Stochastic Simulation Algorithm for effective spreading dynamics on Time-evolving Adaptive NetworX (SSATAN-X)

Modelling and simulating the dynamics of pathogen spreading has been proven crucial to inform public heath decisions, 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 behaviour and thus feed back onto contact dynamics, leading to emergent complex dynamics. However, stochastic simulation of pathogen spreading processes on adaptive networks is currently computationally prohibitive. In this manuscript, we propose SSATAN-X, a new algorithm for the accurate stochastic simulation of pathogen spreading on adaptive networks. The key idea of SSATAN-X is to only capture the contact dynamics that are relevant to the spreading process. We show that SSATAN-X captures the contact dynamics and consequently the spreading dynamics accurately. The algorithm achieves up to 100 fold speed-up over the state-of-art stochastic simulation algorithm (SSA). The speed-up with SSATAN-X further increases when the contact dynamics are fast in relation to the spreading process, i.e. if contacts are short-lived and per-exposure infection risks are small, 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. A C++ implementation of the algorithm is available at https://github.com/nmalysheva/SSATAN-X. Author summary Modelling and simulating of infectious disease spreading supports public heath decisions, such as prevention and containment strategies and allows to perform cost-effectiveness calculations. Detailed modelling approaches consider stochastic pathogen spreading 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 behaviour and thus feed back onto contact dynamics. Stochastic simulation of these complex dynamics is currently computationally prohibitive. We propose a new algorithm (SSATAN-X) that can significantly speed up stochastic simulations on adaptive networks, while being accurate at the same time. Our algorithm achieves this speed-up by only considering the contact dynamics that are relevant to the spreading process. The benefit of algorithm is particularly pronounced when contacts are short-lived and per-exposure infection risks are small, which is applicable to most infectious diseases. We envision that SSATAN-X may allow simulation and analysis of pathogen spreading on more complex adaptive networks than previously possible. Moreover, data sets may be created with SSATAN-X that are useful for benchmarking novel numerical schemes and analytic approaches.