sir function

Compartmental epidemiological models

Simple SIR-type models implemented in various ways. data

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
)

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

Returns

These functions return pomp objects containing simulated data.

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

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

See Also

More examples provided with pomp: blowflies, childhood_disease_data, dacca(), ebola, gompertz(), ou2(), pomp_examples, ricker(), rw2(), verhulst()