# SEIR (CT)¶

In the SEIR model [1], during the course of an epidemics, a node is allowed to change its status from Susceptible (S) to Exposed (E) to Infected (I), then to Removed (R).

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

SEIR 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 to removed with probability gamma (the only transition allowed are S→E→I→R).

This implementation assumes continuous time dynamics for the E->I and I->R transitions.

## Statuses¶

During the simulation a node can experience the following statuses:

Name Code
Susceptible 0
Infected 1
Exposed 2
Removed 3

## Parameters¶

Name Type Value Type Default Mandatory Description
beta Model float in [0, 1]   True Infection probability
gamma Model float in [0, 1]   True Removal probability
alpha Model float in [0, 1]   True Latent period

The initial infection status can be defined via:

• fraction_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.

## Methods¶

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

### Configure¶

class ndlib.models.epidemics.SEIR_ct_Model.SEIRctModel(graph, seed=None)
SEIRctModel.__init__(graph)

Model Constructor

Parameters: graph – A networkx graph object
SEIRctModel.set_initial_status(self, configuration)

Set the initial model configuration

Parameters: configuration – a ndlib.models.ModelConfig.Configuration object
SEIRctModel.reset(self)

Reset the simulation setting the actual status to the initial configuration.

### Describe¶

SEIRctModel.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
SEIRctModel.get_status_map(self)

Specify the statuses allowed by the model and their numeric code

Returns: a dictionary (status->code)

### Execute Simulation¶

SEIRctModel.iteration(self)

Execute a single model iteration

Parameters: node_status – if the incremental node status has to be returned. Iteration_id, (optional) Incremental node status (dictionary node->status), Status count (dictionary status->node count), Status delta (dictionary status->node delta)
SEIRctModel.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. progress_bar – whether to display a progress bar, default False a list containing for each iteration a dictionary {“iteration”: iteration_id, “status”: dictionary_node_to_status}

## Example¶

In the code below is shown an example of instantiation and execution of an SEIR simulation on a random graph: we set the initial set of infected nodes as % 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 as ep

# Network topology
g = nx.erdos_renyi_graph(1000, 0.1)

# Model selection
model = ep.SEIRctModel(g)

# Model Configuration
cfg = mc.Configuration()