EoN.Gillespie_SIS¶
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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.
See Also: fast_SIS which has the same inputs but uses a faster method (esp for weighted graphs).
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 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
Returns: - 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.
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.Gillespie_SIS(G, tau, gamma, tmax = 20, initial_infecteds = range(initial_size)) plt.plot(t, I)