# EoN.Gillespie_SIS¶

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

Performs SIS simulations for epidemics on networks with or without weighted edges.

It assumes that the edges have a weight associated with them and that the transmission rate for an edge is tau*weight[edge]

Based on an algorithm by Petter Holme. It requires a weighted choice of edges and this will be done by tracking the maximum edge weight and then using repeated rejection samples until a successful selection.

fast_SIS which has the same inputs but uses a faster method (esp for weighted graphs).

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 is int(round(G.order()*rho))
tmin number (default 0)
starting time
tmax number
stop time
recovery_weight string (default None)
the string used to define the node attribute for the weight. Assumes that the recovery rate is gamma*G.nodes[u][recovery_weight]. If None, then just uses gamma without scaling.
transmission_weight string (default None)
the string used to define the edge attribute for the weight. Assumes that the transmission rate from u to v is tau*G.adj[u][v][transmission_weight]
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
times, S, I numpy arrays
giving 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.
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.Gillespie_SIS(G, tau, gamma, tmax = 20,
initial_infecteds = range(initial_size))

plt.plot(t, I)