# Threshold¶

The Threshold model was introduced in 1978 by Granovetter [1].

In this model during an epidemics, a node has two distinct and mutually exclusive behavioral alternatives, e.g., the decision to do or not do something, to participate or not participate in a riot.

Node’s individual decision depends on the percentage of its neighbors have made the same choice, thus imposing a threshold.

The model works as follows: - each node has its own threshold; - during a generic iteration every node is observed: iff the percentage of its infected neighbors is grater than its threshold it becomes infected as well.

## Statuses¶

During the simulation a node can experience the following statuses:

Name Code
Susceptible 0
Infected 1

## Parameters¶

Name Type Value Type Default Mandatory Description
threshold Node float in [0, 1] 0.1 False Individual threshold

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.ThresholdModel.ThresholdModel(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.
ThresholdModel.__init__(graph)

Model Constructor

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

Set the initial model configuration

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

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

### Describe¶

ThresholdModel.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
ThresholdModel.get_status_map(self)

Specify the statuses allowed by the model and their numeric code

Returns: a dictionary (status->code)

### Execute Simulation¶

ThresholdModel.iteration(self)

Execute a single model iteration

Returns: Iteration_id, Incremental node status (dictionary node->status)
ThresholdModel.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. 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 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.ThresholdModel as th

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

# Model selection
model = th.ThresholdModel(g)

# Model Configuration
config = mc.Configuration()