%0 Journal Article %1 Boguna2014Simulating %A Bogu\ ná, Marian %A Lafuerza, Luis F. %A Toral, Raúl %A Serrano, M. Ángeles %D 2014 %J Physical Review E %K gillespie, mc-simulations, sync-updates algorithms epidemic-models sis %N 4 %R 10.1103/PhysRevE.90.042108 %T Simulating non-Markovian stochastic processes %U http://dx.doi.org/10.1103/PhysRevE.90.042108 %V 90 %X We present a simple and general framework to simulate statistically correct realizations for a system of non-Markovian discrete stochastic processes. We give the exact analytical solution and a practical an efficient algorithm alike the Gillespie algorithm for Markovian processes, with the difference that now the occurrence rates of the events are stochastic processes themselves. We use our non-Markovian stochastic simulation methodology to investigate the effects of non-exponential inter-event time distributions in two case studies, the susceptible-infected-susceptible model of epidemic spreading and biochemical reactions with time delays. Strikingly, our results unveil the drastic effects that very subtle differences in the modeling of non-Markovian processes have on the global behavior of complex systems, with important implications for their understanding and prediction.

@article{Boguna2014Simulating, abstract = {{We present a simple and general framework to simulate statistically correct realizations for a system of non-Markovian discrete stochastic processes. We give the exact analytical solution and a practical an efficient algorithm alike the Gillespie algorithm for Markovian processes, with the difference that now the occurrence rates of the events are stochastic processes themselves. We use our non-Markovian stochastic simulation methodology to investigate the effects of non-exponential inter-event time distributions in two case studies, the susceptible-infected-susceptible model of epidemic spreading and biochemical reactions with time delays. Strikingly, our results unveil the drastic effects that very subtle differences in the modeling of non-Markovian processes have on the global behavior of complex systems, with important implications for their understanding and prediction.}}, added-at = {2019-06-10T14:53:09.000+0200}, archiveprefix = {arXiv}, author = {Bogu\ {n}\'{a}, Marian and Lafuerza, Luis F. and Toral, Ra\'{u}l and Serrano, M. \'{A}ngeles}, biburl = {https://www.bibsonomy.org/bibtex/2c3506d77cd8e5b0683676acc44ac1443/nonancourt}, citeulike-article-id = {12934826}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/PhysRevE.90.042108}, citeulike-linkout-1 = {http://arxiv.org/abs/1310.0926}, citeulike-linkout-2 = {http://arxiv.org/pdf/1310.0926}, day = 6, doi = {10.1103/PhysRevE.90.042108}, eprint = {1310.0926}, interhash = {9d10246f917bb7d74db9a3e13474f58f}, intrahash = {c3506d77cd8e5b0683676acc44ac1443}, issn = {1550-2376}, journal = {Physical Review E}, keywords = {gillespie, mc-simulations, sync-updates algorithms epidemic-models sis}, month = oct, number = 4, posted-at = {2014-01-23 10:13:50}, priority = {2}, timestamp = {2019-08-22T16:24:38.000+0200}, title = {{Simulating non-Markovian stochastic processes}}, url = {http://dx.doi.org/10.1103/PhysRevE.90.042108}, volume = 90, year = 2014 }