Peak-Weighted Calibration of Implemented Integer-Order, Caputo, and Atangana–Baleanu–Caputo Schemes for Simultaneous COVID-19 and Influenza Transmission
- 1School of Mathematics and Statistics, Guilin University of Technology, Guilin 541004, China
- 2Guangxi Colleges and Universities Key Laboratory of Applied Statistics, Guilin University of Technology, Guilin 541004, China
Abstract
COVID-19 and influenza may produce overlapping waves, yet an overall least-squares fit need not represent their high-activity weeks well. We compare implemented integer-order, Caputo, and Atangana–Baleanu–Caputo (ABC) discrete schemes for a common ten-compartment transition structure with seasonal transmission and external influenza input. The schemes are calibrated with ordinary mean-normalized weighted least squares (J1) and a peak-weighted objective (J2). We fit the first 66 of 83 weekly observation pairs and assess the remaining 17 weeks. ABC gives the smallest training peak root-mean-square error for both series under either objective. Within ABC, J2 reduces COVID-19 and influenza training peak errors by 9.50% and 42.98%, respectively, relative to its J1 fit. Integer order achieves the smallest ordinary loss and lower temporal validation error. The autonomous disease-free and conditional invasion thresholds characterize the underlying unforced vector field, not the fitted seasonal system. These findings support peak-weighted calibration for retrospective high-activity reconstruction in these data, but they do not establish superior future-peak prediction.
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BibTeX
@article{li2026peakweighted,
title = {{Peak-Weighted Calibration of Implemented Integer-Order, Caputo, and Atangana–Baleanu–Caputo Schemes for Simultaneous COVID-19 and Influenza Transmission}},
author = {Tingting Li and Shuangxia Lu and Youming Guo},
journal = {Fractal and Fractional},
year = {2026},
month = oct,
doi = {10.3390/fractalfract10110749},
url = {https://www.mdpi.com/2504-3110/10/11/749},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Peak-Weighted Calibration of Implemented Integer-Order, Caputo, and Atangana–Baleanu–Caputo Schemes for Simultaneous COVID-19 and Influenza Transmission
AU - Tingting Li
AU - Shuangxia Lu
AU - Youming Guo
PY - 2026
DA - 2026/10/27
JO - Fractal and Fractional
DO - 10.3390/fractalfract10110749
UR - https://www.mdpi.com/2504-3110/10/11/749
AB - COVID-19 and influenza may produce overlapping waves, yet an overall least-squares fit need not represent their high-activity weeks well. We compare implemented integer-order, Caputo, and Atangana–Baleanu–Caputo (ABC) discrete schemes for a common ten-compartment transition structure with seasonal transmission and external influenza input. The schemes are calibrated with ordinary mean-normalized weighted least squares (J1) and a peak-weighted objective (J2). We fit the first 66 of 83 weekly observation pairs and assess the remaining 17 weeks. ABC gives the smallest training peak root-mean-square error for both series under either objective. Within ABC, J2 reduces COVID-19 and influenza training peak errors by 9.50% and 42.98%, respectively, relative to its J1 fit. Integer order achieves the smallest ordinary loss and lower temporal validation error. The autonomous disease-free and conditional invasion thresholds characterize the underlying unforced vector field, not the fitted seasonal system. These findings support peak-weighted calibration for retrospective high-activity reconstruction in these data, but they do not establish superior future-peak prediction.
SN - 2504-3110
ER -