simulate_poisson: Simulate a partially observed Poisson branching process with...
In reconhub/branchr: R Estimation from Cluster Sizes

Description Usage Arguments Value Author(s) Examples

For a given reproduction number, this function simulate the incidence of a disease at each generation. The offspring distribution of each individual infected is assumed to follow a Poisson distribution with mean equal to the reproduction number. To simulate under-reporting, users can specify a probability to observe case, this reporting probability is assumed constant through the simulation.

1	simulate_poisson(R, n, s, rho, t_max)

`R`	is the reproduction number, i.e. the average number of secondary cases due to a single case. This can be any positive number. if R is a vector, then the length of R must be 'n' (see below).
`n`	is the number of simulations performed. Each simulation start with 's' individual(s) infected. 'n' must be a positive integer.
`s`	is the number individual(s) initially infected. if s is a vector, then the length of s must be 'n' (see above).
`rho`	is the probability (between 0 and 1) that an incident case is observed, i.e. reporting probability. if rho is a vector, then the length of rho must be 'n' (see below)
`t_max`	is the maximum number of generations simulated. 't_max' must be a positive integer.

The function returns a list including:

true_incidence: the true incidence over time.
reported_incidence: the observed incidence over time accounting for under-reporting (rho).
observed_incidence: same as reported_incidence, but only including simulated outbreaks for which at least a single case was observed (i.e. outbreak for which the observed final size is 0, see below reported_size, are removed).
true_size: the final outbreak sizes for each simulated outbreaks. Note that for outbreaks that are not extinct 'final' by the end of the simulation, z_sim correspond to the cumulative incidence by time t_max.
reported_size: the observed final outbreak sizes accounting for under-reporting (rho).
observed_size: same as reported_size, but only including simulated outbreaks for which at least a single case was observed.

Note that if some simulated outbreaks are not extinct by the end of the simulation, a warning is displayed.

Pierre Nouvellet (p.nouvellet@imperial.ac.uk)