## Epidemics-SIS

The SIS 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). The model is instantiated on a graph having a non-empty set of infected nodes. SIS 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 again to susceptible with probability lambda (the only transition allowed are S→I→S).

Epidemic
645

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

#### Model Description

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# SIS

The SIS 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).

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

SIS 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 again to susceptible with probability lambda (the only transition allowed are S→I→S).

## Statuses

During the simulation a node can experience the following statuses:

Name Code
Susceptible 0
Infected 1

## Parameters

Name Type Value Type Default Mandatory Description
beta Model float in [0, 1]   True Infection probability
lambda Model float in [0, 1]   True Recovery 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.SISModel.SISModel(graph)

Model Parameters to be specified via ModelConfig

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

Model Constructor

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

Set the initial model configuration

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

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

### Describe

SISModel.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
SISModel.get_status_map(self)

Specify the statuses allowed by the model and their numeric code

Returns: a dictionary (status->code)

### Execute Simulation

SISModel.iteration(self)

Execute a single model iteration

Returns: Iteration_id, Incremental node status (dictionary node->status)
SISModel.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}

#### How to Cite

W.O.Kermack (2019). Epidemics-SIS, Model Item, OpenGMS, https://geomodeling.njnu.edu.cn/modelItem/5c37dea1-9ce4-41e9-8ea0-58fc47412f35

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