Temporal Networks¶
Classes to define temporal networks and run stochastic simulations on them.

class
epipack.temporal_networks.
TemporalNetwork
(N, edge_lists, t, tmax, weighted=False, directed=False, loop_network=True)[source]¶ Bases:
object
A simple temporal network class.
 Parameters
N (int)  Static number of nodes in the network.
t (list)  An increasingly ordered list of times.
tmax (float)  The time at which the recording of network changes has concluded (the final time of the temporal network).
edge_lists (list) 
A list of lists of tuples. Each entry i of this list represents an edge list. Each entry j of an edge list is a tuple of format
( source, target, weight )
if
weighted=True
, or( source, target )
otherwise.
source
andtarget
are supposed to be of unsigned integer type in range[0,N)
.weighted (bool, default = False)  Whether or not
edge_lists
contain edge tuples with weightsdirected (bool, default = False)  Whether or not edge tuples will be considered to be directed.
loop_network (bool, default = True)  If True, the temporal network will be looped indefinitely when iterated.
Example
>>> edges = [ [ (0,1) ], [ (0,1), (0,2) ], [] ] >>> temporal_network = TemporalNetwork(3,[0,0.5,0.6],1.0,edges) >>> for edge_list, t, next_t in temporal_network: ... if t >= 3: ... break ... print(t, next_t, edge_list) ... 0 0.5 [(0, 1, 1.0)] 0.5 0.6 [(0, 1, 1.0), (0, 2, 1.0)] 0.6 1.0 [] 1.0 1.5 [(0, 1, 1.0)] 1.5 1.6 [(0, 1, 1.0), (0, 2, 1.0)] 1.6 2.0 [] 2.0 2.5 [(0, 1, 1.0)] 2.5 2.6 [(0, 1, 1.0), (0, 2, 1.0)] 2.6 3.0 []

tmax
¶ The time at which recording of edge changes has concluded (the final time of the temporal network).
 Type

edge_lists
¶ A list of lists of tuples. Each entry i of this list represents an edge list. Each entry j of an edge list is a tuple of format
( source, target, weight )
if
weighted=True
, or( source, target )
otherwise.
source
andtarget
are supposed to be of unsigned integer type in range[0,N)
. Type

class
epipack.temporal_networks.
TemporalNetworkSimulation
(temporal_network, stochastic_epi_model)[source]¶ Bases:
object
Simulation of a StochasticEpiModel on a temporal network.
 Parameters
temporal_network (TemporalNetwork)  A temporal network object.
stochastic_epi_model (epipack.stochastic_epi_models.StochasticEpiModel)  An instance of StochasticEpiModel, initialized with processes and initial conditions.
Example
>>> model = StochasticEpiModel(["S","I","R"],3)\ >>> .set_link_transmission_processes([ >>> ("I", "S", 1.0, "I", "I"), >>> ])\ >>> .set_node_transition_processes([ >>> ("I", 2.0, "R"), >>> ])\ >>> .set_node_statuses([1,0,0]) >>> temporal_network = TemporalNetwork(3,edges,[0,0.5,1.2],1.5) >>> sim = TemporalNetworkSimulation(temporal_network, model) >>> sim.simulate(tmax=100) [ 0. 0.38740794 0.8210494 3.60987397 9.46213129 12.14301704] {'S': array([2., 1., 0., 0., 0., 0.]), 'I': array([1., 2., 3., 2., 1., 0.]), 'R': array([0., 0., 0., 1., 2., 3.])}

temporal_network
¶ A temporal network object.
 Type

model
¶ An instance of StochasticEpiModel, initialized with processes and initial conditions.

simulate
(tmax, return_compartments=None, max_unsuccessful=None, sample_only_on_network_updates=False)[source]¶ Simulate a StochasticEpiModel on a temporal network.
 Parameters
tmax (float)  maximum length of the simulation
return_compartments (list of compartments, default = None:)  The compartments for which to return time series. If
None
, all compartments will be returned.max_unsuccessful (int, default = None)  The number of unsuccessful events after which the true total event rate will be evaluated (it might happen that a network becomes effectively disconnected while nodes are still associated with a maximum event rate). If
None
, this number will be set equal to the number of nodes.sample_only_on_network_updates (funtion, default = None)  A function that's called when a sample is taken
 Returns
t (numpy.ndarray)  times at which compartment counts have been sampled
result (dict)  Dictionary mapping a compartment to a time series of its count.