Modeling the spread of hand, foot, and mouth disease using ABC fractional derivatives: a focus on environmental and vaccination impacts in children - Lamwong, Jiraporn; Pongsumpun, Puntani (My University, 2025)
This research focuses on modeling the spread of Hand, Foot, and Mouth Disease (HFMD) among children below the age of 15 using the Atangana-Baleanu Caputo (ABC) fractional derivative. The model incorporates both environmental contamination and vaccination effects to better capture the transmission dynamics of HFMD. The fractional derivative accounts for memory effects, which are crucial in understanding the prolonged impact of past infection rates on the current epidemic dynamics. Real outbreak data from Thailand (May 2023 to October 2023) was used to fit the model parameters through optimization using the fminunc algorithm in MATLAB. The results showed that the model successfully captured key phases of the epidemic, including the initial rise, peak, and decline in cases, as well as a secondary wave of infections. Notably, incorporating memory effects through the ABC fractional derivative enhanced the accuracy of predictions regarding the epidemic’s duration and severity. Furthermore, our analysis of the basic reproduction number (R0) and global stability confirmed vaccination's effectiveness in controlling the disease's spread. These findings suggest that the model can serve as a valuable tool for informing public health interventions, particularly in environments with high child population densities such as schools and daycare centers. Future research may explore the application of this model to other infectious diseases and investigate additional factors such as varying immunity levels and seasonal variations.
Keywords: Existence of steady state; Global stability analysis; Hand foot mouth disease; Model fitting; The ABC fractional derivative