# SI¶

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].

## 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

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.dynamic.DynSIModel.DynSIModel(graph)

Model Parameters to be specified via ModelConfig

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

Model Constructor

Parameters: graph – A dynetx graph object
DynSIModel.set_initial_status(self, configuration)

Set the initial model configuration

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

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

### Describe¶

DynSIModel.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
DynSIModel.get_status_map(self)

Specify the statuses allowed by the model and their numeric code

Returns: a dictionary (status->code)

### Execute Simulation¶

DynSIModel.iteration(self)

Execute a single model iteration

Returns: Iteration_id, Incremental node status (dictionary node->status)
DynSIModel.execute_snapshots(bunch_size, node_status)
DynSIModel.execute_iterations(node_status)

## Example¶

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)

# Model selection
model = si.DynSIModel(dg)

# Model Configuration
config = mc.Configuration()