compartmental_models {pomp} | R Documentation |

## 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 |

`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*version 5.11.0.0 Index]