# Node Stochastic¶

Node Stochastic compartments are used to evaluate stochastic events attached to network nodes.

Consider the transition rule Susceptible->Infected that requires a probability beta to be satisfied. Such rule can be described by a simple compartment that models Node Stochastic behaviors. Let’s call il NS.

The rule will take as input the initial node status (Susceptible), the final one (Infected) and the NS compartment. NS will thus require a probability (beta) of activation.

During each rule evaluation, given a node n

• if the actual status of n equals the rule initial one
• a random value b in [0,1] will be generated
• if b <= beta then NS is considered satisfied and the status of n changes from initial to final.

Moreover, NS allows to specify a triggering status in order to restrain the compartment evaluation to those nodes that:

1. match the rule initial state, and
2. have at least one neighbors in the triggering status.

## Parameters¶

Name Value Type Default Mandatory Description
ratio float in [0, 1]   True Event probability
triggering_status string None False Trigger

## Example¶

In the code below is shown the formulation of a SIR model using NodeStochastic compartments.

The first compartment, c1, is used to implement the transition rule Susceptible->Infected. It requires a probability threshold - here set equals to 0.02 - and restrain the rule evaluation to all those nodes that have at least an Infected neighbors.

The second compartment, c2, is used to implement the transition rule Infected->Removed. Since such transition is not tied to neighbors statuses the only parameter required by the compartment is the probability of transition.

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

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

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

# Model statuses

# Compartment definition
c1 = cpm.NodeStochastic(0.02, triggering_status="Infected")
c2 = cpm.NodeStochastic(0.01)

# Rule definition