The SIR model was introduced in 1927 by Kermack .
In this model, during the course of an epidemics, a node is allowed to change its status from Susceptible (S) to Infected (I), then to Removed (R).
The model is instantiated on a graph having a non-empty set of infected nodes.
SIR 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 to removed with probability gamma (the only transition allowed are S→I→R).
The dSIR implementation assumes that the process occurs on a directed/undirected dynamic network; this model was introduced by Milli et al. in 2018 .
During the simulation a node can experience the following statuses:
|beta||Model||float in [0, 1]||True||Infection probability|
|gamma||Model||float in [0, 1]||True||Removal 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.
The following class methods are made available to configure, describe and execute the simulation:
Model Parameters to be specified via ModelConfig
- beta – The infection rate (float value in [0,1])
- gamma – The recovery rate (float value in [0,1])
Parameters: graph – A networkx graph object
Set the initial model configuration
Parameters: configuration – a
Reset the simulation setting the actual status to the initial configuration.
Describes the current model parameters (nodes, edges, status)
Returns: a dictionary containing for each parameter class the values specified during model configuration
Specify the statuses allowed by the model and their numeric code
Returns: a dictionary (status->code)
In the code below is shown an example of instantiation and execution of an DynSIR 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 removal probability of 1%.
import networkx as nx import dynetx as dn import ndlib.models.ModelConfig as mc import ndlib.models.dynamic as dm 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 = dm.DynSIRModel(dg) # Model Configuration config = mc.Configuration() config.add_model_parameter('beta', 0.01) config.add_model_parameter('gamma', 0.01) config.add_model_parameter("fraction_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()
|||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.|