SIS Initial State

Module 5: Complex Networks

This page continues SIS Model on Networks. The first chunk repeats the parameters and the make_graph helper you wrote there.

import matplotlib.pyplot as plt
import networkx as nx
import numpy as np

SEED = 7
beta = 0.20  # infection probability per infected neighbour (per step)
mu = 0.10    # recovery probability (per step)
steps = 120
initial_infected = 5
N = 100


def make_graph(model: str, n: int, seed: int = SEED):
    if model == "random":
        return nx.erdos_renyi_graph(n=n, p=6 / (n - 1), seed=seed)
    if model == "small-world":
        return nx.watts_strogatz_graph(n=n, k=6, p=0.08, seed=seed)
    if model == "scale-free":
        return nx.barabasi_albert_graph(n=n, m=3, seed=seed)
    raise ValueError("model must be one of: 'random', 'small-world', 'scale-free'")


G = make_graph("random", n=N)

Initialize States

Store the state of each individual directly on the graph as a node attribute called state.

For example, start with everyone susceptible: create the attribute “state” and set it to “S” for all nodes:

nx.set_node_attributes(G, "S", "state")

print("Node 0:", G.nodes[0])  # node attributes are stored in a dictionary

Node 0: {'state': 'S'}

To infect node 20:

node_20 = G.nodes[20]
node_20["state"] = "I"

print("Node 20:", G.nodes[20])  # now node 20 has state "I"

Node 20: {'state': 'I'}

Alternatively, use a dictionary to set the states of multiple nodes at once:

# Infect nodes 20, 35, and 50
# The rest will be susceptible by default
state_dict = {node: "I" if node in [20, 35, 50] else "S" for node in G.nodes()}
nx.set_node_attributes(G, state_dict, "state")

print("Node 20:", G.nodes[20])  # node 20 is infected
print("Node 21:", G.nodes[21])  # node 21 is susceptible

Node 20: {'state': 'I'}
Node 21: {'state': 'S'}

Exercise

Create a function initialize_state(<graph>) that sets all nodes to “S” and then randomly picks a few nodes to set to “I” (the initial infected). Use a seeded random number generator (np.random.default_rng(seed)) to pick the nodes.

def initialize_state(G, initial_infected=5, seed=SEED):
    # TODO: start everyone as 'S' using node attributes
    # TODO: randomly pick initial_infected nodes and set their node attribute to 'I'
    # Optional: return G (mutated) for convenience
    return G

Solution

The optional rng argument lets a whole simulation share one generator; you will need it on the next page.

def initialize_state(G, initial_infected=5, seed=SEED, rng=None):
    if rng is None:
        rng = np.random.default_rng(seed)

    # Start everyone susceptible
    nx.set_node_attributes(G, "S", "state")

    # Infect a random subset
    infected = rng.choice(list(G.nodes()), size=initial_infected, replace=False)
    for node in infected:
        G.nodes[node]["state"] = "I"

    return G

Always validate your functions. Here, check that the number of infected nodes is correct:

initialize_state(G, initial_infected=initial_infected, seed=SEED)
print(
    "Initially infected:",
    sum(G.nodes[node]["state"] == "I" for node in G.nodes()),
)

Initially infected: 5

What’s Next?

SIS Simulation