S̲tochastic S̲imulation A̲lgorithm For Effective Spreading Dynamics On T̲ime-Evolving A̲daptive N̲etworX̲ (SSATAN-X)

Abstract

Modelling and simulating of pathogen spreading has been proven crucial to inform containment strategies, as well as cost-effectiveness calculations. Pathogen spreading is often modelled as a stochastic process that is driven by pathogen exposure on time-evolving contact networks. In adaptive networks, the spreading process depends not only on the dynamics of a contact network, but vice versa, infection dynamics may alter risk behavior and thus feed back onto contact dynamics, leading to emergent complex dynamics. However, numerically exact stochastic simulation of such processes via the Gillespie algorithm is currently computationally prohibitive. On the other hand, frequently used ‘parallel updating schemes’ may be computationally fast, but can lead to incorrect simulation results. To overcome this computational bottleneck, we propose SSATAN-X. The key idea of this algorithm is to only capture contact dynamics at time-points relevant to the spreading process. We demonstrate that the statistics of the contact- and spreading process are accurate, while achieving ~100 fold speed-up over exact stochastic simulation. SSATAN-X’s performance increases further when contact dynamics are fast in relation to the spreading process, as applicable to most infectious diseases. We envision that SSATAN-X may extend the scope of analysis of pathogen spreading on adaptive networks. Moreover, it may serve to create benchmark data sets to validate novel numerical approaches for simulation, or for the data-driven analysis of the spreading dynamics on adaptive networks.