Influenza-like illness (ILI) serves as a representative climate dependent disease due to its climate sensitivity, widespread transmission, and significant impact on public health and societal functioning, highlighting the urgent need for reliable ILI prediction techniques that combine climate factors to support effective prevention and intervention. Existing compartmental model-based methods have limited ability to incorporate climate data and often struggle to capture the complex ILI transmission patterns. Many deep learning models generally lack interpretability and tend to overlook the interactions between climatic factors and ILI transmission. This study aims to develop a physics-guided framework that leverages the dynamical knowledge embedded in compartmental models and the multi-source data learning and representation capabilities of deep learning. Our materials are the ILI case and climate data from Lanzhou, Gansu Province, China from 1st January 2023 to 26th October 2024 and Xi’an, Shaanxi Province, China from 1st January 2010 to 10th November 2016. Regarding the proposed model, first, we employ a physics-informed neural network (PINN) to learn the underlying dynamical knowledge under differential equation constraints and embed it into a long short-term memory network (LSTM) through a physics-guided representation alignment mechanism. Then, the transferred dynamical knowledge guides the LSTM to learn the mapping from climate and case data to ILI dynamics, enabling more accurate predictions jointly driven by domain knowledge and multi-source data. The results demonstrate that the proposed framework generally achieves better prediction accuracy and trend consistency than five advanced baselines. Specifically, compared with suboptimal baselines in Lanzhou, our model achieves reductions of at least 21.81

Dengue fever, a major mosquito-borne viral disease, poses a significant public health threat, particularly in high-incidence countries like Brazil, where rising cases strain limited medical resources. We analyze the impact of constrained medical resources, specifically hospital bed capacity, on dengue transmission dynamics. A novel compartmental model is developed where the availability of hospital beds (B) is a key parameter governing treatment access. Employing classical linearization theory, we conduct a comprehensive stability analysis of the system equilibrium points. Systematic bifurcation analysis, utilizing center manifold theory and normal form theory, reveals complex dynamical behaviors: backward bifurcation (indicating disease persistence for basic reproduction numbers R0<1), Saddle-node bifurcation, Hopf bifurcation (giving rise to periodic solutions), and a codimension-2 Bogdanov-Takens bifurcation. Model validation is performed using incidence data from the São Paulo, Brazil dengue outbreak, enabling parameter estimation and calculation of R0. Sensitivity analysis identifies key parameters for disease control. Crucially, hospital bed capacity B exhibits a threshold regulatory effect: below a critical value, backward bifurcation occurs, sustaining endemicity even when R0<1; above the critical value, increasing beds initially reduces infection prevalence, but can subsequently induce periodic oscillations via Hopf bifurcation before further reducing disease burden. This demonstrates that medical resource constraints fundamentally alter epidemic outcomes through nonlinear dynamical mechanisms.

Based on the considerations of round-trip in the treatment process, this paper presents a mathematical model aimed at studying the dynamic behaviour and epidemiological trends of HIV/AIDS. We first calculate the basic reproduction number R̅0 and discuss the stability of equilibrium points and the existence of forward bifurcations, validating the theoretical results through numerical simulations. Subsequently, using cumulative HIV/AIDS case data reported in China, we estimate model parameters using the least squares method, achieving a good fit. Furthermore, sensitivity analyses were performed on the model parameters to explain the dependence of the parameters on the infection variables. Finally, the model is applied to evaluate the control effects of treatment coverage at different stages of infection. The results suggest that reducing HIV/AIDS exposure, improving HIV/AIDS screening, promoting infectious disease treatment and increasing disease prevention awareness are the most effective measures to prevent HIV/AIDS infection.

Fusarium crown rot (FCR) has been a serious threat to cereal production in many areas worldwide. Common wheat and barley suffer similar levels of yield loss from this disease, with Fusarium pseudograminearum as the predominant pathogen causing FCR in both crop species. Compared to wheat, barley shows more severe symptoms of stem-base browning and accumulates more fungal biomass under FCR infection. However, unlike wheat, whiteheads are not a common occurrence in FCR-infected barley crops, raising the question of which physiological traits drive yield loss in barley under FCR infection. To address this, 16 barley genotypes were assessed across five field sites over two cropping seasons in Australia. Data on grain yield and yield components, including thousand kernel weight (TKW), kernel number per spike (KNPS), and fertile tiller number (FTN) from both non-inoculated and inoculated treatments were collected and analysed. Significant grain yield loss in the presence of FCR was detected in each of these field trials. Invariably, yield loss caused by FCR infection was attributable to a reduction in the number of fertile tillers, with no significant difference in TKW and KNPS detected in any of the trials. These findings offer new targets for minimising FCR damage through breeding and crop management efforts.

