Single strain dynamics

Question 1

strain dynamics show

Answer 1

self-emergent patterns

Question 2

SI model

Answer 2

• monoparametric (beta)
• flu, Herpesviruses, HIV, syphilis
• S + I = 1.0
• simulate 20years in 30day timesteps with starting frequencies: allows you to define equations

Question 3

Plotting infected and susceptible wrt time

Answer 3

• two states
• I always tends to 1

Question 4

Editing beta

Answer 4

• 1 always tends to one, S always tends to 0

Question 5

SIS model

Answer 5

• biparametric (beta and sigma)

Question 6

sigma

Answer 6

= 1/D

Question 7

edit beta in an SIS

Answer 7

• recovery rate balances transmission; I does not tend to 1
• increasing beta results in an increased epidemic curve
• decreasing beta means I tends towards 0

Question 8

varying B and D while keeping the product constant in an SIS model

Answer 8

Is converge at different rates

Question 9

An epidemic grows when…

Answer 9

• R0 > 1
• (betaS x I) - (sigmaI) > 0
• beta/sigma > 1
• dI/dt > 0

Question 10

initially in populations

Answer 10

S = 1

Question 11

SIR model

Answer 11

• think of lambda as (beta x I)
• S decreases, I and R increase
• I tends towards 0

Question 12

epidemic takeoff

Answer 12

is the same as in an SIS model

Question 13

As S declines

Answer 13

so does dI/dt; becomes negative

Question 14

Plot I(t) and dI/dt with respect to time

Answer 14

• dI/dt becomes negative when the epidemic is at equilibrium

Question 15

null derivative

Answer 15

absence of growth

Question 16

editing sigma in an SIR model

Answer 16

• keep beta > 0 and R0 constant
• plot I(t)
• greater sigma leads to a faster epidemic, shown by an earlier peak

Question 17

Introducing births and mortality

Answer 17

• > 1 epidemic
• herd immunity in the recovered compartment decreases, because the immune population dies
• new S recruitment
• population susceptibility increases

Question 18

Plot log(I)

Answer 18

look for epidemic growth/decay

Question 19

edit life expectancy

Answer 19

• decreasing life expectancy means the second epidemic comes faster
• more epidemics in the same timeframe
• due to greater pop. turnover

Question 20

SIRS model

Answer 20

omega = rate of recovery

Question 21

duration of immunity =

Answer 21

1/omega

Question 22

introducing omega into SIRS model

Answer 22

• primary epidemic peak
• smaller secondary epidemics (susceptible host accumulation, but more importantly, temporary immunity)
• much smaller interepidemic period

Question 23

varying omega

Answer 23

• no effect on initial peak due to slow accumulation
• decreasing omega means longer interepidemic periods
• also means higher immune population at equilibrium (approaches SIS value)
• naive pops recover fast

Question 24

large omega

Answer 24

multiple infections in same epidemic

Question 25

When can’t you use SI?

Answer 25

• multiple strains
• lifelong immunity
• no chronic infection
• complex lifecycle

Question 26

What does R inclusion mean?

Answer 26

• no longer indefinite growth
• as immunity increases, beta decreases
• epidemic peak and decay