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:
- fraction_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, seed=None)¶ 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.
- progress_bar – whether to display a progress bar, default False
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 as ep
# Network topology
g = nx.erdos_renyi_graph(1000, 0.1)
# Model selection
model = ep.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("fraction_infected", 0.05)
model.set_initial_status(cfg)
# Simulation execution
iterations = model.iteration_bunch(200)
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