The ubiquity of spatio-temporal data in the real world presents significant challenges for predictive modeling due to the complex interplay between temporal trends and spatial correlations. This paper introduces the DGI-GRU model, a novel approach that enhances the Gated Recurrent Unit (GRU) architecture by integrating graph convolution with a dynamic adjacency matrix. The salient feature of the model is that it extracts dynamic graph information that leverages both the distance between nodes and time-varying observational data, effectively capturing evolving spatial relationships. Additionally, our improved GRU framework facilitates the simultaneous extraction of temporal and spatial features within a single layer, reducing parameter redundancy. Experimental results on real datasets demonstrate the superior performance of our model in spatio-temporal sequence prediction tasks, outperforming state-of-the-art baselines.

Monkeypox (Mpox) is an emerging infectious disease caused by the Mpox virus (MPX Virus). The outbreak of Mpox epidemic has caused global panic and is now a public health incident. Various approaches have been proposed in the recent literature to study and analyze the epidemiological dynamics of this infection and effective prevention and control measures. Using mathematical model to understand the transmission dynamics and control strategy is a useful way to understand the prevention of Mpox. A new compartment model is established to examine the effectiveness of vaccine on Mpox based on previous studies. Nonlinear least squares fitting is used for model’s parameter estimation. The impact of a series of preventive and control measures on the epidemic control is explored with optimal control theory in conjunction with the official data released by the authorities. Firstly, a stability analysis of the developed model was carried out to show that, under certain circumstances, its equilibrium is both locally and globally stable. Secondly, based on the reported cases of Mpox infection in the United States between 2022 and 2023, the model's optimal parameter values were obtained. A sensitivity analysis of the model parameters was then conducted to identify the key parameters that affect the development of Mpox epidemics in the United States. Lastly, the comparison of control effects under various control strategies showed that implementing the all suggested four control measures at the same time was the most effective way to curb the development of monkeypox epidemic in the United States. This study has theoretical significance for understanding and controlling Mpox virus transmission.

In this paper, we develop an SVIRB cholera transmission dynamic model incorporating both vaccination and media publicity effects. The fundamental properties of the model are investigated, including the non-negativity and boundedness of the solutions, the existence and stability of equilibrium points, and the conditions for the occurrence of forward bifurcation. Subsequently, based on the system and the actual cumulative case data in Somalia, parameter estimation is conducted using the Least Squares Method, and its rationality for the fitting results is assessed. Meanwhile, the calculated basic reproduction number R̅_0=1.9087>1 indicates that cholera has become epidemic in the Somalia region. Furthermore, we also perfrom a sensitivity analysis for the R̅_0 on the system is conducted. Finally, the effects of vaccination rate, vaccine waning rate, and media coverage intensity on the dynamics of cholera infection are studied, respectively. At the same time, based on the analysis results, we built an optimal control problem of cholera transmission dynamics considering vaccination, treatment, and sanitation strategies; the existence of an optimal control pair is proved; and the forward-backward sweep method to evaluate the effectiveness of seven different control strategies in terms of epidemic control and associated costs is employed to find the optimal control strategy. Our results indicate that by continuously monitoring environmental pathogens, establishing immune barriers for susceptible populations, enhancing public awareness of disease prevention, and optimizing medical resources, a multi-level and comprehensive prevention and control strategy for cholera outbreaks can be realized.

With the ongoing global outbreaks of mosquito-borne diseases such as dengue fever, a thorough understanding of how environmental factors influence disease transmission dynamics is crucial for epidemic prediction and control. This study developed a dynamic periodic transmission model incorporating temperature-dependent characteristics of mosquito life history, based on the critical role of climatic factors in mosquito-borne disease transmission, to systematically elucidate the regulatory effects of seasonal temperature variations on dengue transmission dynamics. Model validation demonstrated a high degree of consistency between the simulated results and the actual 2022 dengue outbreak in Singapore. The research results show that: the basic reproduction number [Formula: see text] exhibits high sensitivity to temperature changes; under both constant and seasonally varying temperature conditions, three critical epidemiological characteristics of dengue transmission (final epidemic size, peak number of infections, and epidemic duration) are significantly modulated by temperature. Optimal control analysis further revealed that the timing and strategic selection of intervention measures have decisive impacts on epidemic control effectiveness. This study not only provides important theoretical support for the scientific prevention and control of dengue fever, but also significantly advances our understanding of dengue virus transmission mechanisms.

