compartmental_models: Compartmental epidemiological models

Description

Simple SIR-type models implemented in various ways.

Usage

sir(
  gamma = 26,
  mu = 0.02,
  iota = 0.01,
  beta1 = 400,
  beta2 = 480,
  beta3 = 320,
  beta_sd = 0.001,
  rho = 0.6,
  k = 0.1,
  pop = 2100000,
  S_0 = 26/400,
  I_0 = 0.001,
  R_0 = 1 - S_0 - I_0,
  t0 = 0,
  times = seq(from = t0 + 1/52, to = t0 + 4, by = 1/52),
  seed = 329343545,
  delta.t = 1/52/20
)
sir2(
  gamma = 24,
  mu = 1/70,
  iota = 0.1,
  beta1 = 330,
  beta2 = 410,
  beta3 = 490,
  rho = 0.1,
  k = 0.1,
  pop = 1e+06,
  S_0 = 0.05,
  I_0 = 1e-04,
  R_0 = 1 - S_0 - I_0,
  t0 = 0,
  times = seq(from = t0 + 1/12, to = t0 + 10, by = 1/12),
  seed = 1772464524
)

Value

These functions return ‘pomp’ objects containing simulated data.

Arguments

gamma: recovery rate
mu: death rate (assumed equal to the birth rate)
iota: infection import rate
beta1, beta2, beta3: seasonal contact rates
beta_sd: environmental noise intensity
rho: reporting efficiency
k: reporting overdispersion parameter (reciprocal of the negative-binomial size parameter)
pop: overall host population size
S_0, I_0, R_0: the fractions of the host population that are susceptible, infectious, and recovered, respectively, at time zero.
t0: zero time
times: observation times
seed: seed of the random number generator
delta.t: Euler step size

Details

sir() producees a ‘pomp’ object encoding a simple seasonal SIR model with simulated data. Simulation is performed using an Euler multinomial approximation.

sir2() has the same model implemented using Gillespie's algorithm.

In both cases the measurement model is negative binomial: reports is distributed as a negative binomial random variable with mean equal to rho*cases and size equal to 1/k.

This and similar examples are discussed and constructed in tutorials available on the package website.

Examples

Run this code

# \donttest{
  po <- sir()
  plot(po)
  coef(po)
  
  po <- sir2()
  plot(po)
  plot(simulate(window(po,end=3)))
  coef(po)
  
  po |> as.data.frame() |> head()
# }