Directly transmitted diseases

Question 1

what can we learn from consistent dynamics of the epidemic?

Answer 1

• What can we learn from the consistent dynamics of the epidemics?
  
  • will the disease spread? - the red line goes up?
  • what proportion of the population need sot be susceptible for the incidence to increase?
  • how fast will the increase be originally?
  • what is the size of the epidemic likely to be?

Question 2

What is the difference between R0 and Rn?

Answer 2

for R0 the entire population needs to be susceptible but that’s not always true and in that case we need to use Rn which allows us to take into account the fact that not all individuals are susceptible

Question 3

What is the formula for Rn?

Answer 3

Rn = R0 *S

Question 4

Describe the effects of Rn <1 =1 and >1

Answer 4

• If Rn <1 then incidence will not increase
• the proportion of the population that is susceptible needs to exceed the “epidemic threshold” for Rn>1

Question 5

What is the formula for the epidemic threshold?

Answer 5

epidemic threshold = 1/R0

Question 6

What happens if you have 60% immunity and the epidemic threshold is 0.5?

Answer 6

if you start with 60% immunity there will be no outbreak at all → the epidemic threshold is 0.5 → half of the population needs to be susceptible and with 60% immunity only 0.4 are

Question 7

What happens if you have 60% immunity and the epidemic threshold is 0.5?

Answer 7

if you start with 60% immunity there will be no outbreak at all → the epidemic threshold is 0.5 → half of the population needs to be susceptible and with 60% immunity only 0.4 are

Question 8

What is a herd immunity threshold?

Answer 8

herd immunity threshold - the proportion of the population which should be immune for incidence to stop increasing (Rn=1)

Question 9

What is the formula for the her immunity threshold?

Answer 9

her immunity threshold = 1-(1/R0)

Question 10

Calculate the herd immunity threshold for measles where R0 =13

Answer 10

for example R0=13 for measles → 92% of people need to be immune to measles to prevent an outbreak

Question 11

How can we calculate the initial growth rate of the epidemic?

Answer 11

These observations suggest that we can estimate the actual growth rate in an epidemic using observed empirical data simply by plotting the natural log of the observed number of infectious individuals and calculating the gradient of the resulting line. If (as in most circumstances) data on the numbers of infectious individuals are not available, we can use data on the cumulative incidence of cases instead, since this increases at a similar rate to that of the number of infectious individuals during the early stages of an epidemic

Question 12

What is lambda when talking about the epidemic growth?

Answer 12

‘growth rate of the epidemic’, sometimes denoted by the Greek capital letter Λ (lambda).

Question 13

How can we get to R0 from epidemic growth?

Answer 13

• if pre-infectious period relatively short compared to infectious:
  
  • R0 = 1 +Λ D. where D is the infectious period
• if pre-infectious period and infectious period are similar then :
  
  • R0 = (1+Λ D)(1+ Λ D’)

Question 14

Why does the incidence of immunising infections cycle over time?

Answer 14

peaks in new infections per day depend on birth rate

Question 15

What is the relationship between birth rate and the number of susceptibles?

Answer 15

• relationship between birth rate and susceptibles
  
  1. you don’t have enough susceptible hosts so your epidemic threshold is not surpassed
  2. you keep adding babeis and at some point they reach the epidemic threshold
  3. susceptibles start being removed from the susceptible compartment to the infected compartment and the birth rate can’t match the speed → your susceptibles drop
  4. at some point you are below the epidemic threshold again and the disease doesn’t spread, you have to wait for the birth rate to catch up again and replenish the pool of susceptible hosts and then the whole cycle starts again

Question 16

What is the formula for number of infectious individuals at time t?

Answer 16

Directly transmitted disease lecture