Spatiotemporal patterns are crucial for understanding population distribution dynamics, providing significant theoretical guidance for the conservation of both plants and animals. Delays and the Allee effect often lead to complex dynamical phenomena in temporal population models. Therefore, this paper incorporates the delay and Allee effects into the reaction-diffusion predator-prey model and explore the impact of such ecological effects on spatial-temporal dynamics. In theory, we obtain the critical value of Turing bifurcation and the condition of formation of the pattern, derive the amplitude equation, and calculate the delay-induced Hopf bifurcation and its properties. In numerical simulations, we found that the Allee effect and delays can alter the spatial distribution of populations. Specifically, as the Allee effect threshold increases, patterns evolve from spot patterns to mixed patterns, ultimately forming stripe patterns, while delays can induce the formation of spiral patterns, whose emergence depends on initial conditions. These findings contribute to our understanding of complex, non-equilibrium self-organization phenomena among populations.

The accurate streamflow forecast is of utmost importance in the efficient administration of water resources. In this research, we introduced the DA-BiGRU-RED model, an approach that incorporated the dual attention (DA) mechanism involving both feature and temporal attention into the Bidirectional Gated Recurrent Unit (BiGRU) with a recursive encoder-decoder (RED) structure. The feature attention was derived by allocating weights to the hidden states of the BiGRU in the encoder, enhancing the model's capability to efficiently capture crucial features of the input variables. Concurrently, the temporal attention mechanism was established by jointly weighting the hidden states of the BiGRU in the encoder and decoder, enabling the extraction of temporal message from the input variables. This dual-attention mechanism empowered our model to effectively extract essential information from various kinds and temporal instances of input data, thereby improving the accuracy of multi-step streamflow forecasting. Furthermore, to assess forecasting uncertainty, we employed MC dropout based on Bayesian statistical theory. To gauge the effectiveness of our proposed model, we applied it for 1-day, 3-day, 5day, and 7-day ahead forecasting in the Heihe River basin in Northwest China. Our model consistently outperformed both the BiGRU-ED and BiGRU models, as evidenced by Nash-Sutcliffe coefficient (NSE) values exceeding 0.69 in nearly all prediction scenarios. Additionally, the uncertainty assessment revealed that the DABiGRU-RED model exhibited the highest PUCI values, underscoring its efficacy in extracting key features and temporal information from input variables and providing more accurate and robust forecasting results.

Analytical solutions are practical tools in ocean engineering, but their derivation is often constrained by the complexities of the real world. This underscores the necessity for alternative approaches. In this study, the potential of Physics-Informed Neural Networks (PINN) for solving the one-dimensional vertical suspended sediment mixing (settling-diffusion) equation which involves simplified and arbitrary vertical Ds profiles is explored. A new approach of temporal Normalized Physics-Informed Neural Networks (T-NPINN), which normalizes the time component is proposed, and it achieves a remarkable accuracy (Mean Square Error of 10−5 and Relative Error Loss of 10−4). T-NPINN also proves its ability to handle the challenges posed by long-duration spatiotemporal models, which is a formidable task for conventional PINN methods. In addition, the T-NPINN is free of the limitations of numerical methods, e.g., the susceptibility to inaccuracies stemming from the discretization and approximations intrinsic to their algorithms, particularly evident within intricate and dynamic oceanic environments. The demonstrated accuracy and versatility of T-NPINN make it a compelling complement to numerical techniques, effectively bridging the gap between analytical and numerical approaches and enriching the toolkit available for oceanic research and engineering.

Runoff prediction serves as the cornerstone for the effective management, allocation, and utilization of water resources, playing a key role in hydrological research. This study employs a newly reported deep learning model, Mamba, to forecast river daily runoff and compared the proposed model with various benchmark methods, including statistical models, machine learning methods, recurrent neural networks, and attention-based models. Application of these models is implemented on three hydrological stations situated along the middle and lower reaches of the Mississippi River. Daily runoff from 1983 to 2023 were used to build the model for 7-day prediction. Findings demonstrate the superiority of the Mamba model over its counterparts, showcasing its potential as a backbone model. In response to the necessity for a more lightweight approach, a refined variant of the Mamba model is proposed, called LightMamba. LightMamba incorporates partial normalization and MPM (Multi-Path-Mamba) to enhance its efficacy in discerning nonlinear trends and capturing long-term dependencies within the streamflow data. Notably, LightMamba achieves commendable performance with an average NSE of 0.904, 0.907, and 0.900 on the three stations. This study introduces an innovative backbone model for time series forecasting, which offers a novel approach to hybrid modeling for future daily runoff prediction.

