Introduction: This study investigates the mutual influence between online medical search and online medical consultation. It focuses on understanding the health information needs that drive these health information-seeking behaviors by utilizing insights from behavioral big data.Methods: We used actual behavioral data from Chinese internet users on Baidu platform’s “Epidemic Index” from November 26, 2022, to January 25, 2023. Data modeling was conducted to ensure the reliability of the model. Drawing on the logistic model, we constructed a foundational model to quantify the evolutionary patterns of online medical search and online medical consultation. An impact function was defined to measure their mutual influence. Additionally, a pattern detection experiment was conducted to determine the structure of the impact function with maximum commonality through data fitting.Results: The analysis allowed us to build a mathematical model that quantifies the nonlinear correlation between online medical search and online medical consultation. Numerical analysis revealed a predation mechanism between online medical consultation and online medical search, highlighting the role of health information needs in this dynamic.Discussion: This study offers a novel practical approach to better meet the public’s health information needs by understanding the interplay between online medical search and consultation. Additionally, the modeling method used here is broadly applicable, providing a framework for quantifying nonlinear correlations among different behaviors when appropriate data is available.

In the context of the COVID-19 pandemic, a large amount of information is gathered on Internet platforms, through which people express their opinions and vent their emotions. Emotional guidance of netizens has become an important part of social governance during turbulences caused by a so-called “infodemic”. This study focuses on the evolution and interaction of netizens' emotions after the occurrence of network public opinion events. First, the transfer model of netizens' emotions is constructed, and the significance of each parameter in the model is studied through simulation. Then, based on the model, we put forward the optimization method and quantitative method of guidance strategy of netizens' emotions. Finally, the empirical study proves the effectiveness of the model, which can provide a theoretical basis for the emotional guidance strategies after the outbreak of network public opinion events.

In the context of social system resilience, the role of information negentropy—a measure of order and structural stability—remains underexplored during emergencies. This study investigates the evolutionary mechanisms of information negentropy under crisis conditions, aiming to quantify how emergencies disrupt and reshape social order through dual internal and external feedback. By integrating dissipative structure theory with a dynamic differential equation model, we propose a novel framework that captures the interplay between entropy increase and negentropy production. The model incorporates internal system dynamics (parameterized by \(\:\alpha\:\)) and external behavioral influences (parameterized by \(\:\beta\:\)), simulating how crises trigger transitions in social systems via “double-S” or “multi-S” evolutionary trajectories. Empirical validation using Baidu Index data from five brand-related public opinion crises demonstrates the model’s predictive accuracy, revealing that high-quality information dissemination and coordinated public behavior significantly amplify negentropy accumulation. Key findings indicate that emergencies elevate the upper limit of information negentropy by a factor of \(\:{H}_{\infty\:}\), enabling systemic upgrades rather than mere disorder suppression. This study advances crisis management strategies by emphasizing proactive negentropy activation, offering actionable insights for enhancing social adaptability through real-time monitoring and parameter optimization. This work bridges theoretical gaps in entropy-driven social dynamics and provides a computational toolset for fostering resilience in complex information ecosystems.

This study examines the bidirectional tension between public and scientific attention amid informatization, analyzing their mutualistic symbiosis to address science communication challenges. We constructed a mathematical model of mutualistic symbiosis in their relationship was developed based on the Logistic Model. Subsequently, numerical simulations were employed to investigate the evolutionary trends and patterns of scientific attention, public attention, and the effectiveness of science communication under varying modes of public attention and initial values of scientific attention. Furthermore, using “COVID-19” as a case study, an empirical analysis was conducted on to assess the correlation between public attention and scientific attention and evaluate the constructed mathematical Model, verifying its scientific validity and effectiveness. This study underscores the critical role of science communication in fostering advantageous interactions between scientific and public attention. Nonetheless, it is imperative to adopt tailored science communication strategies that accommodate diverse public attention modes and initial levels of scientific attention while selecting appropriate symbiotic models for specific contexts. This proposed approach ensures the effective dissemination of scientific information and fosters a robust science communication ecosystem.

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.

This study primarily addresses the analytical problem of the mathematical mechanism underlying the associative impact between online searches and vaccine uptake, a relationship that has become increasingly relevant in the context of public health management. As internet search behaviors reflect public interest and sentiment, understanding their impact on vaccination trends is crucial for real-time health decision-making. A Logistic model is constructed to observe the fundamental evolutionary patterns between online searches and vaccine uptake. To explore their mutual influence, an impact function is defined, and the common structural factors with the highest fitness are determined through data fitting. Subsequently, a dynamic detection model of the associative impact between online data and societal objects, based on the mathematical mechanism, is established. Using this model, dynamic predictions are conducted to verify its predictive capability at certain stages. Through research, a symbiotic effect between online searches and vaccine uptake is identified, revealing a nonlinear correlation between the two. The model demonstrates the ability to predict vaccine uptake trends based on online search data, with certain prediction windows showing high accuracy. This research not only clarifies the mathematical mechanism underlying this relationship but also demonstrates the advantage of integrated analysis and prediction. It provides a new method for predicting online searches and vaccine uptake, offering theoretical and empirical support for public health and social science research.