Extracting Simulation Information#

StaticNetworkContagion objects save their compartmental histories. These can be retrieved via their history attribute.

The user may only be interested in recalling the set of source vertices of a simulation named contagion; this is achievable via contagion.get_source(). By passing an additional return_subgraph=True argument, the source set will be returned as the subgraph induced by the source nodes.

Source inference algorithms require information about the contagion’s status. We begin with standard graph generation and contagion simulation (as outlined in the previous section):

import networkx as nx
import cosasi
import random
import numpy as np

seed = 42
random.seed(seed)
np.random.seed(seed)

G = nx.fast_gnp_random_graph(200, 0.01, seed=seed)

contagion = cosasi.StaticNetworkContagion(
    G=G,
    model="si",
    infection_rate=0.2,
    number_infected = 4,
    seed=seed
)
contagion.forward(steps=100)

The most common information type in source inference literature is a “snapshot,”” where complete information about the infection is provided for a particular time step:

>>> contagion.get_infected_indices(step=5)

[1, 6, 19, 22, 28, 38, 40, 54, 82, 99, 119, 163, 171, 176, 177, 182, 189, 194]

retrieves the indices of all vertices in the infected compartment at simulation step 10, and

>>> I = contagion.get_infected_subgraph(step=5)

returns the induced subgraph of the vertices in the infected compartment at the provided step. The infection subgraph is provided as a NetworkX graph:

>>> type(I)

<class 'networkx.classes.graph.Graph'>

Alternately, some algorithms employ “observers,” a handful of vertices that are designated to record when they become infected. In our implementation, the user specifies the number of observers, and the particular selection is performed uniformly at random:

>>> contagion.get_observers(observers=5)

{163: 0, 28: 0, 6: 0, 189: 0, 70: inf}

An infection time of inf indicates that the node was not infected at all during the diffusion process.

Note that, if the infection model is SIS, nodes may be reinfected, so observers record a list of the timestamps at which they are infected. Otherwise, observers record one timestamp (step number) only.

An analytical tool used in some algorithms is the infection frontier, which is the set of infected vertices with infected neighbors:

>>> contagion.get_frontier(step=5)

{1, 38, 40, 171, 176, 177, 82, 19, 22, 119, 182}

This is especially pertinent to the SI epidemic model, because vertices do not recover. In this case, the frontier set consists of nodes that may have been infected last, by the given timestep.

Running a Simulation

Source Inference