Threshold¶
The Threshold model was introduced in 1978 by Granovetter [1].
In this model during an epidemic, a node has two distinct and mutually exclusive behavioral alternatives, e.g., the decision to do or not do something, to participate or not participate in a riot.
Node’s individual decision depends on the percentage of its neighbors that have made the same choice, thus imposing a threshold.
The model works as follows: - each node has its own threshold; - during a generic iteration every node is observed: if the percentage of its infected neighbors is greater than its threshold it becomes infected as well.
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 |
|---|---|---|---|---|---|
| threshold | Node | float in [0, 1] | 0.1 | False | Individual threshold |
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.
Example¶
In the code below is shown an example of instantiation and execution of a Threshold model simulation on a random graph: we set the initial set of infected nodes as 1% of the overall population, and assign a threshold of 0.25 to all the nodes.
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.ThresholdModel(g)
# Model Configuration
config = mc.Configuration()
config.add_model_parameter('fraction_infected', 0.1)
# Setting node parameters
threshold = 0.25
for i in g.nodes():
config.add_node_configuration("threshold", i, threshold)
model.set_initial_status(config)
# Simulation execution
iterations = model.iteration_bunch(200)
| [1] |
|