Epidemics-Kertesz Threshold

the model distinguishes three kinds of node: Blocked (B), Susceptible (S) and Adoptiong (A). The latter class breaks into two categories: vulnerable and stable nodes. A node can adopt either under its neighbors’ influence, or spontaneously, due to endogenous effects.

Epidemics
  869

Contributor(s)

Initial contribute: 2019-05-09

Authorship

Homepage:  
View
Is authorship not correct? Feed back

Classification(s)

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

Model Description

English {{currentDetailLanguage}} English

Kertesz Threshold

The Kertesz Threshold model was introduced in 2015 by Ruan et al. [1]and it is an extension of the Watts threshold model [2].

The authors extend the classical model introducing a density r of blocked nodes – nodes which are immune to social influence – and a probability of spontaneous adoption p to capture external influence.

Thus, the model distinguishes three kinds of node: Blocked (B), Susceptible (S) and Adoptiong (A). The latter class breaks into two categories: vulnerable and stable nodes. A node can adopt either under its neighbors’ influence, or spontaneously, due to endogenous effects.

Statuses

During the simulation a node can experience the following statuses:

Name Code
Susceptible 0
Infected 1
Blocked -1

Parameters

Name Type Value Type Default Mandatory Description
adopter_rate Model float in [0, 1] 0 False Exogenous adoption rate
percentage_blocked Model float in [0, 1] 0.1 False Blocked nodes
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 initial blocked nodes can be defined via:

  • percentage_blocked: Model Parameter, float in [0, 1]
  • Blocked: Status Parameter, set of nodes

In both cases, 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.KerteszThresholdModel.KerteszThresholdModel(graph)
Node/Model Parameters to be specified via ModelConfig
Parameters:
  • threshold – The node threshold. As default a value of 0.1 is assumed for all nodes.
  • adopter_rate – The probability of spontaneous adoptions. Defaults value 0.
  • percentage_infected – The percentage of blocked nodes. Default value 0.1.
KerteszThresholdModel.__init__(graph)

Model Constructor

Parameters: graph – A networkx graph object
KerteszThresholdModel.set_initial_status(selfconfiguration)

Set the initial model configuration

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

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

Describe

KerteszThresholdModel.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
KerteszThresholdModel.get_status_map(self)

Specify the statuses allowed by the model and their numeric code

Returns: a dictionary (status->code)

Execute Simulation

KerteszThresholdModel.iteration(self)

Execute a single model iteration

Returns: Iteration_id, Incremental node status (dictionary node->status)
KerteszThresholdModel.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.
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 a Kertesz Threshold model simulation on a random graph: we set the initial infected as well blocked node sets equals to the 10% of the overall population, assign a threshold of 0.25 to all the nodes and impose an probability of spontaneous adoptions of 40%.

import networkx as nx
import ndlib.models.ModelConfig as mc
import ndlib.models.epidemics.KerteszThresholdModel as ks

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

# Model selection
model = ks.KerteszThresholdModel(g)

# Model Configuration
config = mc.Configuration()
config.add_model_parameter('adopter_rate', 0.4)
config.add_model_parameter('percentage_blocked', 0.1)
config.add_model_parameter('percentage_infected', 0.1)

# 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]
  1. Ruan, G. In ̃iguez, M. Karsai, and J. Kertész, “Kinetics of social contagion,” Phys. Rev. Lett., vol. 115, p. 218702, Nov 2015.
[2]
    1. Watts, “A simple model of global cascades on random networks,” Proceedings of the National Academy of Sciences, vol. 99, no. 9, pp. 5766–5771, 2002.

How to Cite

Z.Ruan (2019). Epidemics-Kertesz Threshold, Model Item, OpenGMS, https://geomodeling.njnu.edu.cn/modelItem/86281e23-7a3c-4785-9b4e-544c2b05078e
Copy

QR Code

Contributor

Initial contribute: 2019-05-09

Co-contributor(s)

Authorship

Homepage:  
View
Is authorship not correct? Feedback

QR Code

×

{{curRelation.overview}}
{{curRelation.author.join('; ')}}
{{curRelation.journal}}









Related Items

You can link resource from repository to this model item, or you can create a new {{typeName.toLowerCase()}}.

Drop the file here, orclick to upload.
Select From My Space
+ add

These authorship information will be submitted to the contributor to review.

Cancel Submit
Cancel Submit
Localizations + Add
{{ item.label }} {{ item.value }}
Model Name :
Cancel Submit Cancel Submit
Name:
Version:
Model Type:
Model Domain:
Scale:
Purpose:
Principles:
Incorporated models:

Model part of

larger framework

Process:
Information:
Initialization:
Hardware Requirements:
Software Requirements:
Inputs:
Outputs:
Cancel Submit
Title Author Date Journal Volume(Issue) Pages Links Doi Operation
Cancel Submit
Add Cancel

{{articleUploading.title}}

Authors:  {{articleUploading.authors[0]}}, {{articleUploading.authors[1]}}, {{articleUploading.authors[2]}}, et al.

Journal:   {{articleUploading.journal}}

Date:   {{articleUploading.date}}

Page range:   {{articleUploading.pageRange}}

Link:   {{articleUploading.link}}

DOI:   {{articleUploading.doi}}

Yes, this is it Cancel

The article {{articleUploading.title}} has been uploaded yet.

OK
Cancel Confirm