Fractional derivative model in COVID-19 dynamics: application to symptom severity and hospital resource allocation in South Korea - Herdicho, Faishal Farrel; Jose, Sayooj Aby; Jirawattanapanit, Anuwat; Park, Taesung (Journal of applied mathematics & computing, 2025)
COVID-19, caused by SARS-CoV-2, has profoundly affected societies worldwide. The high number of cases, along with its widespread effects on health systems, economies, and daily life, has made COVID-19 a critical subject of study. In addition, the limited capacity of healthcare systems and the surge in COVID-19 cases have placed significant pressure on healthcare management. Focusing on the wide range of symptoms with varying severity, this study categorizes symptoms as mild or severe and develops a mathematical model to describe the spread of COVID-19 while accounting for symptom severity. The model incorporates both integer and fractional derivatives, using the Caputo operator, provides a more accurate representation of disease dynamics by capturing long-term dependencies in time-series data. Key properties of the model are analyzed, including solution boundedness, positivity, and the stability of equilibrium points. The model is applied to South Korea’s COVID-19 data from June 1 to September 30, 2022, as training data, and from October 1 to 15, 2022, as testing data. The results show superior accuracy of the fractional model over the integer model, as measured by the Mean Absolute Percentage Error (MAPE). A key finding of this study is that prioritizing treatment for mild cases enhances hospital efficiency due to higher recovery rates, offering an effective strategy for managing patient flow under hospital constraints. This modified model, incorporating a saturated form of hospitalization rates, optimizes COVID-19 patient management by aligning treatment strategies with symptom severity, aiming to improve recovery outcomes while balancing the demands on healthcare systems.