Contagious disease outbreaks: Distinguishing between constant and variable order using the SEIAR model

Abstract

The purpose of this study is to present a comprehensive framework for analyzing contagious diseases. The primary objective is to determine whether the outbreak dynamics of a contagious disease follow a constant or variable non-integer order. The methodology involves a three-phase process: selecting an appropriate model, estimating its parameters, and identifying the order of derivation. To address this, the SEIAR non-integer order dynamic model is employed, enhancing the precision of disease spread estimation. A heuristic approach is proposed for parameter estimation using a Genetic Optimization Algorithm, which evaluates all possible scenarios for the order and suggests parameter sets that perform well across these scenarios. Subsequently, an adaptive identification method is introduced to estimate the variable order of the model while keeping the parameters constant. The approach is validated on the Delta and Omicron variants of the Coronavirus epidemic in Iran. The variable-order model achieves a Mean Absolute Percentage Error (MAPE) of 0.80 % for the Delta variant and 0.51 % for the Omicron variant, significantly outperforming the best constant-order models with MAPEs of 0.92 % and 1.32 %, respectively. These results demonstrate the model's superior accuracy in predicting the epidemic's progression. These findings significantly contribute to the understanding and management of contagious diseases. Evidence is provided that the pandemic in Iran follows a variable non-integer order dynamic model, supporting the hypothesis that disease outbreaks exhibit variable non-integer order behavior due to their inherent complexity. The proposed framework can be generalized to other diseases and regions, offering a robust tool for epidemic analysis and decision-making. © 2025