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.




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

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.


During the simulation a node can experience the following statuses:

Name Code
Susceptible 0
Infected 1
Blocked -1


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.


The following class methods are made available to configure, describe and execute the simulation:


Node/Model Parameters to be specified via ModelConfig
  • 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.

Model Constructor

Parameters: 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

Returns: 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 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)


# Simulation execution
iterations = model.iteration_bunch(200)
  1. Ruan, G. In ̃iguez, M. Karsai, and J. Kertész, “Kinetics of social contagion,” Phys. Rev. Lett., vol. 115, p. 218702, Nov 2015.
    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.



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


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}}