omega
omega(tau)
Infectiousness probability at time tau.
This functions defines the infection probability as a function of the time elapsed since infection. The distribution is a Weibull distribution with the given shape and scale
INPUT
- tau: np.array - time since infection
OUTPUTS
- p: pandas dataframe - infectiousness probability
beta
beta(tau)
Infectiousness at time tau, used by the continuous model.
This functions defines the infectiousness as a function of the time elapsed since infection. The result is a the value of the infectioun probability, scaled by R0.
INPUT
- tau: np.array - time since infection
OUTPUTS
- inf: np.array - infectiousness
beta_exposure
beta_exposure(e, beta_t=0.002)
Infectiousness as a function of the contact duration.
This functions defines component of the infectiousness that is a function of the duration of a contact in the network.
INPUT
- e: float - contact duration in seconds
- beta_t: float DEFAULT = 0.002 - istantaneous infection robability (i.e. per unit time)
OUTPUTS
- val: float - infectiousness
beta_dist_sign
beta_dist_sign(ss)
Infectiousness as a function of the signal strength.
This functions defines component of the infectiousness that is a function of the signal strenght (roughly: distance) of a contact in the network.
INPUT
- ss: float - signal strenght
OUTPUTS
- val: float - infectiousness
beta_data
beta_data(tau, ss, e, beta_t, omega=omega, beta_exposure=beta_exposure, beta_dist_sign=beta_dist_sign)
Infectiousness at time tau, used by the network simulation.
This functions defines the infectiousness as a function of the time elapsed since infection, on the distance of a contact, and on the signal strength (if not None) of a contact.
INPUT
- tau: np.array - time since infection
- ss: float - signal strenght
- e: float - contact duration in seconds
- beta_t: float DEFAULT = 0.002 - istantaneous infection robability (i.e. per unit time)
- omega: function - probability at time tau
- beta_exposure: function - infectiousness as a function of the contact duration.
- beta_dist: function - infectiousness as a function of the signal strength
OUTPUTS
- val: float - infectiousness
convert_dist_to_s
convert_dist_to_s(dist)
Convert a distance to a signal strenght.
The function converts a distance to a signal strenght.
INPUT
- dist: float - distance
OUTPUTS
- val: float - signal strength
convert_s_to_dist
convert_s_to_dist(x)
Convert a signal strenght to a distance.
The function converts a signal strength to a distance. The conversion is not accurate, and it is only use for the definition of beta_dist.
INPUT
- x: float - signal strength
OUTPUTS
- val: float - distance
onset_time
onset_time(mean=MEAN, std=STD, symptomatics=SYMPTOMATICS, testing=TESTING, delay=DELAY)
Sample from the probability distribution of the symptoms onset.
This functions returns a time (days) which is a sample from the distribution that describes the probability for an infected individual to be detected at a certain time, either because it becomes symptomatic, or because it is randomly tested.
The distribution is a lognormal with delayed mean, scaled to [0, symptomatics], and then lifted up by relative_testing (the sample is converted to seconds).
INPUT
- mean: float - mean onset time
- std: float - std onset time
- symptomatics: float DEFAULT = 0.8 - fraction of symptomatic people
- testing: float DEFAULT = 0.25 - fraction of testing of asymptomatics
- delay: float DEFAULT = 2 - delay in the reporting (in days)
OUTPUTS
- s_tau: float - probability to be detected before time tau
epsilon
epsilon(tau)
Infectiousness at time tau.
This functions defines the infectiousness as a function of the time elapsed since infection. The result is a the value of the infectioun probability, scaled by R0.
INPUT
- tau: np.array - time since infection
OUTPUTS
- eps_I: np.array - isolation efficiency
- eps_T: np.array - tracing efficiency