Epidemics-Generalised Threshold

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.




Initial contribute: 2019-05-09


Is authorship not correct? Feed back


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

Detailed Description

English {{currentDetailLanguage}} English

Generalised Threshold

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:

  1. At time t nodes become Infected with rate mu t/tau
  2. Nodes for which the ratio of the active friends dropped below the threshold are moved to the Infected queue
  3. Nodes in the Infected queue become infected with rate tau. If this happens check all its friends for threshold


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:


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.

Model Constructor :param graph: A networkx graph object


Set the initial model configuration

Parameters: configuration – a `ndlib.models.ModelConfig.Configuration` object

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



Describes the current model parameters (nodes, edges, status)

Returns: a dictionary containing for each parameter class the values specified during model configuration

Specify the statuses allowed by the model and their numeric code

Returns: a dictionary (status->code)

Execute Simulation


Execute a single model iteration :return: Iteration_id, Incremental node status (dictionary node->status)


Execute a bunch of model iterations

  • 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}


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)


# 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



János Török (2019). Epidemics-Generalised Threshold, Model Item, OpenGMS, https://geomodeling.njnu.edu.cn/modelItem/69475016-6f27-40ce-a8ad-1b9694cbfb3b


Initial contribute : 2019-05-09



Is authorship not correct? Feed back

QR Code


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



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


Cancel Submit
{{htmlJSON.Cancel}} {{htmlJSON.Submit}}
{{htmlJSON.Localizations}} + {{htmlJSON.Add}}
{{ item.label }} {{ item.value }}
{{htmlJSON.Cancel}} {{htmlJSON.Submit}}
名称 别名 {{tag}} +
系列名 版本号 目的 修改内容 创建/修改日期 作者
摘要 详细描述
{{tag}} + 添加关键字
* 时间参考系
* 空间参考系类型 * 空间参考系名称

起始日期 终止日期 进展 开发者
* 是否开源 * 访问方式 * 使用方式 开源协议 * 传输方式 * 获取地址 * 发布日期 * 发布者

编号 目的 修改内容 创建/修改日期 作者

时间分辨率 时间尺度 时间步长 时间范围 空间维度 格网类型 空间分辨率 空间尺度 空间范围
{{tag}} +
* 类型

* 名称 * 描述
示例描述 * 名称 * 类型 * 值/链接 上传

{{htmlJSON.Cancel}} {{htmlJSON.Submit}}
Title Author Date Journal Volume(Issue) Pages Links Doi Operation
{{htmlJSON.Cancel}} {{htmlJSON.Submit}}
{{htmlJSON.Add}} {{htmlJSON.Cancel}}


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.

{{htmlJSON.Cancel}} {{htmlJSON.Confirm}}