Transmission Distributions

List of the current distributions available to generate infection times.

Available Transmission Distributions

Gamma

A gamma-distributed transmission time model.

Constructor

transmission_time_gamma(double mean, double variance, double pinf=0.0)

- mean: The mean transmission time. - variance: The variance of the transmission time. - pinf: (Optional) Probability that the transmission does not occur (default: 0.0).

Example:

psi = nn.transmission_time_gamma(3.0, )

Weibull

A Weibull-distributed transmission time model.

Constructor

transmission_time_weibull(double shape, double scale, double pinf=0.0)

- shape: The shape parameter of the Weibull distribution. - scale: The scale parameter of the Weibull distribution. - pinf: (Optional) Probability that the transmission does not occur (default: 0.0).

Example:

psi = nn.transmission_time_weibull(2.0, 5.0)

Lognormal

A lognormal-distributed transmission time model.

Constructor

transmission_time_lognormal(double mean, double variance, double pinf=0.0)

- mean: The mean of the lognormal distribution. - variance: The variance of the lognormal distribution. - pinf: (Optional) Probability that the transmission does not occur (default: 0.0).

Example:

psi = nn.transmission_time_lognormal(3.0, 1.2)

Exponential

An exponentially-distributed transmission time model.

Constructor

transmission_time_exponential(double rate)

- rate: The rate parameter of the exponential distribution, where mean transmission time is 1/rate.

Example:

psi = nn.transmission_time_exponential(0.5)

Delta (deterministic)

A deterministic transmission time model where all transmission times are fixed.

Constructor

transmission_time_deterministic(double tau)

- tau: The fixed transmission time.

Example:

psi = nn.transmission_time_deterministic(4)

Infectiousness (custom distribution)

A transmission time \(\psi(\tau)\) that is defined from the infectiousness, or hazard rate \(\lambda(\tau)\). The user enters an array tau and an array infectiousness of same length to represent \(\lambda(\tau)\). The resulting distribution is then given by $$ \psi(\tau)=\lambda(\tau)\exp\left(-\int_0^\tau \lambda(\tau')\mathrm{d}\tau'\right).$$

Constructor

transmission_time_infectiousness(double tau)

- tau: The fixed transmission time.

Example:

tmax = 10
dt = 0.1
tau = [ dt * j for j in range(int(tmax/dt))]
infectiousness = [3 for t in tau]
psi = nn.transmission_time_infectiousness(tau,infectiousness)

Remark - transmission_time_infectiousness linearly interpolates the values of the infectiousness. - Beyond tmax, the infectiousness is assumed to be constant and takes the last value of the infectiousness array. - The first value of the infectiousness array cannot be zero currently (v.0.4.0). - This function can be particularly useful for simulations on temporal networks where the user might be more interested in defining the infection times from the infectiousness, or hazard rate, rather than the first infection time attempt.