Optimized Gillespie algorithms for the simulation of Markovian epidemic processes on large and heterogeneous networks: SIS-OGA
This code is part of the article "Optimized Gillespie algorithms for the simulation of Markovian epidemic processes on large and heterogeneous networks" [ArXiv].
NetworkX implementation
Fortran implementation - for performance
Python implementation - learn and use
(this) NetworkX Python implementation - range of options
GA Fortran implementation - Statistically exact, but NOT optimized
Full bibliographic details: Computer Physics Communications 219C (2017) pp. 303-312
DOI information: 10.1016/j.cpc.2017.06.007
@article{COTA2017303,
title = "Optimized Gillespie algorithms for the simulation of Markovian epidemic processes on large and heterogeneous networks",
journal = "Computer Physics Communications",
volume = "219",
number = "",
pages = "303 - 312",
year = "2017",
note = "",
issn = "0010-4655",
doi = "http://dx.doi.org/10.1016/j.cpc.2017.06.007",
url = "http://www.sciencedirect.com/science/article/pii/S0010465517301893",
author = "Wesley Cota and Silvio C. Ferreira",
keywords = "Complex networks",
keywords = "Markovian epidemic processes",
keywords = "Gillespie algorithm",
abstract = "Numerical simulation of continuous-time Markovian processes is an essential and widely applied tool in the investigation of epidemic spreading on complex networks. Due to the high heterogeneity of the connectivity structure through which epidemic is transmitted, efficient and accurate implementations of generic epidemic processes are not trivial and deviations from statistically exact prescriptions can lead to uncontrolled biases. Based on the Gillespie algorithm (GA), in which only steps that change the state are considered, we develop numerical recipes and describe their computer implementations for statistically exact and computationally efficient simulations of generic Markovian epidemic processes aiming at highly heterogeneous and large networks. The central point of the recipes investigated here is to include phantom processes, that do not change the states but do count for time increments. We compare the efficiencies for the susceptible–infected–susceptible, contact process and susceptible–infected–recovered models, that are particular cases of a generic model considered here. We numerically confirm that the simulation outcomes of the optimized algorithms are statistically indistinguishable from the original GA and can be several orders of magnitude more efficient."
}
This code is a implementation of the SIS-OGA algorithm, as detailed in our paper. It receives as input a NetworkX graph object and the dynamical parameters.
For performance, see https://github.com/wcota/dynSIS (Fortran implementation)
Python 3 is required, and also the NumPy and NetworkX libraries.
Import:
import networkx as nx
import dynSIS
After defining the NetworkX graph, just call
dynSIS.dyn_run(<nx.graph_Object>, <output_file_path>, <number_of_samples>, <infection_rate>, <maximum_time_steps>, <fraction_of_initial_infected_vertices>)
where <output_file_path> will be written with the average density of infected vertices versus time.
This uses the Karate Club network generated by NetworkX. To run, just use
python example_karate.py <output_file>
and type the asked parameters.
You need to provide a file containing the list of edges (in and out, two collumns). ID of the vertices must be enumerated sequentially as 1, 2, 3,..., N, where N is the total number of vertices of the network. Here, we assume undirected and unweighted networks without multiple neither self connections.
Consider, for example, a network with N=5 vertices represented by:
1,2
1,3
2,4
2,5
3,4
Examples of datasets and their specifications are available at http://wcota.me/dynSISdatasets.
To run, just use
python example_read.py <edges_file> <output_file>
and type the asked parameters.
Alternatively, use (Linux):
bash run_read.sh <edges_file> <output_file> <number of samples> <infection rate lambda> <maximum time steps> <fraction of infected vertices (initial condition)>
Example:
bash run_read.sh edges/s01.edges.dat "s01.lb0.002_100-samples.dat" 100 0.002 1000000 0.5
This code is under GNU General Public License v3.0.