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

class ndlib.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(self, configuration)

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(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.
Returns:

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 SIS 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 probability of recovery of 0.5%.

import networkx as nx
import ndlib.models.ModelConfig as mc
import ndlib.models.epidemics.SISModel as sis

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

# Model selection
model = sis.SISModel(g)

# Model Configuration
cfg = mc.Configuration()
cfg.add_model_parameter('beta', 0.01)
cfg.add_model_parameter('lambda', 0.005)
cfg.add_model_parameter("percentage_infected", 0.05)
model.set_initial_status(cfg)

# Simulation execution
iterations = model.iteration_bunch(200)
[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