in R0
package)
If we let the generation time (average interval from theinfection to primary case to the infection to secondarycase, approximated by serial interval) T,
R0=1+(βS(0)–γ)T– If we know or can assume T, R can be obtained0
using the Maximum Likelihood method ("ML" in R0
package)
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For the flu epidemic data at the boarding
school in UK, I made the R code to estimate
R0 using R0 package.
https://minato.sip21c.org/tiid/R0.R
In R0 package, implemented estimation
methods are, in addition to "EG" and "ML","AR", "TD", and "SB", though "AR" is notapplicable to this data.
– "AR" is based on the equation by Dietz(2013). Let the incidence rate per total
population AR,
R0 = – ln((1–AR)/S(0))/(AR–(1–S(0)))– "TD" assumes time-dependency in the
reproduction number, suggested by
Cauchemez et al. AJE (2006).
– "SB" is Sequential Bayes method, which
also assumes time-dependent
reproduction number, suggested by
Bettencourt & Ribeiro (2008).
R0 estimates by "EG" → 8.91 [ 7.57, 10.52 ]R0 estimates by "ML" → 6.83 [ 6.10, 7.62 ]Time-dependent R0 series estimates– by "SB" → 3.96, 4.57, 4.15, 4.22, ...
– by "TD" → 11.78, 8.82, 6.22, 3.65, ...
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Example of SARS, and if
vaccine would be available?
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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 R 0
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, R is 15. Even if V is 100%, V has to be larger than 93% to reduce R below0ect
1; (1 – 1/15)/1 = 0.933… ≈ 0.93
– If R is 2 and V is 95%, V needs to be larger than 53% to reduce R below 1; (1 –1/2) /0.95 = 0.526…
0ect≈ 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 and coveragecorresponds to the proportion of people ever infected and recovered (herd immunity threshold)–●11/27/22

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Estimation methods of Rt
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Cori et al. (2013) https://doi.org/10.1093/aje/kwt133 and https://doi.org/10.1140/epjp/s13360-021-01339-6: EpiEstim package of R
Rough and simple approximation (Niid, 2021): (Newly reported cases within the recent 7 days) / (Generation time earlier newly
reported cases within 7 days) https://www.niid.go.jp/niid/ja/diseases/ka/corona-virus/2019-ncov/2502-idsc/iasr-in/10465-496d04.html
Toyo Keizai (https://toyokeizai.net/articles/-/351826?page=3): {(Newly reported cases within recent 7 days) / (Newly reported cases
within 14-8 days before)}^{(average generation time)/(reporting interval)}See, https://minato.sip21c.org/epispecial/libuseTokyoRt.R

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Glossary of key terms (slightly modified
from the textbook and some added)
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Case Fatality Risk (CFR): Same as Case Fatality Ratio. Number of death due to a disease divided by the number of infected caseswith diagnosis. Indicates severity. Rabies: 100%, Ebola virus infection: 60%, Spanish flu: 2-2.5%, seasonal flu: 0.01-0.02%, COVID19: 0.6-6%. If the denominator is symptomatic cases instead of confirmed cases, it should be written as sCFR (Nishiura et al., 2010).
Infection Fatality Risk (IFR): In the pandemic of COVID-19, transmission of the disease occurred from asymptomatic cases and thepatients in latent period and thus CFR largely varied by the situation of diagnostic testing. Therefore, Nishiura (2020) suggested to use
IFR as the number of death due to a disease divided by the total number of infected cases including asymptomatic cases. Based on
CFR estimated in China where mostly moderate or severe cases were tested (3-6%) and the total number of infected people was 10times more, IFR of COVID-19 was estimated as 0.3-0.6%.
Communicable: capable of person-to-person transmission
Generation time: the time interval between one person getting infected and another person getting infected from the first
Herd immunity: a prevalence of susceptibles in a population low enough so that transmission cannot be sustained
Immunity: resistance to infection
Inapparent infection: infected without any symptoms. (eg.) Almost 100% of JC virus infection causes no symptoms
Incubation period (Latent period): the time interval between getting infected and developing symptoms
Index of infection to symptomatic cases: The proportion of symptomatic cases among all infected. Untreated rabies: 100%,
Measles: 99%, Seasonal flu: 60%, Poliomyelitis: 0.1-1%, Japanese encephalitis: 0.1-3%.
Reproduction number: the average number of infected persons resulting from contact with a single infected person. Incl. R0 and Rt
Reservoir: the host population for an infectious agent
Secondary cases: cases of infection that occur from contact with a primary caseSecondary attack rate: risk of infection among susceptibles exposed to an infected source
Susceptibility: at risk of contracting disease (lack of immunity)
Transmission probability: probability of transmission from an infected person to susceptible person during a contact
Vector: an animal that transmits disease from an infected person to an uninfected person
Virulence: the degree to which a pathogen can cause disease and death

