Parameter Estimation in Epidemiological Models Using the Sum of Absolute Deviations Method

Title: Parameter Estimation in Epidemiological Models Using the Sum of Absolute Deviations Method Yisa Abolade, Yichuan Zhao, Gerado Chowel Abstract: Reliable parameter estimation is vital for accurate predictions in infectious disease modeling, especially during public health emergencies. The Least Squares (LSQ) method is traditionally favored for its computational efficiency and closed-form solutions, assuming normally distributed errors. However, LSQ is highly sensitive to outliers, which can lead to biased parameter estimates when dealing with noisy data which is a common scenario in real-world epidemiological studies. To address this issue, we introduce the Sum of Absolute Deviations (SAD) as a robust estimation technique that minimizes the absolute differences between observed and predicted values. Unlike LSQ, SAD is less affected by outliers because it imposes a linear penalty on residuals, making it better suited for handling heavy-tailed error distributions epidemiological datasets. This study evaluates the performance of SAD using both simulated and real-world infectious disease data, demonstrating its advantages over LSQ in scenarios with outliers or non-normally distributed errors. By adapting concepts from signal processing, where SAD has proven effective in recovering signals from corrupted data, we apply these techniques to epidemiological modeling. Our findings indicate that SAD not only enhances the robustness of parameter estimation but also improves the accuracy of epidemic forecasts, offering a promising alternative to conventional LSQ methods. These results have significant implications for real-time epidemic tracking, where robust estimation methods are crucial for guiding timely public health interventions. This research contributes to the expanding literature on robust parameter estimation methods and provides a framework for applying SAD to epidemiological models. We believe that SAD, given its successful application in other fields like signal processing, holds considerable potential for improving the reliability of forecasts in infectious disease modeling, ultimately supporting more effective public health strategies. KEYWORDS Parameter estimation, real-time forecasting and performance, SAD, LSQ.