Epidemics-SIR

The SIR model was introduced in 1927 by Kermack . In this model, during the course of an epidemics, a node is allowed to change its status from Susceptible (S) to Infected (I), then to Removed (R). The model is instantiated on a graph having a non-empty set of infected nodes. SIR assumes that if, during a generic iteration, a susceptible node comes into contact with an infected one, it becomes infected with probability beta, than it can be switch to removed with probability gamma (the only transition allowed are S→I→R).

Epidemics
2107

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

SIR

The SIR 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 from Susceptible (S) to Infected (I), then to Removed(R).

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

SIR assumes that if, during a generic iteration, a susceptible node comes into contact with an infected one, it becomes infected with probability beta, than it can be switch to removed with probability gamma (the only transition allowed are S→I→R).

Statuses

During the simulation a node can experience the following statuses:

Name Code
Susceptible 0
Infected 1
Removed 2

Parameters

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

Methods

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

Configure

classndlib.models.epidemics.SIRModel.SIRModel(graph)

Model Parameters to be specified via ModelConfig

Parameters: beta – The infection rate (float value in [0,1]) gamma – The recovery rate (float value in [0,1])
SIRModel.__init__(graph)

Model Constructor

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

Set the initial model configuration

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

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

Describe

SIRModel.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
SIRModel.get_status_map(self)

Specify the statuses allowed by the model and their numeric code

Returns: a dictionary (status->code)

Execute Simulation

SIRModel.iteration(self)

Execute a single model iteration

Returns: Iteration_id, Incremental node status (dictionary node->status)
SIRModel.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 an SIR simulation on a random graph: we set the initial set of infected nodes as 5% of the overall population, a probability of infection of 1%, and a removal probability of 0.5%.

import networkx as nx
import ndlib.models.ModelConfig as mc
import ndlib.models.epidemics.SIRModel as sir

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

# Model selection
model = sir.SIRModel(g)

# Model Configuration
cfg = mc.Configuration()
model.set_initial_status(cfg)

# Simulation execution
iterations = model.iteration_bunch(200)

 [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

How to Cite

W.O.Kermack (2019). Epidemics-SIR, Model Item, OpenGMS, https://geomodeling.njnu.edu.cn/modelItem/8dc31bef-28a2-4a23-8c07-67d1ff32d486

Authorship

Homepage:
View
Is authorship not correct? Feedback

QR Code

• {{curRelation.name}}
{{curRelation.name}}

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

Related Items
{{props.row.name}}

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

{{ props.row.description }}
{{ props.row.description }}
Drop the file here, orclick to upload.
File size should not exceed 10m.
Select From My Space

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

Cancel Submit
Cancel Submit
{{ item.label }} {{ item.value }}
{{props.row.localName}}
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

Yes, this is it Cancel

OK
Cancel Confirm
Model Classifications 1
Model Classifications 2
Title Author Date Journal Volume(Issue) Pages Links Doi Operation

NEW

Name:
Affiliation:
Email:
Homepage:

Yes, this is it Cancel

Confirm
path
:
/{{path.name}}
search results of '{{searchContentShown}}'

No content to show

{{item.name}}

.

{{item.suffix}}

.{{item.suffix}}

Max: {{toDecimal1(capacity/1073741824)}} GB
Copy
Delete
Rename
/{{path.label}}
Change
/{{path.name}}
Select File
Cancel Confirm
path
:
/{{path.name}}
/..
Cancel Confirm
{{ data.name }}
You have select  {{multipleSelection.length+multipleSelectionMyData.length}} data .
• My Uploaded Data
• Output Data
• {{item.computableName}}@{{formatDate(item.runTime)}}
{{scope.row.type}}
{{ scope.row.tag }}
• Fork Data
{{it.category}}

NEW

Name:
Affiliation:
Email:
Homepage:
previous next conform
Model Classifications

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

Related Items
{{ props.row.description }}
{{ props.row.description }}
Cancel OK