The SI model was introduced in 1927 by Kermack .
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 .
During the simulation a node can experience the following statuses:
|beta||Model||float in [0, 1]||True||Infection 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
Parameters: beta – The infection rate (float value in [0,1])
Parameters: graph – A dynetx 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 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 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.DynSIModel(dg) # Model Configuration config = mc.Configuration() config.add_model_parameter('beta', 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.|