2026· International Conference on Conceptual Structures· pp. 373-387· 0 citations· 22 references
Computer Science
TL;DR
The findings suggest that the combination of fractional-order memory with physics-informed learning constitutes an effective and interpretable model for dengue forecasting, providing a sound model for epidemic forecasting.
Accurate dengue forecasting is crucial for public health planning, but remains challenging because incidence series are often short, noisy, non-stationary, nonlinear, and often affected by long-range temporal dependence. Fractional differencing in Autoregressive Fractionally Integrated Moving Average (ARFIMA) helps balance non-stationarity and persistence, but its linear structure limits its ability to capture nonlinear dynamics. Deep neural networks can model nonlinear patterns, but usually require large training samples and do not explicitly encode statistical long memory. Echo State Networks (ESNs), a widely used reservoir computing framework, are attractive in this setting because they retain nonlinear recurrent dynamics while training only a simple readout, making them suitable for data-scarce scenarios. However, standard ESNs lack long-term memory from a time-series perspective. This study proposes a long-memory reservoir computing framework that integrates dedicated long-memory and short-memory ESN reservoirs with a ridge-regression readout. We introduce two variants: Fractional ESN (fESN), which incorporates fractional-differencing dynamics into the reservoir to encode long-range dependence directly, and Wavelet ESN (wESN), which extracts stable low-frequency components through wavelet smoothing before modeling them with a memory-aware reservoir. We establish theoretical guarantees for closed-loop reservoir dynamics, showing that standard ESNs induce short-memory processes under mild conditions, whereas the proposed long-memory reservoirs generate polynomially decaying dependence consistent with statistical long memory. Across multiple dengue datasets and forecasting horizons, fESN and wESN outperform statistical and deep learning baselines. Combining conformal prediction with fESN and wESN provides distribution-free calibrated uncertainty intervals.
R. Goswami, Shinjini Paul, P. Ghosh et al.· 0 citations
This study proposes a Fractional-Order Physics-Informed Neural Network (FPINN) framework for solving inverse parameter estimation problems in both fractional SIR and augmented SEIR epidemiological models and demonstrates that the proposed method accurately reconstructs epidemic trajectories and captures the influence of memory effects on disease evolution.
S. Naveen, V. Parthiban· Network Modeling Analysis in...· 0 citations
Outbreaks and epidemics of infectious diseases have continuously driven the iterative development of epidemiological models. However, in reality, epidemic data often contains missing values due to delayed updates and incomplete reporting, which weakens the model's ability to characterize the transmission process and increases the difficulty of prediction. Therefore, this study proposes a loss-constrained time-varying parameter estimation neural network (L-TPENN), which directly incorporates the structural information of missing data into the objective loss function, enabling the model to handle the uncertainty caused by missing data during training. This method combines the powerful solution capabilities of Physics-Informed Neural Network under differential equation constraints with the advantages of Gated Recurrent Unit in capturing dynamic data features and handling missing data. By introducing a masking mechanism at the GRU input layer, the model can utilize the data's inherent temporal structure to execute adaptive estimation without dependence on traditional missing value imputation steps, thereby fundamentally enhancing the robustness of the estimation process. Numerical simulations show that L-TPENN achieves superior fitting performance compared to Quantile Regression Bidirectional Gated Recurrent Unit, Hybrid Grey Genetic Algorithm-based Maximum Likelihood Method and Iterated imputation estimation. Empirical analysis section, experimental results based on real pandemic data from Minnesota, demonstrate that this method can accurately fit and forecast real-world data, In furtherance of this, to make effective estimates of the time-varying parameters within the model.
Xiang-Lei Li, Jun Wang, Yue-Cai Han· Journal of Data and Dynamic...· 0 citations
A high-resolution forecasting framework that integrates daily dengue case data with meteorological drivers to improve predictions in Bangladesh and provides an efficient, reproducible, and scalable approach that can strengthen dengue preparedness in public health systems with limited resources is developed.
Mahadee Al Mobin, Arju Manara Begum· PLOS Global Public Health· 0 citations
This study presents a novel discrete fractional-order mathematical framework for modeling and forecasting the coupled progression of diabetes and cardiovascular complications, with emphasis on population dynamics in Saudi Arabia. Using the discrete Caputo fractional operator, the model captures memory effects and long-term disease dependence not represented by classical integer-order systems. The population is divided into five interacting compartments: susceptible, exposed, diabetic without major complications, diabetic with severe complications, and cardiovascular-affected individuals. A rigorous qualitative analysis establishes equilibrium points and examines their local stability under fractional discrete dynamics. Stability regions are identified in parameter space, clarifying the mechanisms governing disease persistence and progression. A feedback-based control strategy is proposed to restore stability of the disease-free equilibrium when destabilization occurs. To enhance predictive performance, a Reservoir Computing framework is integrated and compared with Long Short-Term Memory networks, demonstrating improved accuracy and lower computational cost. Numerical simulations validate theoretical findings and highlight key epidemiological influences. Future work will extend the model by incorporating optimal control strategies aimed at minimizing infections through targeted interventions such as vaccination, improved hygiene, and environmental sanitation. The integration of fractional-order dynamics with control theory offers valuable insights for public health decision-making and epidemic mitigation.
A. Elsonbaty, A. Aldurayhim, Waleed Adel· Journal of Nonlinear Mathema...· 0 citations
Accurate forecasts of seasonal influenza are imperative to successfully manage public health resources. However, epidemiological time series data often show significant spiky volatility along with heavy-tailed distributions that do not satisfy the normality assumption required by traditional linear models. This paper proposes a new model called Robust Laplace-ARDL, which uses a Double Exponential (Laplace) distribution instead of the standard normal distribution to accommodate heavy-tailed distributions. Using 792 weekly observations (2005–2020) and benchmarking against a Long Short-term Memory (LSTM) model, the Laplace-ARDL
(
p
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5
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model reduces the mean square error (MSE) by
33.5
\%
compared to the LSTM model. This paper provides empirical evidence that it is vital to solve the leptokurtic distribution in infection data for obtaining stable forecasts.
Gokul Thanigaivasan, Ratha Jeyalakshmi T, Ramani Mani et al.· Model Assisted Statistics an...· 0 citations