Efficient and accurate simulation of infectious diseases on adaptive networks

Mathematical modelling of infectious disease spreading on temporal networks has recently gained popularity in complex systems science to understand the intricate interplay between social dynamics and epidemic processes. As analytic solutions can usually not be obtained, one has to resort to exact stochastic simulation algorithms, yet these have remained infeasible for the large sizes of realistic systems. Here, we introduce a rejection-based stochastic sampling algorithm with high acceptance probability (‘high-acceptance sampling’; HAS), tailored to simulate disease spreading on adaptive networks. We prove that HAS is exact and can be multiple orders faster than Gillespie’s algorithm. While its computational efficacy is dependent on model parameterization, we show that HAS is applicable regardless on whether contact dynamics are faster, on the same time-scale, or slower than the concurrent disease spreading dynamics. The algorithm is particularly suitable for processes where the spreading- and contact processes are co-dependent (adaptive networks), or when assumptions regarding time-scale separation become violated as the process unfolds. To highlight potential applications, we study the impact of diagnosis- and incidence-driven behavioural changes on virtual Mpox- and COVID-like epidemic and examine the impact of adaptive behaviour on the spreading processes.Author summary: Infectious disease spreading is often affected by the dynamics of human-human contacts. These contact dynamics may change over time, and in direct response to infection kinetics, through e.g. self-isolation, risk-aversion, or any adaptive behaviour, which can generate complex dynamics as seen in recent outbreaks with e.g. COVID-19, as well as Mpox clade IIb (2022). Agent-based models (ABMs) are often derived and numerically simulated to study the complex interplay between epidemic- and contact dynamics and to derive insights for disease control. However, numerical simulation of these models denotes a computational bottleneck and limits the applicability of large ABMs. We introduce a novel numerical method called ‘high-acceptance sampling’ (HAS), which allows for the exact simulation of outbreaks with adaptive contact behaviour. We prove that HAS is exact, show that it is faster, and that runtime grows with at least an order of magnitude less than state-of-the art exact simulation methods. This enables simulation of outbreaks on large populations, as well as parameter estimation for large systems. We apply HAS to study an Mpox- and COVID-like pandemic and the impact of adaptive behaviour on different time-evolving contact networks.