Network Models

The epimodels.network module simulates epidemics directly on contact networks with an event-driven (Gillespie) algorithm: infection fires along each susceptible–infectious edge at rate beta and each infected node recovers at rate gamma.

Graphs can be networkx graphs (install the network extra: pip install epimodels[network]), plain adjacency dictionaries {node: [neighbors]} or symmetric adjacency matrices.

SIR on a network

import networkx as nx
from epimodels.network import NetworkSIR

G = nx.barabasi_albert_graph(1000, 3, seed=0)  # scale-free contact network

model = NetworkSIR(G)
model(
    5,                       # 5 initially infected nodes (or a list of nodes)
    [0, 50],                 # simulation time range
    {"beta": 0.3, "gamma": 0.1},
    n_sims=20,               # stochastic replicates
    seed=0,
)

model.traces["I"].shape      # (20, 101) — replicates x time grid
model.final_size()           # attack rate per replicate
model.get_mean()             # mean trajectories
model.get_quantiles(0.95)    # 95% band
model.plot_traces("I")       # spaghetti plot + mean

SIS on a network

NetworkSIS sends recovered nodes back to the susceptible pool, so infection can become endemic:

from epimodels.network import NetworkSIS

G_small = nx.barabasi_albert_graph(300, 3, seed=0)
model = NetworkSIS(G_small)
model(5, [0, 50], {"beta": 0.6, "gamma": 0.1}, n_sims=10, seed=0)

model.traces["I"][:, -1].mean()   # mean prevalence at tmax

Note:

The event-driven sampler picks the next infector proportionally to its susceptible-neighbor count, which is O(infected) per event. Long-running SIS simulations on large graphs (persistent epidemics generate many events) are therefore slow; prefer smaller graphs or shorter horizons.

Targeting specific nodes

Instead of a count, pass the identifiers of the initially infected nodes — useful for studying super-spreading from hubs:

hub = max(G.nodes(), key=G.degree)
model([hub], [0, 50], {"beta": 0.3, "gamma": 0.1}, n_sims=5, seed=1)

Working without networkx

Adjacency dictionaries and matrices avoid the networkx dependency:

from epimodels.network import NetworkSIR

adjacency = {0: [1, 2], 1: [0], 2: [0]}
model = NetworkSIR(adjacency)
model(1, [0, 20], {"beta": 0.5, "gamma": 0.2}, n_sims=3, seed=0)

Note:

Network models follow the library conventions (parameters, traces, summary()) but take the graph at construction time and the number of initially infected nodes in place of inits; there is no totpop argument since the population is the set of nodes.