China aims to carbon peak emissions before 2030 and achieve carbon neutrality by 2060 in response to climate change challenges. Studying the feasibility of this goal, identifying potential gaps, and formulating corresponding emission reduction pathways are urgent issues that need to be addressed. This study creatively integrates Logarithmic Mean Divisia Index into Long-range Energy Alternatives Planning System to assess energy consumption and carbon emissions in Gansu Province from 2001 to 2060, historical and scenario analysis was conducted from a novel perspective. Results indicate that the economic development effect is the most significant driving factor for the emission growth of 131.54 million tons from 2001 to 2020, and its contribution rate is 176.31 %. The leading negative driving factor is the energy intensity effect, contributing at a rate of -62.00 %. Additionally, the energy structure and industrial structure effects also play minor negative roles. Scenario analysis suggests achieving a carbon peak by 2030 requires a 29.53 % reduction in energy intensity from the 2020 baseline, with electricity consumption must reach 46.37 % and clean energy generating 64 %. Carbon peak emissions are projected to be 220.37 million tons, with reduction of carbon emissions by 123.84 million tons by 2060.

Reliable and accurate streamflow forecasting is critical in the domain of water resources management. However, the inherently non-stationary and stochastic nature of streamflow poses a formidable challenge to achieving accuracy in streamflow forecasting. In this study, we introduce an MVMD-ensembled Transformer model (MVMD-Transformer). This model employs the MVMD technique, which allows for simultaneous time–frequency analysis of streamflow and other potential influencing factors. The model aligns common modes in the decomposition results, ensuring that the different variables corresponding to each mode have the same center frequency. This alignment overcomes frequency mismatches and helps uncover the intrinsic patterns and essential features between streamflow and associated variables. During the forecasting phase, the Transformer component of the MVMD-Transformer model establishes connections among streamflow and other influencing factors across pairs of nodes in each mode. We tested the effectiveness of the MVMD-Transformer model on streamflow forecasting in the Shiyang River, Heihe River, and Shule River basins situated in the Hexi Corridor of Northwest China, with 1-, 3-, 5-, and 7-day forecasting horizons. The MVMD-Transformer model harnesses MVMD for the simultaneous decomposition of forecast variables (precipitation, air temperature, air pressure, soil moisture) and the response variable (streamflow). Subsequently, the resulting modes from the MVMD were fed into the Transformer, serving as the forecast analytics engine, for streamflow forecasting. Furthermore, we conducted a comprehensive performance evaluation by comparing the MVMD-Transformer model against four alternatives: the VMD-ensembled Transformer model (VMD-Transformer), CEEMDAN-ensembled Transformer model (CEEMDAN-Transformer), stand-alone Transformer model, and LSTM model. The results indicate that MVMD-Transformer outperformed all other models, achieving Nash-Sutcliffe coefficient (NSE) values exceeding 0.85 in the majority of the forecasting scenarios. This superior performance highlights the proficiency of the MVMD approach in more accurately unraveling the intricate interdependencies between streamflow and its various potential influencing factors, thus significantly improving the precision of streamflow forecasting.

Lake temperature forecasting is crucial for understanding and mitigating climate change impacts on aquatic ecosystems. The meteorological time series data and their relationship have a high degree of complexity and uncertainty, making it difficult to predict lake temperatures. In this study, we propose a novel approach, Probabilistic Quantile Multiple Fourier Feature Network (QMFFNet), for accurate lake temperature prediction in Qinghai Lake. Utilizing only time series data, our model offers practical and efficient forecasting without the need for additional variables. Our approach integrates quantile loss instead of L2-Norm, enabling probabilistic temperature forecasts as probability distributions. This unique feature quantifies uncertainty, aiding decision-making and risk assessment. Extensive experiments demonstrate the method’s superiority over conventional models, enhancing predictive accuracy and providing reliable uncertainty estimates. This makes our approach a powerful tool for climate research and ecological management in lake temperature forecasting. Innovations in probabilistic forecasting and uncertainty estimation contribute to better climate impact understanding and adaptation in Qinghai Lake and global aquatic systems.

