## Epidemics-Threshold

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.

Epidemic
639

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Method-focused categoriesProcess-perspectiveBiological process calculation
Method-focused categoriesProcess-perspectiveHuman-activity calculation

#### Model Description

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# 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

classndlib.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(selfconfiguration)

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(selfbunch_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()

# Setting node parameters
threshold = 0.25
for i in g.nodes():

model.set_initial_status(config)

# Simulation execution
iterations = model.iteration_bunch(200)

 [1] Granovetter, “Threshold models of collective behavior,” The American Journal of Sociology, vol. 83, no. 6, pp. 1420–1443, 1978.

#### How to Cite

M.Granovetter (2019). Epidemics-Threshold, Model Item, OpenGMS, https://geomodeling.njnu.edu.cn/modelItem/1f675de1-d8ea-41be-9111-dace3ce4638a

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