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New behaviour mechanism should rely on hospitalisations #135

@pratikunterwegs

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@pratikunterwegs

This issue is to change how the new behavioural mechanism added in PR #129 works. The reduction in transmission rate is a function of the ratio of hospital occupancy and hospital capacity, so that there is a stronger reduction as hospital capacity is overwhelmed by demand.

This leads to the perverse-incentive outcome of more deaths at higher hospital capacities, when the behavioural mechanism is active (any $\delta > 0$). See the figure below.

The proposed fix is to make the reduction in transmission rate a function of hospital occupancy alone, which is similar to the 'old' behavioural mechanism. The responsiveness parameter $k_2$ will need to scaled down by 1-2 orders of magnitude to account for this change, as hospital occupancy or demand can be in the low millions for some infections.

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