sir: Compartmental epidemiological models

In pomp: Statistical Inference for Partially Observed Markov Processes

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
)

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.

Value

These functions return ‘pomp’ objects containing simulated data.

See Also

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

Examples

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

pomp documentation built on Sept. 13, 2024, 1:08 a.m.