Lecture 8. Dynamics 4: Immunisation and Control Flashcards
When is the basic reproductive number used?
Used when the entire population is susceptible
What does the basic reproductive rate tell us?
Tells us about whether an infection can invade
What equation is used to calculate the basic reproductive number?
R₀ = β/(γ+m+d)
Loss of infected individuals through disease induced mortality (m) and natural death (d) - as well as recovery
When is the effective reproductive number used?
Used when only a proportion of the population is susceptible
What does the effective reproductive number tell us?
Can either tell us about growth during an epidemic, or whether an infection can invade with control measures in place:
What equation is used to calculate the effective reproductive number?
Rt = β/(γ+m+d) * S/N
N includes that are susceptible (just S if populations expressed as proportions)
In the equation Rt = β/(γ+m+d) * S, what types of control influence β (rate of infection)?
Anti-virals
Social Distancing
Public awareness
In the equation Rt = β/(γ+m+d) * S, what types of control influence γ (rate of recovery)?
Anti-virals
Treatment
Isolation/quarantine
In the equation Rt = β/(γ+m+d) * S, what types of control influence S (susceptible population)?
Immunisation
Anti-virals
Culling (cannot do for human diseases)
In the equation Rt = β/(γ+m+d) * S, what types of control influence m (disease induced mortality) and d (natural death)?
Culling (cannot do for human diseases)
How does vaccination act?
By eliciting an immune response in the host - thereby developing immunity to the pathogen (successful immunisation)
When considering vaccination against endemic diseases, what can be ignored?
The time between infection and the development of immunity
When can’t the time gap between vaccination and immunisation be ignored?
When controlling novel epidemics (time can be critical)
When is someone successfully immunised?
When a successful immune response has been raised
What assumptions are made when modelling with vaccinations?
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
What is the purpose of adding adjuvants to vaccines?
Helps raise the chances of immunity developing?
How well does the seasonal flu vaccination work in old people?
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.
What differential equations are used for a SIR model with vaccination?
dS/dt = +(1-p)B - βSI - dS
dI/dt = +βSI - γI - dI
dR/dt = +γI - dR + pB
p = fraction of births that are vaccinated
What is Pc?
The vaccination threshold
Pc = 1 - 1/R₀
If vaccination is constant and there is no infection, what does R and S equal in terms of p (proportion immune due to vaccination)?
R = p
S = 1-p
When R₀ is just above 1, is vaccination necessary?
Not really (Pc = 9-33% enough for herd immunity)
When R₀ is between 2-4, what can occur?
Outbreaks can occur but are can be prevented (Pc = 50-75%)
When vaccination coverage increases, what happens to the prevalence of infection?
Linear reduction in the prevalence of infection with increasing amounts of vaccination
Eliminated above the critical threshold
At endemic equilibrium without vaccination, what does S* equal?
1/R₀
At the threshold what does S equal?
1/R₀
What happens to the proportion of susceptible before the vaccination threshold is reached?
Proportion susceptible remains constant until past vaccination threshold - then decreases linearly
When you vaccinate the susceptible group does not get smaller
Before elimination, what does the reduction in transmission events exactly compensate for?
The amount of immunisation
What is the honeymoon effect?
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)
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?
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
Once the WAIFW matrix of the 20% HR and 80% LR population has been created, what might be done now?
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
How can targeted vaccination be optimised?
When the total population reaches a minimum point
Can always do as well random vaccination
What are the main messages of target vaccination?
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
What may vaccination cause an increase in?
Disease (not infection)
For Rubella (German measles), what is the aim of the vaccination program?
Not to minimise the level of infection, but to minimise the number of cases in pregnant women
For diseases with high R₀ , what can moderate levels of vaccination lead to?
Actually increase the number of cases in older age- groups - making the disease worse
What is isolation/quarantining and how does it work?
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.
When are isolation wards allowed to be full?
With a full isolation ward control is much more difficult and only happens at far lower R₀ values
When there is sufficient space in an isolation ward to contain an epidemic, what happens?
Cases are rare and can be controlled
What happens when the numbers of cases become too great at an isolation ward and becomes full?
Control is no longer possible
What is culling?
Very powerful way of controlling an infection - as (in most cases) it instantly stops transmission
Effective for livestock, wildlife and plant infections
What is the complex trade-off of culling?
Too little culling and the infection is not controlled
Too much culling and the control is worse that the disease
What is the optimum strategy when it comes to culling?
Minimise loss, which is not the best strategy to shorten the outbreak
