DISEASE E&E (Models)

Question 1

Purpose of epidemiological models:

Answer 1

-tools that help scientists understand whether and how infectious disease will spread through the host population
-can lead to surprising insights
-that about what features or aspects of infectious disease we need to know more about

Question 2

Epidemiological models allow us to:

Answer 2

-compare the outcome of different control strategies
-make predictions that help policy makers make decisions

Question 3

Deterministic compartment models:

Answer 3

-different compartments
-arrows show transitions between compartments
-SIR, SIRS, SEIR models

Question 4

Compartments:

Answer 4

-host individuals in different states
>susceptible
>infectious
>recovered
>pre-infectious

Question 5

SIRS model:

Answer 5

-S become I
-I become R
-R become S again

Question 6

SEIR model:

Answer 6

-pre-infectious (latent) stage where individuals have been exposed but are not yet infectious

Question 7

SIR model:

Answer 7

-S become I via transmission
I become R via clearance, immunity
*closed population (host population size remains constant over time)

Question 8

S:

Answer 8

-susceptible individuals
-can acquire the infection from infected individuals

Question 9

I:

Answer 9

-infected individuals
-can transmit infection to susceptible individuals
-can become recovered individuals that are resistant to future infection

Question 10

R:

Answer 10

-resistant individuals
-individuals have developed resistance (ie. Immunity) against future infections

Question 11

N:

Answer 11

-total population size
N=S+I+R

Question 12

Beta:

Answer 12

-proportionality constant for infection
-transmission coefficient

Question 13

v (mu):

Answer 13

-rate of recovery of infected hosts

Question 14

When would SIR model be appropriate?

Answer 14

-for a pathogen with a short incubation (ex. virus) that spreads quickly through the host population in a matter of weeks

Question 15

S to I, closed population (ordinary differential equation):

Answer 15

=(-beta)(S)(I)
-S can only be lost which is why there is a negative

Question 16

Rate of I produced, closed population (ordinary differential equation)

Answer 16

=(beta)(S)(I) – (vI)
-produced at a rate of BSI
-lost once they recover and develop resistance (why there is a negative)

Question 17

Rate of R produced, closed population (ordinary differential equation):

Answer 17

=vl
-loss of the I population are gains for the R population

Question 18

R0, basic reproductive number of disease:

Answer 18

=(beta x S) / (v)
-average number of new infections caused by a single infection over its duration
*needs to be greater than 1 for the disease to invade a host population

Question 19

How does beta influence disease invasion?

Answer 19

-increase beta=probability of disease invasion increases

Question 20

How does S influence disease invasion?

Answer 20

-increase S=probability of disease invasion increases

Question 21

How does v influence disease invasion?

Answer 21

-increase v=probability of disease invasion decreases
>decrease the average duration of an infection

Question 22

What does SIR model show about population size?

Answer 22

-shows that population size determines R0 and disease invasion!
*if population is too small, disease can’t invade!

Question 23

Dynamics of SIR model:

Answer 23

-S decreases over time
-I originally increases and then decreases over time
-R increases over time
*at equilibrium the disease has died out and there are no infected individuals in the population
>the host population now consists of susceptible and recovered individuals

Question 24

Epidemic of influenza B in Midwest region (2007-2008):

Answer 24

-showed number of observed cases and the predicted number of cases from the SIR model
-can use the data to estimate parameters that are difficult to measure (ex. beta)
-knowledge of the parameters is important for public health strategies

Question 25

SIR model with births and deaths:

Answer 25

-open population
-2 parameters: birth rate (b) and death rate (mu)
-birth rate = death rate so N is constant in size
-S, I, R all have the same birth and death rates

Question 26

With the introduction of births:

Answer 26

-now a constant input of naïve susceptible individuals

Question 27

With the introduction of death:

Answer 27

-R individuals die and leave the population

Question 28

Under what condition will the disease invade the host population (SIR open population):

Answer 28

-if the rate of infected individuals is GREATER than 0

Question 29

R0 SIR open population:

Answer 29

-definition of R0 depends on the structure of the model
-still must be greater than 1 for the level of infection to increase

Question 30

Minimum human population size to maintain measles:

Answer 30

*many infectious diseases can only persist if the host population passes a critical threshold
-measles needs 200,000 or more
-it couldn’t have existed before agricultural revolution

Question 31

Evidence that measles needs a minimum population size to persist:

Answer 31

-compared oceanic islands over a 16 year period
-can persist 100% when population size is 500,000
-islands with smaller population sizes, measles goes extinct and it must be RE-INTRODUCED from the outside world

Question 32

3000 years of urban growth:

Answer 32

-many historically important infectious diseases (measles, pertussis, scarlet fever, diphtheria) need relatively large human population sizes to persist
*most directly transmitted infectious diseases have emerged recently (within last 2000 years)

Question 33

Vaccination and disease invasion:

Answer 33

-disease invasion and persistence depends on S
-vaccination converts S individuals into R individuals
-decrease S=vaccination can prevent disease invasion

Question 34

Reff:

Answer 34

-only use R0 when population is 100% susceptible
-depends on fraction of S individuals
=(S/N)*R0
-disease wont invade if it is less than 1
*essentially the product of R0 and the fraction of unvaccinated individuals

Question 35

Susceptible and vaccinated individuals

Answer 35

-host population consists of S and vaccinated (Q) (this is before a breakout of a disease)
-s=proportion of S individuals
-q=proportion of Q individuals
-s+q=1

Question 36

Critical vaccination threshold:

Answer 36

-proportion of host population that must be vaccinated to prevent the infectious disease from invading the host population
-depends on R0
Qcrit=1-(1/R0)

Question 37

R0 and critical vaccination threshold:

Answer 37

-higher R0 value=higher critical proportion of hosts that must be vaccinated
-R0=2, qcrit=0.50
-R0=10=0.90

Question 38

R0 of human infectious disease:

Answer 38

-number of people that one sick person will infect
-measles=18, so about 94% of population must be vaccinated

Question 39

Why disease persist in developing and developed countries:

Answer 39

-developing: limited access to vaccines
-developed: vaccine hesitancy among a substantial fraction of population

Question 40

Herd immunity threshold (HIT):

Answer 40

-% of individuals that must become infected to prevent the infection from spreading
-HIT=qcrit
-natural immunity and vaccination both reduce S and prevent spread of disease
-with natural immunity, people have to contract the disease

Question 41

Herd immunity vs. vaccination:

Answer 41

-more mortality and morbidity (suffering) with herd immunity
>also caring for all the sick individuals which takes a toll on health care professionals and is costly for society

Question 42

Herd immunity and public health strategy:

Answer 42

-UK government considered herd immunity to fight COVID-19
-assumed R0=2,5
-qcrit=0.6 (60%)
-40million people would get ill
-case fatality rate (CFR) was 0.6% (240,000 would die)
*unacceptable level of mortality and decided to abandon the idea of her immunity