A novel discrete-time approach to the continuous-time SIS dynamics

Despite extensive efforts to the continuous-time Markov process of the susceptible-infected-susceptible (SIS) model, there remains a dearth of efficient methods for numerically simulating the continuous-time spreading paths in complex networks using discrete-time simulations. In typical discrete-time approaches to the SIS model, time is discretized into small uniform intervals, and synchronous updating schemes are commonly employed to update the states of nodes. However, in this study, we demonstrate that the synchronous updating scheme introduces undesired noise, such as period-doubling and chaotic behaviors, into the spreading paths, diverging from the continuous-time SIS model. Additionally, we observe that the classical synchronous discrete-time scheme underestimates the spreading ability as compared to the corresponding continuous-time SIS model, a discrepancy that is dependent on the length of the time intervals. Leveraging the Taylor formalism, we propose a novel synchronous discrete-time updating method that addresses these issues associated with the classical synchronous discrete-time scheme. Importantly, our proposed method achieves high accuracy regardless of the length of the time intervals, which can be further exploited to enhance simulation speed. Experiments in both artificial and real networks show that our method approximates the continuous-time spreading paths better and costs less computing time than the classical discrete-time synchronous method.