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Basic reproduction number for several infectious diseases
Table 1.2 Approximate serial intervals, basic reproduction numbers and implied crude herd immunity
thresholds (as 1 – 1/R0) for common potentially vaccine-preventable diseases.
Disease name

Serial interval (range)

R0

Herd immunity threshold (%)

Diphtheria

2-30 days

6-7

85

Influenza

2-4 days

2-4

50-75

Malaria

20 days

5-100

80-99

Measles

7-16 days

12-18

83-94

Mumps

8-32 days

4-7

75-86

Pertussis5-35 days

12-17

92-94

Polio

2- 45 days

2-4, 8-14 (a)Controversial (immunity toinfection is not solid)

Rubella7-28 days

6-7

83-85

Smallpox

9-45 days

5-7

80-85

Tuberculosis

Months-Years

Not established because contacts over time
may largely change during long serial interval(a) R0 of polio depends on hygienic condition (if poor, it becomes large).
Cited from EMILIA VYNNYCKY and RICHARD G WHITE (2010) “AN INTRODUCTION OF INFECTIOUS DISEASE
MODELLING”.Oxford Univ. Press
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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

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Serial interval and generation time

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Generation time (from time at infection to the primary case to average time at infection to
the secondary cases) is usually assumed to match with serial interval (from time at onsetof symptom in the primary case to average time at onsets of symptoms in the secondary
cases).
However, if the half of transmission is shared by presymptomatic cases like in covid-19 (assuggested by Nishiura et al. (2020) [https://dx.doi.org/10.1016%2Fj.ijid.2020.02.060](Figure 2 shown top left)), it was not sure a priori.
Ganyani et al. (2020) [https://dx.doi.org/10.2807%2F1560-7917.ES.2020.25.17.2000257]
showed the matches of generation time and serial interval in the covid-19 data (top right).

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Simple mathematical model (SI)
S

b

I

g

immune / death

Kermack-McKendrick model (1927)
for plague outbreak in Bombay from
December 17, 1905 to July 21,
1906.
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SIR model for flu epidemic

800

Example: The data in English boys
boarding school in 1978

400
200
0

plot(0:14, c(1, NI), pch=16, type="p",ylim=c(0, 800), xlab="time (days)", ylab="infected")lines(0:14, sir.I(762, 1, 0, 1:14, 0.0026, 0.5, 0.0001), col="red", lty=1)

infectedsir.I <- function(S0=762, I0=1, R0=0, days=1:14,
beta=0.0026, gamma=0.5, delta=0.0001) {S <- I <- R <- double(length(days)+1)
S[1] <- S0
I[1] <- I0
R[1] <- R0
for (i in days) {S[i+1] <- S[i] - beta*S[i]*I[i] + delta*R[i]I[i+1] <- I[i] + beta*S[i]*I[i] - gamma*I[i]R[i+1] <- R[i] + gamma*I[i] - delta*R[i]}return(I)}600

NI <- c(3, 8, 28, 75, 221, 291, 255, 235, 190, 125, 70, 28,
12, 5)

0

2

4

6

8

time (days)

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THE REED-FROST EPIDEMIC MODEL●●●

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 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 theinfection to a susceptible person with whom there is contact
See, Figure 6-2: Reed-Frost projection of epidemic curve for infected, susceptible,
and immune subpopulations among 100 people with one initial infected person andan effective contact probability of 4% (high R 0 in upper panel) and 1.5% (low R0 in
lower panel). The time scale is measured in generation times.

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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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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

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