Lecture 8. Dynamics 4: Immunisation and Control

Question 1

When is the basic reproductive number used?

Answer 1

Used when the entire population is susceptible

Question 2

What does the basic reproductive rate tell us?

Answer 2

Tells us about whether an infection can invade

Question 3

What equation is used to calculate the basic reproductive number?

Answer 3

R₀ = β/(γ+m+d)
Loss of infected individuals through disease induced mortality (m) and natural death (d) - as well as recovery

Question 4

When is the effective reproductive number used?

Answer 4

Used when only a proportion of the population is susceptible

Question 5

What does the effective reproductive number tell us?

Answer 5

Can either tell us about growth during an epidemic, or whether an infection can invade with control measures in place:

Question 6

What equation is used to calculate the effective reproductive number?

Answer 6

Rt = β/(γ+m+d) * S/N
N includes that are susceptible (just S if populations expressed as proportions)

Question 7

In the equation Rt = β/(γ+m+d) * S, what types of control influence β (rate of infection)?

Answer 7

Anti-virals
Social Distancing
Public awareness

Question 8

In the equation Rt = β/(γ+m+d) * S, what types of control influence γ (rate of recovery)?

Answer 8

Anti-virals
Treatment
Isolation/quarantine

Question 8

In the equation Rt = β/(γ+m+d) * S, what types of control influence S (susceptible population)?

Answer 8

Immunisation
Anti-virals
Culling (cannot do for human diseases)

Question 9

In the equation Rt = β/(γ+m+d) * S, what types of control influence m (disease induced mortality) and d (natural death)?

Answer 9

Culling (cannot do for human diseases)

Question 10

How does vaccination act?

Answer 10

By eliciting an immune response in the host - thereby developing immunity to the pathogen (successful immunisation)

Question 11

When considering vaccination against endemic diseases, what can be ignored?

Answer 11

The time between infection and the development of immunity

Question 12

When can’t the time gap between vaccination and immunisation be ignored?

Answer 12

When controlling novel epidemics (time can be critical)

Question 13

When is someone successfully immunised?

Answer 13

When a successful immune response has been raised

Question 14

What assumptions are made when modelling with vaccinations?

Answer 14

The result of vaccination is simply to reduce the proportion of susceptibles in the population. We will also assume that people are vaccinated at (or closely after) birth

Question 15

What is the purpose of adding adjuvants to vaccines?

Answer 15

Helps raise the chances of immunity developing?

Question 16

How well does the seasonal flu vaccination work in old people?

Answer 16

In >65 age group, the vaccine typically works less well than in other adults and children
In 2016-17, the data suggest that the inactivated flu vaccine did not work at all in people aged over 65.

Question 17

What differential equations are used for a SIR model with vaccination?

Answer 17

dS/dt = +(1-p)B - βSI - dS
dI/dt = +βSI - γI - dI
dR/dt = +γI - dR + pB
p = fraction of births that are vaccinated

Question 18

What is Pc?

Answer 18

The vaccination threshold
Pc = 1 - 1/R₀

Question 19

If vaccination is constant and there is no infection, what does R and S equal in terms of p (proportion immune due to vaccination)?

Answer 19

R = p
S = 1-p

Question 20

When R₀ is just above 1, is vaccination necessary?

Answer 20

Not really (Pc = 9-33% enough for herd immunity)

Question 21

When R₀ is between 2-4, what can occur?

Answer 21

Outbreaks can occur but are can be prevented (Pc = 50-75%)

Question 22

When vaccination coverage increases, what happens to the prevalence of infection?

Answer 22

Linear reduction in the prevalence of infection with increasing amounts of vaccination
Eliminated above the critical threshold

Question 23

At endemic equilibrium without vaccination, what does S* equal?

Answer 23

1/R₀

Question 24

At the threshold what does S equal?

Answer 24

1/R₀

Question 25

What happens to the proportion of susceptible before the vaccination threshold is reached?

Answer 25

Proportion susceptible remains constant until past vaccination threshold - then decreases linearly
When you vaccinate the susceptible group does not get smaller

Question 26

Before elimination, what does the reduction in transmission events exactly compensate for?

Answer 26

The amount of immunisation

Question 27

What is the honeymoon effect?

Answer 27

Onset of vaccination combined with dynamics leads to low number of cases, honeymoon wears off and prevalence of infection starts to increase again (can induce substantial peaks and creates a ‘new’ equilibrium level of infection for given level of vaccination)

Question 28

In a population divided into 20% high risk and 80% low risk with the vaccinated proportion in the high risk group is pH, and pL in the low risk group, what does the WAIFW matrix look like?

Answer 28

R = [2(1-pH) 0.2(1-pH)]
[0.8(1-pL) 1.6(1-pL)]
2, 0.2, 0.8 and 1.6 are the R₀ values, scaled by how much vaccination is done

Question 29

Once the WAIFW matrix of the 20% HR and 80% LR population has been created, what might be done now?

Answer 29

Fix pH and find the value of pL that gives Rt = 1, then calculate the total amount vaccinated = 0.2 pH + 0.8 pL
Note that even if pL=1 (everyone in low-risk group is vaccinated) we still need pH>0.5 to control the infection

Question 30

How can targeted vaccination be optimised?

Answer 30

When the total population reaches a minimum point
Can always do as well random vaccination

Question 31

What are the main messages of target vaccination?

Answer 31

We can always do at least as well as random vaccination. For random vaccination we still have pc = 1 - 1/R₀
It is generally better to target vaccination towards to highest risk groups - although not exclusively - we need a biased mix
If there is uncertainty then it is better to over target the high-risk group, rather than under target

Question 32

What may vaccination cause an increase in?

Answer 32

Disease (not infection)

Question 33

For Rubella (German measles), what is the aim of the vaccination program?

Answer 33

Not to minimise the level of infection, but to minimise the number of cases in pregnant women

Question 34

For diseases with high R₀ , what can moderate levels of vaccination lead to?

Answer 34

Actually increase the number of cases in older age- groups - making the disease worse

Question 35

What is isolation/quarantining and how does it work?

Answer 35

Works by removing infected people from the population at large
It is also pathogen independent. Isolation works on any directly transmitted infection, even if the causative agent is unknown. For this reason it is often the most commonly used control measure in the early stages of an outbreak.
Unfortunately isolation only works if you have sufficient resources to isolate all cases.

Question 36

When are isolation wards allowed to be full?

Answer 36

With a full isolation ward control is much more difficult and only happens at far lower R₀ values

Question 37

When there is sufficient space in an isolation ward to contain an epidemic, what happens?

Answer 37

Cases are rare and can be controlled

Question 38

What happens when the numbers of cases become too great at an isolation ward and becomes full?

Answer 38

Control is no longer possible

Question 39

What is culling?

Answer 39

Very powerful way of controlling an infection - as (in most cases) it instantly stops transmission
Effective for livestock, wildlife and plant infections

Question 40

What is the complex trade-off of culling?

Answer 40

Too little culling and the infection is not controlled
Too much culling and the control is worse that the disease

Question 41

What is the optimum strategy when it comes to culling?

Answer 41

Minimise loss, which is not the best strategy to shorten the outbreak