Project
EF45-2
Effective Stochastic Simulation of Adaptive AB Models
Project Heads
Max von Kleist
Project Members
Nils Gubela
Project Duration
01.05.2023 – 31.12.2025
Located at
FU
Description
Agent-based models (ABMs) are increasingly used to study complex phenomena. We are interested in a class of ABMs that constitute stochastic (Markovian) contact-, as well as reaction dynamics. Using this setup, a state of the ABM can be represented by a temporal graph where the contact dynamics change the set of edges and the reaction dynamics alter the vertices.
While ABMs may differ in their setup, they typically involve adaptive processes. In epidemiological applications, adaptivity may entail measures of self-isolation (quarantine) upon infection, altering the dynamics of edges in temporal graph, whereas in biochemical systems, molecular complex formation alters diffusion and attraction of neighboring molecules. Thus, adaptivity creates feedback, which can lead to emergent complex behavior. Analytical solutions can only be obtained in very few special cases and thus numerical studies based on stochastic simulations are often indispensable to explore the dynamical behavior of these ABMs.
However, when simulating these ABMs, the main interest is in determining the evolution of the reaction dynamics. I.e. the main interest is in the state of the agents. Exact numerical methods suffer from the immense computational overhead of simulating the contact dynamics of agents in order to accurately capture the relevant reaction dynamics. Inexact stochastic simulation based on time discretization, and (a-)synchronous parallel updating of edges and vertices are most commonly implemented in epidemiological simulation software, yielding unreliable results.
We recently developed a rejection-based approach for simulating effective reaction dynamics on aforementioned ABMs, called SSATAN-X [1]. The central idea is to bulk update the contact dynamics between two epidemic reactions.
In this project, we aim to further advance SSATAN-X simulation method for adaptive ABMs. The goals of the project are threefold: error-analysis of the bulk-updating scheme, increasing computational efficacy and application to different (adaptive) network models.
High acceptance sampling of infection events
The epidemic ABM comprises two distinct processes: network processes and epidemic processes. While the update of the network process contributes significantly to the computational overhead, it offers minimal insight into the underlying epidemic events. To address this limitation, we propose an acceptance-rejection based algorithm that updates only the relevant network components at any given time point. Our analysis demonstrates that this method is exact and, when compared to SSA, is multiple orders of magnitude faster, enabling computations that were previously infeasible. With this new model, we are able to analyse how changes in behaviour shape the epidemic curve.
Project Webpages
Selected Publications
- Malysheva N, Wang J, von Kleist M. S̲tochastic S̲imulation A̲lgorithm For Effective Spreading Dynamics On T̲ime-Evolving A̲daptive N̲etworX̲ (SSATAN-X) Math. Model. Nat. Phenom. 2022; 17:35.
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