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SEIR model with time-varying transmission parameter

Source: R/simulation-utils.R
sim_seir_model.Rd

This function simulates an SEIR (Susceptible-Exposed-Infectious-Recovered) model where the transmission rate (beta) varies over time.

Usage

sim_seir_model(
  changes = dplyr::tibble(t = c(0, 30), dBeta = c(1, 0.5)),
  mean_latent_period,
  mean_gen_time,
  R0 = 2.5,
  fn_dBeta = cfg_step_fn(changes),
  N = 10000,
  imports = 10,
  max_time = 104,
  seed = Sys.time()
)

Arguments

changes

a dataframe holding change time points (t) and the proportional increase in the transmission rate in the dBeta column

mean_latent_period

Mean time from infection to becoming infectious (E to I), assumed to be exponentially distributed.

mean_gen_time

The average generation time (will be latent period+infectious duration).

R0

the initial reproduction number

fn_dBeta

A function of time t that returns the multiple of transmission rate at that time point. Transmission (beta) at time zero is defined by R0 and the infectious duration, This is multiplied at each time by this factor.

N

Total population size. Defaults to 10,000.

imports

Initial number of infectious individuals. Defaults to 10.

max_time

Maximum simulation time (in days or time units). Defaults to 100.

seed

a random seed

Value

A dataframe containing the following columns:

  • statistic (character) - An identifier for the statistic, whether that be infections, admissions, deaths

  • count (positive_integer) - Positive case counts associated with the specified time frame

  • time (ggoutbreak::time_period + group_unique) - A (usually complete) set of singular observations per unit time as a time_period

Minimally grouped by: statistic (and other groupings allowed).

Details

The latent period (time from infection to becoming infectious) is assumed to be exponentially distributed. The infectious period is derived from the given mean of the generation time and the latent period.

The model assumes:

  • Latent period ~ Exponential(sigma), where sigma = 1 / mean_latent_period

  • Infectious period ~ Exponential(gamma), where gamma = 1 / (mean_gen_time - mean_latent_period)

  • Generation time ~ Exponential(sigma) + Exponential(gamma)

  • beta0 = R0 * gamma

  • Transmission rate beta(t) = fn_dBeta(t) * beta0

The generation time is defined as the sum of the latent and infectious periods.

Examples

# Example: Lockdown after day 30

seir_output <- sim_seir_model(
  mean_latent_period = 4,
  mean_gen_time = 7,
  R0 = 2.5,
  fn_dBeta = function(t) ifelse(t < 30, 1, 0.5)
)

if (interactive()) {
  plot_ip(attr(seir_output,"ip"))
  plot_counts(seir_output)
}