The SI model was introduced in 1927 by Kermack1.
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).
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:
- 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:
ndlib.models.epidemics.SIModel.SIModel
ndlib.models.epidemics.SIModel.SIModel.__init__(graph)
ndlib.models.epidemics.SIModel.SIModel.set_initial_status(self, configuration)
ndlib.models.epidemics.SIModel.SIModel.reset(self)
ndlib.models.epidemics.SIModel.SIModel.get_info(self)
ndlib.models.epidemics.SIModel.SIModel.get_status_map(self)
ndlib.models.epidemics.SIModel.SIModel.iteration(self)
ndlib.models.epidemics.SIModel.SIModel.iteration_bunch(self, bunch_size)
In the code below is shown an example of instantiation and execution of an SI simulation on a 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 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.SIModel(g)
# Model Configuration
cfg = mc.Configuration()
cfg.add_model_parameter('beta', 0.01)
cfg.add_model_parameter("fraction_infected", 0.05)
model.set_initial_status(cfg)
# Simulation execution
iterations = model.iteration_bunch(200)
- 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.