The SI model was introduced in 1927 by Kermack . In this model, during the course of an epidemics, a node is allowed to change its status only from Susceptible (S) to Infected (I). The model is instantiated on a graph having a non-empty set of infected nodes. SI assumes that if, during a generic iteration, a susceptible node comes into contact with an infected one, it becomes infected with probability β: once a node becomes infected, it stays infected (the only transition allowed is S→I).

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Geography Subject Human Geography Health Geography

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Geography Subject GIScience & Remote Sensing Network Analysis

The SI model was introduced in 1927 by Kermack [1].

In this model, during the course of an epidemics, a node is allowed to change its status only from **Susceptible** (S) to **Infected** (I).

The model is instantiated on a graph having a non-empty set of infected nodes.

SI assumes that if, during a generic iteration, a susceptible node comes into contact with an infected one, it becomes infected with probability β: once a node becomes infected, it stays infected (the only transition allowed is S→I).

During the simulation a node can experience the following statuses:

Name | Code |
---|---|

Susceptible | 0 |

Infected | 1 |

Name | Type | Value Type | Default | Mandatory | Description |
---|---|---|---|---|---|

beta | Model | float in [0, 1] | True | Infection probability |

The initial infection status can be defined via:

percentage_infected: Model Parameter, float in [0, 1]Infected: Status Parameter, set of nodes

The two options are mutually exclusive and the latter takes precedence over the former.

The following class methods are made available to configure, describe and execute the simulation:

*class*`ndlib.models.epidemics.SIModel.`

`SIModel`

(*graph*)-
Model Parameters to be specified via ModelConfig

Parameters: **beta**– The infection rate (float value in [0,1])

`SIModel.`

`__init__`

(*graph*)-
Model Constructor

Parameters: **graph**– A networkx graph object

`SIModel.`

`set_initial_status`

(*self*,*configuration*)-
Set the initial model configuration

Parameters: **configuration**– a``ndlib.models.ModelConfig.Configuration``

object

`SIModel.`

`reset`

(*self*)-
Reset the simulation setting the actual status to the initial configuration.

`SIModel.`

`get_info`

(*self*)-
Describes the current model parameters (nodes, edges, status)

Returns: a dictionary containing for each parameter class the values specified during model configuration

`SIModel.`

`get_status_map`

(*self*)-
Specify the statuses allowed by the model and their numeric code

Returns: a dictionary (status->code)

`SIModel.`

`iteration`

(*self*)-
Execute a single model iteration

Returns: Iteration_id, Incremental node status (dictionary node->status)

`SIModel.`

`iteration_bunch`

(*self*,*bunch_size*)-
Execute a bunch of model iterations

Parameters: **bunch_size**– the number of iterations to execute**node_status**– if the incremental node status has to be returned.

Returns: a list containing for each iteration a dictionary {“iteration”: iteration_id, “status”: dictionary_node_to_status}

W.O. Kermack (2019). Epidemics-SI, Model Item, OpenGMS,
https://geomodeling.njnu.edu.cn/modelItem/be715b91-9a3a-4fb1-9d62-ed28aab50e29

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