Cascading Composition

Since each compartment identifies an atomic condition it is natural to imagine rules described as chains of compartments.

A compartment chain identify and ordered set of conditions that needs to be satisfied to allow status transition (it allows describing an AND logic).

To implement such behaviour each compartment exposes a parameter (named composed) that allows to specify the subsequent compartment to evaluate in case it condition is satisfied.

Example

In the code below is shown the formulation of a model implementing cascading compartment composition.

The rule Susceptible->Infected is implemented using three NodeStochastic compartments chained as follows:

  • If the node n is Susceptible
    • c1: if at least a neighbor of the actual node is Infected, with probability 0.5 evaluate compartment c2
    • c2: with probability 0.4 evaluate compartment c3
    • c3: with probability 0.2 allow the transition to the Infected state

Indeed, heterogeneous compartment types can be mixed to build more complex scenarios.

import networkx as nx
import ndlib.models.ModelConfig as mc
import ndlib.models.CompositeModel as gc
import ndlib.models.compartments.NodeStochastic as ns

# Network generation
g = nx.erdos_renyi_graph(1000, 0.1)

# Composite Model instantiation
model = gc.CompositeModel(g)

# Model statuses
model.add_status("Susceptible")
model.add_status("Infected")

# Compartment definition and chain construction
c3 = ns.NodeStochastic(0.2)
c2 = ns.NodeStochastic(0.4, composed=c3)
c1 = ns.NodeStochastic(0.5, "Infected", composed=c2)

# Rule definition
model.add_rule("Susceptible", "Infected", c1)

# Model initial status configuration
config = mc.Configuration()
config.add_model_parameter('percentage_infected', 0.1)

# Simulation execution
model.set_initial_status(config)
iterations = model.iteration_bunch(100)