An Efficient Adaptive Time-stepping Method for the Modeling of Epidemic Dynamics

초록

"In this study, we present a novel and efficient adaptive time-stepping method for modeling epidemic dynamics. Examples of mathematical epidemic models include the susceptible-infected-recovered (SIR) model, the susceptible-exposed-infected-recovered (SEIR) model, the susceptible -infected-susceptible (SIS) model, the susceptible-infected-recovered-susceptible (SIRS) model, and the susceptible-infected-quarantined-recovered (SIQR) model. More complex models include the maternal immunity susceptible-infected-recovered (MSIR) model, the age-structured SEIR model, and stochastic epidemic models. These models are designed to capture specific disease characteristics, such as latency, immunity duration, and intervention impacts, and are essential tools for studying the dynamics of infectious diseases in diverse populations. The proposed adaptive time-stepping method is based on the total magnitude of the summation of compartment population differences after a single time step. Unlike other adaptive methodologies, the proposed algorithm does not require recalculations to satisfy a given tolerance and achieves the desired accuracy with a single update. Therefore, the adaptive time-stepping method is both straightforward and efficient. Several numerical tests are conducted to demonstrate the superior performance of the proposed method. © 2025 The Author(s).

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