EoN.fast_SIS

EoN.fast_SIS(G, tau, gamma, initial_infecteds=None, rho=None, tmin=0, tmax=100, transmission_weight=None, recovery_weight=None, return_full_data=False, sim_kwargs=None)

Fast SIS simulations for epidemics on weighted or unweighted networks, allowing edge and node weights to scale the transmission and recovery rates. Assumes exponentially distributed times to recovery and to transmission.

From figure A.5 of Kiss, Miller, & Simon. Please cite the book if using this algorithm.

Arguments:

G networkx Graph

The underlying network

tau positive float

transmission rate per edge

gamma number

recovery rate per node

initial_infecteds node or iterable of nodes

if a single node, then this node is initially infected if an iterable, then whole set is initially infected if None, then choose randomly based on rho. If rho is also None, a random single node is chosen. If both initial_infecteds and rho are assigned, then there is an error.

rho number

initial fraction infected. number infected is int(round(G.order()*rho))

tmin number (default 0)

starting time

tmax number (default 100)

stop time

transmission_weight string (default None)

the label for a weight given to the edges. transmission rate is G.adj[i][j][transmission_weight]*tau

recovery_weight string (default None)

a label for a weight given to the nodes to scale their recovery rates gamma_i = G.nodes[i][recovery_weight]*gamma

return_full_data boolean (default False)

Tells whether a Simulation_Investigation object should be returned.

sim_kwargs keyword arguments

Any keyword arguments to be sent to the Simulation_Investigation object Only relevant if return_full_data=True

Returns:

times, S, I each a numpy array

times and number in each status for corresponding time

or if return_full_data=True

full_data Simulation_Investigation object

from this we can extract the status history of all nodes. We can also plot the network at given times and even create animations using class methods.

SAMPLE USE:

import networkx as nx
import EoN
import matplotlib.pyplot as plt

G = nx.configuration_model([1,5,10]*100000)
initial_size = 10000
gamma = 1.
tau = 0.2
t, S, I = EoN.fast_SIS(G, tau, gamma, tmax = 10,
                            initial_infecteds = range(initial_size))

plt.plot(t, I)