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.
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].
During the simulation a node can experience the following statuses:
| Name | Code |
|---|---|
| Susceptible | 0 |
| Infected | 1 |
| 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.
The following class methods are made available to configure, describe and execute the simulation:
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.
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) |
|---|
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)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)
dg.add_interactions_from(g.edges(), t)
# Model selection
model = si.DynSIModel(dg)
# Model Configuration
config = mc.Configuration()
config.add_model_parameter('beta', 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] |
|
| [2] | Letizia Milli, Giulio Rossetti, Fosca Giannotti, Dino Pedreschi. “Diffusive Phenomena in Dynamic Networks: a data-driven study”. Accepted to International Conference on Complex Networks (CompleNet), 2018, Boston. |
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.
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