Examiners: Peter Ashcroft + someone else from the research group
Protocol: one additional person
Time: ~20 min total
BLOCK 1: STRUCTURED MODELS
exercise 7.3.1 of the script
- write down the Jacobian (of the I-equations) (without plugging in the numbers)
- use the Jacobian to reformulate the system as a matrix equation
- how would you calculate R0 from this Jacobian’s eigenvalues?
- why can we calculate R0 using a Jacobian for just the I-equations?
-> this particular system has no demography, the total population is constant: S_H = S_H(0)-I_H
-> I_H and I_L are the only free variables
- verbally define R0 for a model like this with heterogeneous risk structure
- if r=0 (infecteds never recover) then what is R0?
BLOCK 2: STOCHASTIC MODELS
- what is Galton-Watson Branching Process (describe setup and process)
- what assumptions does this model make (no density effects i.e. no S-depletion)
- what are examples of things that you can calculate using this model (and how would you do each)
- R0
- extinction probabilities (even for R0 > 1)
- in a particular generation
- ultimate extinction probability
BLOCK 3: further questions
- define an SIR model, then incorporate vaccination (equations OR diagram)
- given R0, how would you calculate the critical vaccination percentage - also in case of <100% vaccine effectiveness
- where does this 1-1/R0 term come from (derivation)