# 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¶

class ndlib.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(self, configuration)

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(self, bunch_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()