Accurate streamflow prediction is crucial for effective water resource management. However, reliable prediction remains a considerable challenge because of the highly complex, non-stationary, and non-linear processes that contribute to streamflow at various spatial and temporal scales. In this study, we utilized a convolutional neural network (CNN)-Transformer-Long short-term memory (LSTM) (CTL) model for streamflow prediction, which replaced the embedding layer with a CNN layer to extract partial hidden features, and added a LSTM layer to extract correlations on a temporal scale. The CTL model incorporated Transformer's ability to extract global information, CNN's ability to extract hidden features, and LSTM's ability to capture temporal correlations. To validate its effectiveness, we applied it for streamflow prediction in the Shule River basin in northwest China across 1-, 3-, and 6-month horizons and compared its performance with Transformer, CNN, LSTM, CNN-Transformer, and Transformer-LSTM. The results demonstrated that CTL outperformed all other models in terms of predictive accuracy with Nash-Sutcliffe coefficient (NSE) values of 0.964, 0.912, and 0.856 for 1-, 3-, 6-month ahead prediction. The best results among the five comparative models were 0.908, 0.824, and 0.778, respectively. This indicated that CTL is an outstanding alternative technique for streamflow prediction where surface data are limited.

Deep learning methods have gained considerable interest in the numerical solution of various partial differential equations (PDEs). One particular focus is physics-informed neural networks (PINN), which integrate physical principles into neural networks. This transforms the process of solving PDEs into optimization problems for neural networks. To address a collection of advection-diffusion equations (ADE) in a range of difficult circumstances, this paper proposes a novel network structure. This architecture integrates the solver, a multi-scale deep neural networks (MscaleDNN) utilized in the PINN method, with a hard constraint technique known as HCPINN. This method introduces a revised formulation of the desired solution for ADE by utilizing a loss function that incorporates the residuals of the governing equation and penalizes any deviations from the specified boundary and initial constraints. By surpassing the boundary constraints automatically, this method improves the accuracy and efficiency of the PINN technique. To address the ``spectral bias'' phenomenon in neural networks, a subnetwork structure of MscaleDNN and a Fourier-induced activation function are incorporated into the HCPINN, resulting in a hybrid approach called SFHCPINN. The effectiveness of SFHCPINN is demonstrated through various numerical experiments involving ADE in different dimensions. The numerical results indicate that SFHCPINN outperforms both standard PINN and its subnetwork version with Fourier feature embedding. It achieves remarkable accuracy and efficiency while effectively handling complex boundary conditions and high-frequency scenarios in ADE.

The COVID-19 pandemic led to significant disruptions in schooling worldwide. This study aims to evaluate and compare the impact of the pandemic on student mathematics achievement across eight representative countries/regions, using data from the Programme for International Student Assessment (PISA) 2022. The multilevel random forest (RF) method was employed to account for the effects of national, school, family, and individual contexts, as well as the hierarchical structure of the PISA data. The results show that the multilevel RF model outperformed the traditional multilevel model in terms of predictive accuracy. School closures were found to have the most significant negative impact, while school support and self-directed learning had positive effects. Additionally, the impact of COVID-19 on student mathematics achievement varied substantially across different countries/regions and subgroups. The findings are discussed regarding the resilience of education system, educational inequities, and their implications for policy and methodology.

The interest in predicting online learning performance using ML algorithms has been steadily increasing. We first conducted a scientometric analysis to provide a systematic review of research in this area. The findings show that most existing studies apply the ML methods without considering learning behavior patterns, which may compromise the prediction accuracy and precision of the ML methods. This study proposes an integration framework that blends learning behavior analysis with ML algorithms to enhance the prediction accuracy of students' online learning performance. Specifically, the framework identifies distinct learning patterns among students by employing clustering analysis and implements various ML algorithms to predict performance within each pattern. For demonstration, the integration framework is applied to a real dataset from edX and distinguishes two learning patterns, as in, low autonomy students and motivated students. The results show that the framework yields nearly perfect prediction performance for autonomous students and satisfactory performance for motivated students. Additionally, this study compares the prediction performance of the integration framework to that of directly applying ML methods without learning behavior analysis using comprehensive evaluation metrics. The results consistently demonstrate the superiority of the integration framework over the direct approach, particularly when integrated with the best-performing XGBoosting method. Moreover, the framework significantly improves prediction accuracy for the motivated students and for the worst-performing random forest method. This study also evaluates the importance of various learning behaviors within each pattern using LightGBM with SHAP values. The implications of the integration framework and the results for online education practice and future research are discussed.