Non-linear correlation analysis between internet searches and epidemic trends.

Introduction: This study uses a non-linear model to explore the impact mechanism of change rates between internet search behavior and confirmed COVID-19 cases. The research background focuses on epidemic monitoring, leveraging internet search data as a real-time tool to capture public interest and predict epidemic development. The goal is to establish a widely applicable mathematical framework through the analysis of long-term disease data.

Methods: Data were sourced from the Baidu Index for COVID-19-related search behavior and confirmed COVID-19 case data from the National Health Commission of China. A logistic-based non-linear differential equation model was employed to analyze the mutual influence mechanism between confirmed case numbers and the rate of change in search behavior. Structural and operator relationships between variables were determined through segmented data fitting and regression analysis.

Results: The results indicated a significant non-linear correlation between search behavior and confirmed COVID-19 cases. The non-linear differential equation model constructed in this study successfully passed both structural and correlation tests, with dynamic data fitting showing a high degree of consistency. The study further quantified the mutual influence between search behavior and confirmed cases, revealing a strong feedback loop between the two: changes in search behavior significantly drove the growth of confirmed cases, while the increase in confirmed cases also stimulated the public's search behavior. This finding suggests that search behavior not only reflects the development trend of the epidemic but can also serve as an effective indicator for predicting the evolution of the pandemic.

Discussion: This study enriches the understanding of epidemic transmission mechanisms by quantifying the dynamic interaction between public search behavior and epidemic spread. Compared to simple prediction models, this study focuses more on stable common mechanisms and structural analysis, laying a foundation for future research on public health events.