Generalised Threshold¶

The Generalised Threshold model was introduced in 2017 by Török and Kertesz [1].

In this model, during an epidemics, a node is allowed to change its status from Susceptible to Infected.

The model is instantiated on a graph having a non-empty set of infected nodes.

The model is defined as follows:

At time t nodes become Infected with rate mu t/tau
Nodes for which the ratio of the active friends dropped below the threshold are moved to the Infected queue
Nodes in the Infected queue become infected with rate tau. If this happens check all its friends for threshold

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
tau	Model	int		True	Adoption threshold rate
mu	Model	int		True	Exogenous timescale

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.GeneralisedThresholdModel(g)

# Model Configuration
config = mc.Configuration()
config.add_model_parameter('fraction_infected', 0.1)
config.add_model_parameter('tau', 5)
config.add_model_parameter('mu', 5)

# 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)