# Create a SISe_sp model

### Description

Create a `SISe_sp`

model to be used by the simulation
framework.

### Usage

1 2 3 4 5 |

### Arguments

`u0` |
A |

`tspan` |
An increasing sequence of points in time where the state of the system is to be returned. |

`events` |
a |

`phi` |
A numeric vector with the initial environmental infectious pressure in each node. Default NULL which gives 0 in each node. |

`upsilon` |
Indirect transmission rate of the environmental infectious pressure |

`gamma` |
The recovery rate from infected to susceptible |

`alpha` |
Shed rate from infected individuals |

`beta_t1` |
The decay of the environmental infectious pressure in the first interval of the year. |

`beta_t2` |
The decay of the environmental infectious pressure in the second interval of the year. |

`beta_t3` |
The decay of the environmental infectious pressure in the third interval of the year. |

`beta_t4` |
The decay of the environmental infectious pressure in the fourth interval of the year. |

`end_t1` |
The non-inclusive day that ends interval 1. |

`end_t2` |
The non-inclusive day that ends interval 2. |

`end_t3` |
The non-inclusive day that ends interval 3. |

`end_t4` |
The non-inclusive day that ends interval 4. |

`epsilon` |
The background infectious pressure |

`coupling` |
The coupling between neighboring nodes |

`distance` |
The distance matrix between neighboring nodes |

### Details

The argument `u0`

must be a `data.frame`

with one row for
each node with the following columns:

- S
The number of sucsceptible

- I
The number of infected

### Value

`SISe_sp`

### Beta

The time dependent beta is divided into four intervals of the year

1 2 3 4 5 6 7 8 9 10 11 12 | ```
where 0 <= day < 365 and
0 <= end_t1 < end_t2 < end_t3 < end_t4 <= 365
or
0 <= end_t4 < end_t1 < end_t2 < end_t3 < 364
Case 1: end_t1 < end_t4
INTERVAL_1 INTERVAL_2 INTERVAL_3 INTERVAL_4 INTERVAL_1
[0, end_t1) [end_t1, end_t2) [end_t2, end_t3) [end_t3, end_t4) [end_t4, 365]
Case 2: end_t4 < end_t1
INTERVAL_4 INTERVAL_1 INTERVAL_2 INTERVAL_3 INTERVAL_4
[0, end_t4) [end_t4, end_t1) [end_t1, end_t2) [end_t2, end_t3) [end_t3, 365)
``` |