Joel C. Miller

# Ethical Intervention

Designing ethical policy requires that penalties & rewards do not exceed the impact of the desired behaviour change. An important aspect of this is understanding the role of an individual. Surprisingly to some, the impact of individual behaviour change is largest when the reproduction number is just above 1, which is where the benefit to individuals of changing behaviour is almost zero.

### Constant Effort Intervention

Under a constant-effort intervention (for SIR disease), the impact of an individual on the final size of an epidemic can be studied analytically, and we can even predict the distribution of possible outcomes from an individual's actions.

### Dynamic impact in compartmental models

The dynamic impact is much harder to calculate. Basically we need to write down equations for perturbations to the usual SIR equations, and then integrate the perturbations (likely numerically). This will give us the expected impact of individuals

### Impact in Stochastic Simulations

In a stochastic simulation, we would like to compare two simulations with one individual changing behaviour. Naively, this could be done by having a chosen random seed and changing one individual's action. Unfortunately when the first random event changes, this will shift the sequence of random numbers for later events. Thus we do not have a true counterfactual. Designing simulations that properly produce counterfactuals requires more careful effort.

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