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

Abstract

In this study, we present a novel adaptive time-stepping method for efficient simulation of the epidemic models. Some examples of mathematical epidemic models are the susceptible–infected–removed (SIR) model, the susceptible–exposed–infected–removed (SEIR) model, the susceptible–infected–susceptible (SIS) model, the susceptible–infected–removed–susceptible (SIRS) model, and the susceptible–infected–quarantined–recovered (SIQR) model. Additionally, more complex models include the maternal immunity susceptible–infected–removed (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, or 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 each compartment population differences after a single time step. Unlike other adaptive methodologies, the proposed algorithm requires no recalculation 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.