In this model, during an epidemics, a node is allowed to change its status from Susceptible to Infected. The model is instantiated on a graph having a non-empty set of infected nodes.
The Generalised Threshold model was introduced in 2017 by Török and Kertesz [1].
In this model, during an epidemics, a node is allowed to change its status from Susceptible to Infected.
The model is instantiated on a graph having a non-empty set of infected nodes.
The model is defined as follows:
During the simulation a node can experience the following statuses:
| Name | Code |
|---|---|
| Susceptible | 0 |
| Infected | 1 |
| Name | Type | Value Type | Default | Mandatory | Description |
|---|---|---|---|---|---|
| threshold | Node | float in [0, 1] | 0.1 | False | Individual threshold |
| tau | Model | int | True | Adoption threshold rate | |
| mu | Model | int | True | Exogenous timescale |
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:
ndlib.models.epidemics.GeneralisedThresholdModel.GeneralisedThresholdModel(graph)Node Parameters to be specified via ModelConfig
| Parameters: | threshold – The node threshold. If not specified otherwise a value of 0.1 is assumed for all nodes. |
|---|
GeneralisedThresholdModel.__init__(graph)Model Constructor :param graph: A networkx graph object
GeneralisedThresholdModel.set_initial_status(self, configuration)Set the initial model configuration
| Parameters: | configuration – a `ndlib.models.ModelConfig.Configuration` object |
|---|
GeneralisedThresholdModel.reset(self)Reset the simulation setting the actual status to the initial configuration.
GeneralisedThresholdModel.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 |
|---|
GeneralisedThresholdModel.get_status_map(self)Specify the statuses allowed by the model and their numeric code
| Returns: | a dictionary (status->code) |
|---|
GeneralisedThresholdModel.iteration(self)Execute a single model iteration :return: Iteration_id, Incremental node status (dictionary node->status)
GeneralisedThresholdModel.iteration_bunch(self, bunch_size)Execute a bunch of model iterations
| Parameters: |
|
|---|---|
| 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 a Threshold model simulation on a random graph: we set the initial set of infected nodes as 1% of the overall population, and assign a threshold of 0.25 to all the nodes.
import networkx as nx
import ndlib.models.ModelConfig as mc
import ndlib.models.epidemics.GeneralisedThresholdModel as gth
# Network topology
g = nx.erdos_renyi_graph(1000, 0.1)
# Model selection
model = gth.GeneralisedThresholdModel(g)
# Model Configuration
config = mc.Configuration()
config.add_model_parameter('percentage_infected', 0.1)
config.add_model_parameter('tau', 5)
config.add_model_parameter('mu', 5)
# Setting node parameters
threshold = 0.25
for i in g.nodes():
config.add_node_configuration("threshold", i, threshold)
model.set_initial_status(config)
# Simulation execution
iterations = model.iteration_bunch(200)
| [1] | János Török and János Kertész “Cascading collapse of online social networks” Scientific reports, vol. 7 no. 1, 2017 |
In this model, during an epidemics, a node is allowed to change its status from Susceptible to Infected. The model is instantiated on a graph having a non-empty set of infected nodes.
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