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