SWIR

The SWIR model was introduced in 2017 by Lee et al. [1].

In this model, during the epidemics, a node is allowed to change its status from Susceptible (S) to Weakened (W) or Infected (I), then to Removed (R).

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

At time t a node in the state I is selected randomly and the states of all neighbors are checked one by one. If the state of a neighbor is S then this state changes either i) to I with probability kappa or ii) to W with probability mu. If the state of a neighbor is W then the state W changes to I with probability nu. We repeat the above process for all nodes in state I and then changes to R for each associated node.

Statuses

During the simulation a node can experience the following statuses:

Name Code
Susceptible 0
Infected 1
Weakened 2
Removed 3

Parameters

Name Type Value Type Default Mandatory Description
kappa Model float in [0, 1]   True  
mu Model float in [0, 1]   True  
nu Model float in [0, 1]   True  

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.SWIRModel.SWIRModel(graph)
SWIRModel.__init__(graph)
SWIRModel.set_initial_status(self, configuration)

Set the initial model configuration

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

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

Describe

SWIRModel.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
SWIRModel.get_status_map(self)

Specify the statuses allowed by the model and their numeric code

Returns:a dictionary (status->code)

Execute Simulation

SWIRModel.iteration(self)
SWIRModel.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.SWIRModel as swir

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

# Model selection
model = swir.SWIRModel(g)

# Model Configuration
cfg = mc.Configuration()
cfg.add_model_parameter('kappa', 0.01)
cfg.add_model_parameter('mu', 0.005)
cfg.add_model_parameter('nu', 0.05)
cfg.add_model_parameter("percentage_infected", 0.05)
model.set_initial_status(cfg)

# Simulation execution
iterations = model.iteration_bunch(200)
[1]
  1. Lee, W. Choi, J. Kertész, B. Kahng. “Universal mechanism for hybrid percolation transitions”. Scientific Reports, vol. 7(1), 5723, 2017.