Diffusion Network-SI

In this model, during the course of an epidemics, a node is allowed to change its status only from Susceptible (S) to Infected (I). The model is instantiated on a graph having a non-empty set of infected nodes.

Diffusion Network



Initial contribute: 2019-05-09


Is authorship not correct? Feed back


Application-focused categoriesHuman-perspectiveSocial activities
Method-focused categoriesProcess-perspectiveBiological process calculation

Detailed Description

English {{currentDetailLanguage}} English


The SI model was introduced in 1927 by Kermack [1].

In this model, during the course of an epidemics, a node is allowed to change its status only from Susceptible (S) to Infected (I).

The model is instantiated on a graph having a non-empty set of infected nodes.

SI assumes that if, during a generic iteration, a susceptible node comes into contact with an infected one, it becomes infected with probability β: once a node becomes infected, it stays infected (the only transition allowed is S→I).

The dSI implementation assumes that the process occurs on a directed/undirected dynamic network; this model was introduced by Milli et al. in 2018 [2].


During the simulation a node can experience the following statuses:

Name Code
Susceptible 0
Infected 1


Name Type Value Type Default Mandatory Description
beta Model float in [0, 1]   True Infection probability

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:



Model Parameters to be specified via ModelConfig

Parameters: beta – The infection rate (float value in [0,1])

Model Constructor

Parameters: graph – A dynetx 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)


In the code below is shown an example of instantiation and execution of an DynSI simulation on a dynamic random graph: we set the initial set of infected nodes as 5% of the overall population and a probability of infection of 1%.

import networkx as nx
import dynetx as dn
import ndlib.models.ModelConfig as mc
import ndlib.models.dynamic.DynSIModel as si
from past.builtins import xrange

# Dynamic Network topology
dg = dn.DynGraph()

for t in xrange(0, 3):
    g = nx.erdos_renyi_graph(200, 0.05)
    dg.add_interactions_from(g.edges(), t)

# Model selection
model = si.DynSIModel(dg)

# Model Configuration
config = mc.Configuration()
config.add_model_parameter('beta', 0.01)
config.add_model_parameter("percentage_infected", 0.1)

# Simulate snapshot based execution
iterations = model.execute_snapshots()

# Simulation interaction graph based execution
iterations = model.execute_iterations()
    1. Kermack and A. McKendrick, “A Contribution to the Mathematical Theory of Epidemics,” Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, vol. 115, no. 772, pp. 700–721, Aug. 1927.
[2] Letizia Milli, Giulio Rossetti, Fosca Giannotti, Dino Pedreschi. “Diffusive Phenomena in Dynamic Networks: a data-driven study”. Accepted to International Conference on Complex Networks (CompleNet), 2018, Boston.



Letizia Milli (2019). Diffusion Network-SI, Model Item, OpenGMS, https://geomodeling.njnu.edu.cn/modelItem/3448ae07-5c12-41cf-bef0-b0e7eb9b17a9


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}}