Helper functions to prepare <daedalus_behaviour> class responses
corresponding to either old or new behavioural change mechanisms.
Inherits from <daedalus_response> to allow for more control in future over
when these mechanisms are active.
Usage
daedalus_old_behaviour(rate = 0.001, lower_limit = 0.2)
daedalus_new_behaviour(
hospital_capacity,
behav_effectiveness = 0.5,
baseline_optimism = 0.5,
responsiveness = 1.5,
k0 = 4.59,
k1 = -9.19
)
is_daedalus_behaviour(x)
# S3 method for class 'daedalus_behaviour'
print(x, ...)Arguments
- rate
The marginal rate of decrease in the scaling factor for each additional daily death in the 'old' behavioural model.
- lower_limit
The lower limit of the scaling factor in the 'old' behavioural model; prevents scaling factor from reaching zero.
- hospital_capacity
The emergency hospital capacity of a country, but may also be a
<daedalus_country>object from which the hospital capacity is extracted. See \(\bar H\) in Details.- behav_effectiveness
A single double value for the effectiveness of adopting behavioural measures against the risk of infection. Expected to be in the range \([0, 1]\), where 0 represents no effectiveness, and 1 represents full effectiveness. See \(\delta\) in Details. Defaults to 0.5.
- baseline_optimism
A single double value for the baseline optimism about pandemic outcomes. Expected to be in the range \([0, 1]\). See \(\bar B\) in Details. Defaults to 0.5.
- responsiveness
A single double value for the population responsiveness to an epidemic signal. Must have a lower value of 0, but the upper bound is open. See \(k_2\) in Details. Defaults to 1.5.
- k0
A single, optional double value which is a scaling parameter for the sigmoidal relationship between \(p_t\) and
behav_effectiveness. See \(k_0\) in Details. Defaults to 4.59.- k1
A single, optional double value which is another scaling parameter for the sigmoidal relationship between \(p_t\) and
behav_effectiveness. See \(k_1\) in Details. Defaults to -9.19. Expected to be a negative number.- x
A
<daedalus_behaviour>object.- ...
Other arguments passed to
format().
Value
An object of class <daedalus_behaviour> which inherits from
<daedalus_response>. This is primarily a list holding behavioural
parameters.
Details
Daedalus currently supports two behavioural models (and the option to have neither model active). These models simulate population-level changes towards adopting behaviours that help reduce the risk of infection, which might be expected during a major disease outbreak.
In both models, the transmission rate of the infection \(\beta\) is reduced for all transmissions by a scaling factor; the models differ in how the scaling factor is calculated.
Note that a major issue with including this in a model run (any value
other than "off") is that it leads to substantially lower response costs,
and generally better health outcomes (lives lost), without accounting for
any attendant economic or social costs. As such, please treat the
behavioural models as experimental.
Deaths-based public concern model
This model existed prior to daedalus v0.2.25 and is referred to as the
"old" behavioural model.
The scaling factor for \(\beta\) in this model is $$ (1 - \text{rate})^{\Delta D} \times (1 - L) + L $$ where \(\text{rate}\) is the marginal rate of reduction for each additional death per day (\(\Delta D\)), and \(L\) is the lower limit of the scaling factor to prevent the FOI going to zero.
Optimism-responsiveness-effectiveness model
This model is referred to as the "new" behavioural model, and the scaling
factor for \(\beta\) is given by
$$ \mathcal{B}(p_t, \delta) = p_t(1 - \delta)[p_t(1 - \delta) + (1 - p_t)] + (1 - p_t)[p_t(1 - \delta) + (1 - p_t)] $$
where \(p_t\) is the proportion of the population taking protective behaviour and \(\delta\) is the effectiveness of the behaviour, both in the range \([0, 1]\). When either is zero, \(\beta\) is not scaled down.
\(p_t\) is computed during the model run, and is given by
$$ p_t = \frac{1}{1 + \text{exp}\left\{-\left(k_0 + k_1 \bar B + k_2 \frac{H_t}{\bar H}\right)\right\}} $$
where \(k_0 = 4.59, k_1 = -9.19, k_2\) are scaling parameters. \(k_0, k_1\) have constant values that cannot be changed by the user, and these have been chosen to produce a sigmoidal relationship between \(\bar B\) and \(p_t\).
\(k_2\) a constant user-supplied parameter that should be interpreted as population responsiveness to a signal of epidemic severity \(H_t / \bar H\), which is the relative burden on hospital capacity (\(H_t\): hospital demand at time \(t\), and \(\bar H\): emergency hospital capacity).
\(\bar B\) is a constant user-supplied parameter that captures the baseline population optimism about the outbreak.