Mechanistic compartmental models such as SIR provide interpretability and enforce conservation of population, but their predictive performance can degrade in heterogeneous settings where transmission varies over time and across regions. Conversely, spatiotemporal graph neural networks (GNNs) can learn flexible spatial interactions from data, yet unconstrained predictors may yield epidemiologically inconsistent dynamics. We propose MechGNN-Epi, a hybrid framework that couples a spatiotemporal graph encoder with a differentiable SIR update. Rather than directly predicting future infections, the model learns region- and time-specific transmission and recovery parameters from graph-based latent representations and then propagates compartments through a mechanistic solver. This design yields epidemiologically constrained trajectories and produces region- and time-indexed parameter proxies that can be inspected as diagnostic signals, while not being guaranteed as causally identifiable mechanistic parameters. We evaluate the pipeline on U.S. state/territory COVID-19 surveillance data using strict chronological splits and report variability across multiple random seeds, multi-horizon rollouts, and ablation/sensitivity studies against graph and model variants.
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 = 5 ) 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.
Count data observed in numerous real-world applications, particularly in fields such as epidemiology, highway safety and insurance often exhibit overdispersion, excess number of zeros and spatio-temporal heterogeneity. To address these issues, in this article, zero-inflated generalized Poisson(ZIGP) mixed model is utilized, which simultaneously accounts for overdispersion and excess zeros while incorporating random effects to capture spatio-temporal heterogeneity. The ZIGP mixed model consists of binary component that models the probability of structural zeros and generalized Poisson component that models count observations including sampling zeros. Random effects are introduced to incorporate spatial effects and temporal dependence. The count predictions are derived from the estimated parameters of ZIGP mixed model obtained using the ML-Laplace approximation algorithm. The method for estimating percentile bootstrap confidence intervals for the parameters is outlined. The data set under study consists of malaria cases recorded across different regions for several months over the years. It is characterized by a high proportion of zero counts and influence of spatio-temporal effects which emphasizes the need for suitable statistical framework. The ZIGP mixed model is applied to malaria case data to predict counts along with its root squared prediction error.
The assumption of normality is fundamental to many statistical methods, and violation of this assumption may result in biased interpretations and inferences. This paper evaluates the performance of seven formal normality tests for time series data including Shapiro-Wilk (SW), Kolmogorov-Smirnov (KS), Jarque-Bera (JB), Lilliefors (LF), Cramer-von Mises (CvM), Vasicek-Song (VS) and Anderson-Darling (AD) in various settings. A simulation study with symmetric and asymmetric distributions was carried out to find the detection rates, considering the most important time series characteristics, including trend, seasonality, and presence of outliers. The tests were evaluated based on their ability to correctly classify normal and non-normal data, and their performance was summarized using accuracy metrics. The results indicate that Cramer-von Mises, Lilliefors, Anderson-Darling and Vasicek-Song tests provide superior performance as compared to the other tests in various situations. Shapiro-Wilk test showed good performance for data with trend and seasonality and Kolmogorov-Smirnov test was most effective in detecting non-normality. Anderson-Darling, Lilliefors and Cramer-von Mises test demonstrated good performance with the presence of outliers. These findings suggest that one should select normality tests based on the specifics of the data. We suggest supplementing formal tests with graphical procedures to have a more detailed and reliable test of distributional assumptions.
The COVID-19 pandemic has presented unprecedented challenges to global healthcare systems, underscoring the critical need for accurate prediction of infection cases to facilitate effective resource allocation and decision-making. This study evaluates the performance of two widely used time-series forecasting models, ARIMA and LSTM in predicting COVID-19 infection trends. Using a dataset of daily infection cases spanning January 2020 to June 2020, both models were trained and evaluated. The results demonstrate that the LSTM model achieves superior performance compared to the ARIMA model, as evidenced by lower Mean Absolute Error (MAE) and Mean Squared Error (MSE). The LSTM models ability to capture complex patterns and non-linear relationships in the data contributes significantly to its enhanced predictive accuracy. These findings highlight the potential of LSTM models to deliver more reliable forecasts of COVID-19 infection cases, providing healthcare authorities with valuable insights to inform strategic planning and preparedness for future outbreaks.
