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].
Fortran implementation - for performance
(this) Python implementation - learn and use
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 network file, containing a list of edges and read, via terminal, the dynamical parameters.
For performance, see https://github.com/wcota/dynSIS (Fortran implementation)
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 https://wcota.me/dynSISdatasets.
Python 3 is required, and also the NumPy library.
If you want to manually input the dynamical parameters, just type:
python dynamics.py <edges_file> <output_file>
where <output_file> will be written with the average infected vertices density versus time.
Alternatively, use (Linux):
bash run.sh <edges_file> <output_file> <number of samples> <infection rate lambda> <maximum time steps> <fraction of infected vertices (initial condition)>
Example:
bash run.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.