EoN.Gillespie_complex_contagion¶

EoN.
Gillespie_complex_contagion
(G, rate_function, transition_choice, get_influence_set, IC, return_statuses, tmin=0, tmax=100, parameters=None, return_full_data=False, sim_kwargs=None)[source]¶ Initially intended for a complex contagion. However, this can allow influence from any nodes, not just immediate neighbors.
The complex contagion must be something that all nodes do something simultaneously
This is not the same as if node
v
primes nodeu
and later nodew
causesu
to transition. This will require that bothv
andw
have the relevant states at the moment of transition and it has forgotten any previous history.Arguments:  G (NetworkX Graph)
 The underlying network
 rate_function
A function that will take the network, a node, and the statuses of all the nodes and calculate the rate at which the node changes its status.
The function is called like
 if parameters is None:
 rate_function(G, node, status)
 else:
 rate_function(G, node, status, parameters)
where G is the graph, node is the node, status is a dict such that status[u] returns the status of u, and parameters is the parameters passed to the function.
it returns a number, the combined rate at which
node
might change status. transition_choice
A function that takes the network, a node, and the statuses of all the nodes and chooses which event will happen. The function should be called [with or without
parameters
] if
parameters
isNone
: transition_choice(G, node, status)
 else:
transition_choice(G, node, status, parameters)
where
G
is the graph,node` is the node, ``status` is a dict such that ``status[u]
returns the status of u, andparameters
is the parameters passed to the function.It should return the new status of
node
based on the fact that the node is changing status. if
 get_influence_set
When a node
u
changes status, we want to know which nodes may have their rate altered. We need to update their rates. This function returns all nodes that may be affected byu
(either in its previous state or its current state). We will go through and recalculate the rates for all of these nodes. For a contagion, we can simply choose all neighbors, but it may be faster to leave out any nodes that it wouldn’t have affected before or after its transition (e.g., R or I neighbors in SIR). if
parameters
is None: get_influence_set(G, node, status)
 else:
get_influence_set(G, node, status, parameters)
where G is the graph, node is the node, status is a dict such that status[u] returns the status of u, and parameters is the parameters passed to the function.
it should return the set of nodes whose rates need to be recalculated.
Most likely, it is
 def get_influence_set(G, node, status):
 return G.neighbors(node)
 if
 IC
 A dict. IC[node] returns the status of node.
 return_statuses list or other iterable (but not a generator)
 The statuses that we will return information for, in the order we will return them.
 tmin number (default 0)
 starting time
 tmax number (default 100)
 stop time
 return_full_data boolean
 currently needs to be False. True raises an error.
 parameters list/tuple.
 Any parameters of the functions rate_function, transition_choice, influence_set We assume all three functions can accept parameters. Examples: recovery rate, transmission rate, …
Returns:  (times, status1, status2, …) tuple of numpy arrays
 first entry is the times at which events happen.
second (etc) entry is an array with the same number of entries as
times
giving the number of nodes of status ordered as they are inreturn_statuses
SAMPLE USE: This simply does an SIR epidemic, by saying that the rate of becoming infected is tau times the number of infected neighbors.
import networkx as nx import EoN import matplotlib.pyplot as plt from collections import defaultdict #makes defining the initial condition easier def rate_function(G, node, status, parameters): #This function needs to return the rate at which node changes status. # tau,gamma = parameters if status[node] == 'I': return gamma elif status[node] == 'S': return tau*len([nbr for nbr in G.neighbors(node) if status[nbr] == 'I']) else: return 0 def transition_choice(G, node, status, parameters): #this function needs to return the new status of node. We already #know it is changing status. # #this function could be more elaborate if there were different #possible transitions that could happen. if status[node] == 'I': return 'R' elif status[node] == 'S': return 'I' def get_influence_set(G, node, status, parameters): #this function needs to return any node whose rates might change #because ``node`` has just changed status. # #the only neighbors a node might affect are the susceptible ones. return {nbr for nbr in G.neighbors(node) if status[nbr] == 'S'} G = nx.fast_gnp_random_graph(100000,0.00005) gamma = 1. tau = 0.5 parameters = (tau, gamma) IC = defaultdict(lambda: 'S') for node in range(200): IC[node] = 'I' t, S, I, R = EoN.Gillespie_complex_contagion(G, rate_function, transition_choice, get_influence_set, IC, return_statuses=('S', 'I', 'R'), parameters=parameters) plt.plot(t, I)