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Parameter Estimation for the SEIR Model via Gradient-Based Optimization with Biological Priors: A Multi-Country Study of COVID-19 First Waves | ||
| Caspian Journal of Mathematical Sciences | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 20 آبان 1405 | ||
| نوع مقاله: Research Articles | ||
| شناسه دیجیتال (DOI): 10.22080/cjms.2026.32048.1863 | ||
| نویسندگان | ||
| Hossein Kheiri* ؛ Yones Yousefpur Azar | ||
| Faculty of mathematics, Statistics, and computer science, University of Tabriz, Tabriz, Iran | ||
| تاریخ دریافت: 17 خرداد 1405، تاریخ بازنگری: 24 شهریور 1405، تاریخ پذیرش: 27 شهریور 1405 | ||
| چکیده | ||
| Estimating epidemiological parameters from incidence data alone is notoriously challenging due to the structural unidentifiability of compartmental models. We present a flexible framework that recovers the transmission rate $\beta$, incubation rate $\sigma$, recovery rate $\gamma$, and reporting delay from daily new case counts by combining a physics-informed loss function with soft biological constraints. The SEIR dynamics are embedded in a differentiable simulation, and all free parameters are learned simultaneously using gradient descent. We apply the method to the first COVID-19 wave in Ireland, Italy, Japan, and South Africa, demonstrating that the approach yields epidemiologically meaningful estimates ($\beta/\gamma$ in the range 2.9--4.1, incubation periods of 5--7 days, infectious periods of 7--14 days) while preserving excellent fit to the data. We show that the standard SEIR model, when paired with weak biological priors and a differentiable delay, is sufficient to resolve the identifiability issue across multiple countries. Our method converges in minutes, whereas a Bayesian Markov chain Monte Carlo baseline fails to converge in 30 hours, and a constrained least-squares alternative yields boundary-clamped estimates that are clinically unrealistic. These comparisons highlight the practical advantage of soft regularisation for rapid and interpretable model calibration. | ||
| کلیدواژه‌ها | ||
| SEIR model؛ Parameter identifiability؛ Gradient-based optimization؛ COVID-19؛ Soft biological priors | ||
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