In the SEIS model, during the course of an epidemics, a node is allowed to change its status from Susceptible (S) to Exposed (E) to Infected (I), then again to Susceptible (S). The model is instantiated on a graph having a non-empty set of infected nodes. SEIS assumes that if, during a generic iteration, a susceptible node comes into contact with an infected one, it becomes infected after an exposition period with probability beta, than it can switch back to susceptible with probability lambda (the only transition allowed are S→E→I→S).

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Geography Subject Human Geography Health Geography

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Geography Subject GIScience & Remote Sensing Network Analysis

In the SEIS model, during the course of an epidemics, a node is allowed to change its status from **Susceptible** (S) to **Exposed** (E) to **Infected** (I), then again to **Susceptible** (S).

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

SEIS assumes that if, during a generic iteration, a susceptible node comes into contact with an infected one, it becomes infected after an exposition period with probability beta, than it can switch back to susceptible with probability lambda (the only transition allowed are S→E→I→S).

During the simulation a node can experience the following statuses:

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

Susceptible | 0 |

Infected | 1 |

Exposed | 2 |

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

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

lambda | Model | float in [0, 1] | True | Removal probability | |

alpha | Model | float in [0, 1] | True | Incubation period |

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.SEISModel.`

`SEISModel`

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

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

`SEISModel.`

`__init__`

(*graph*)-
Model Constructor

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

`SEISModel.`

`set_initial_status`

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

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

object

`SEISModel.`

`reset`

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

`SEISModel.`

`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

`SEISModel.`

`get_status_map`

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

Returns: a dictionary (status->code)

`SEISModel.`

`iteration`

(*self*)-
Execute a single model iteration

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

`SEISModel.`

`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}

In the code below is shown an example of instantiation and execution of an SEIS simulation on a random graph: we set the initial set of infected nodes as 5% of the overall population, a probability of infection of 1%, a removal probability of 0.5% and an incubation period of 5% (e.g. 20 iterations).

```
import networkx as nx
import ndlib.models.ModelConfig as mc
import ndlib.models.epidemics.SEISModel as seis
# Network topology
g = nx.erdos_renyi_graph(1000, 0.1)
# Model selection
model = seis.SEISModel(g)
# Model Configuration
cfg = mc.Configuration()
cfg.add_model_parameter('beta', 0.01)
cfg.add_model_parameter('lambda', 0.005)
cfg.add_model_parameter('alpha', 0.05)
cfg.add_model_parameter("percentage_infected", 0.05)
model.set_initial_status(cfg)
# Simulation execution
iterations = model.iteration_bunch(200)
```

NDlib (2019). Epidemics-SEIS, Model Item, OpenGMS,
https://geomodeling.njnu.edu.cn/modelItem/b2c982ed-dc91-4890-b567-6ddd1a20ac62

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