1. Epidemiology
Epidemiology is the branch of medical science that investigates
all the factors that determine the presence or absence of
diseases and disorders – NIH
The study of the incidence, distribution, and control of
2. Q: What is
Epidemiology
to me?
A: Ecology
• Humans are animals
• Ecologists study the population dynamics of
plants, animals, bacteria, even viruses.
• What causes populations to change in
number?
• Resources
• Sun, space, food, mates, etc
• Predators
• Competition
• Intra and interspecific
• Parasites
• This is where epidemiology comes
in
• However, all of the above
determines the presence and
population sizes of parasites as
well.
4. Back to
humans
• In ecology we care about everything
• In medicine we only care about humans
(and maybe our pets)
• The population dynamics of humans (and
everything else)
Are determined by:
• Life expectancy
• Fecundity (how many, when, and
for how long)
• All of those are functions of the factors
we mentioned before
8. World demographic
pyrimad
• Current growth rate 1.05%
• Peak was in 1960 2.2%
• 1.8 billion women at reproductive age
• Increases each year
• Aged out replaced with young
women
10. Epidemiology
• Host pathogen dynamics
• More complicated than simple growth
formulas
• Nt+1 = Growth rate x Nt0
• Nt = Growth ratet x Nt0
• Types of individuals in a population
• Susceptible
• Infected
• Recovered/immune
11. Also…
1) Differences in infection at different
ages
2) Latent period of infection (infected
but not transmissible)
3) Vertical transmission (mother to
newborn)
These models can get very
complicated
We will simplify for sanity
12. Threshold density
• What you really want to know
• You may have heard of
something called ‘herd
immunity’
• An infectious disease will only
spread if the susceptible hosts
exceed the threshold density.
• Math! No really, fun math.
13. Variables
• S = density of susceptible individuals
• I = density of infected individuals
• For spread to occur, a susceptible individual must ‘contact’ an infected
individual.
• The likelihood of that encounter is a function of the density of both.
• S*I
• If the population is 80% susceptible and 20% infected:
• .80*.20 = .16 so there would be a 16% chance any encounter
between two individuals will be with an infected person.
14. But… an encounter does not mean infection
• The next big variable is the transmission coefficient 𝛽 (beta)
• How easily the disease is transmitted from the infected to the
susceptible
• Some diseases (measles for example) have an incredibly high 𝛽
other diseases do not. In many cases, specific to the interaction
(sex, physical contact, bodily fluid, etc)
• Therefore, 𝛽𝑆𝐼 is the disease transmission.
• How much the disease is spreading
15. • As the disease spreads (at the rate
determined by 𝛽𝑆𝐼) the density of
infected individuals increase,
increasing that rate of rise.
• But what happens to infected
individuals? This isn’t “Girl with all
the Gifts”
• Individuals die or recover
• Not much difference to the
disease, neither (normally)
can be infected
• New variable: 𝑚=death or
recovery rate.
16. Bringing it all
together
•
ⅆ𝐼
ⅆ𝑡
= 𝛽𝑆𝐼 − 𝑚𝐼
•
ⅆ𝐼
ⅆ𝑡
is the change in the density of infected
individuals at each instant in time.
• A disease will establish and spread when the
numbers of infected individuals increases over
time.
•
ⅆ𝐼
ⅆ𝑡
> 0 or 𝛽𝑆𝐼 − 𝑚𝐼 > 0
17. Threshold density
• We can rearrange 𝛽𝑆𝐼 − 𝑚𝐼 > 0
• 𝑠 >
𝑚
𝛽
• And to figure out what number of susceptible individuals necessary
are for the disease to spread:
• 𝑠𝑡 =
𝑚
𝛽
This is the Threshold density
18. • So let’s do an example
• How many susceptible
individuals do we need to
have on campus for Covid to
spread?
• Can we figure out our
variables?
20. • As long as there are 90 susceptible individuals, the disease will spread
• This would mean heard immunity at 90% immunized or recovered.
beta 0.5 raw
by
population
m 0.05 St 0.06 90
population 900
beta 0.5 raw
by
population
m 0.01 St 0.02 18
population 900
beta 0.8 raw
by
population
m 0.01 St 0.0125 11.25
population 900
21.
22. R0 : How
many people
each person
will infect
• Infectious period in days (how long you can get
people sick)
• 𝜏
• Infectious contacts per day
• 𝛽
• 𝑅0 = 𝜏𝛽
• We know R0 = 8
• We know infectious period for Delta is 5 days
• 8 = 5 * 1.6
• 𝛽 = 1.6 infectious contacts per day
23. R0 First
conclusions:
• 𝑅0 = 𝜏𝛽
• What does this tell us we could do to
reduce R0
• Reduce contact
• Reduce proportion of contacts
resulting in infection
• How do we do these things?
24. Another way
of thinking
about 𝑅0
• 𝑅0 = 𝑐𝑇𝜏
• 𝑐 = rate of contact between susceptible
and infected (per day)
• T = transmissibility
• Can we do something with 𝜏? (days
infectious)
