SEIR

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).

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 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.

Methods

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

Configure

class ndlib.models.epidemics.SEIRModel.SEIRModel(graph)
SEIRModel.__init__(graph)
SEIRModel.set_initial_status(self, configuration)

Set the initial model configuration

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

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

Describe

SEIRModel.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
SEIRModel.get_status_map(self)

Specify the statuses allowed by the model and their numeric code

Returns:a dictionary (status->code)

Execute Simulation

SEIRModel.iteration(self)
SEIRModel.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}

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.SEIRModel as seir

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

# Model selection
model = seir.SEIRModel(g)

# Model Configuration
cfg = mc.Configuration()
cfg.add_model_parameter('beta', 0.01)
cfg.add_model_parameter('gamma', 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)
[1]J.L. Aron and I.B. Schwartz. Seasonality and period-doubling bifurcations in an epidemic model. Journal Theoretical Biology, 110:665-679, 1984