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).

The dSIS implementation assumes that the process occurs on a directed/undirected dynamic network.

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

class ndlib.models.dynamic.DynSISModel.DynSISModel(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])
DynSISModel.__init__(graph)

Model Constructor

Parameters:graph – A networkx graph object
DynSISModel.set_initial_status(self, configuration)

Set the initial model configuration

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

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

Describe

DynSISModel.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
DynSISModel.get_status_map(self)

Specify the statuses allowed by the model and their numeric code

Returns:a dictionary (status->code)

Execute Simulation

DynSISModel.iteration(self)

Execute a single model iteration

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

Example

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

import networkx as nx
import dynetx as dn
import ndlib.models.ModelConfig as mc
import ndlib.models.dynamic.DynSISModel as sis

# Dynamic Network topology
dg = dn.DynGraph()

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

# Model selection
model = sis.DynSISModel(dg)

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

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

# Simulation interaction graph based execution
iterations = model.execute_iterations()
[1]
    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