Infectious diseases remain among the top contributors to human illness and death worldwide, among which many diseases produce epidemic waves of infection. The unavailability of specific drugs and ready-to-use vaccines to prevent most of these epidemics makes the situation worse. These force public health officials and policymakers to rely on early warning systems generated by reliable and accurate forecasts of epidemics. Accurate forecasts of epidemics can assist stakeholders in tailoring countermeasures, such as vaccination campaigns, staff scheduling, and resource allocation, to the situation at hand, which could translate to reductions in the impact of a disease. Unfortunately, most of these past epidemics exhibit nonlinear and non-stationary characteristics due to their spreading fluctuations based on seasonal-dependent variability and the nature of these epidemics. We analyse a wide variety of epidemic time series datasets using a maximal overlap discrete wavelet transform (MODWT) based autoregressive neural network and call it EWNet model. MODWT techniques effectively characterize non-stationary behavior and seasonal dependencies in the epidemic time series and improve the nonlinear forecasting scheme of the autoregressive neural network in the proposed ensemble wavelet network framework. From a nonlinear time series viewpoint, we explore the asymptotic stationarity of the proposed EWNet model to show the asymptotic behavior of the associated Markov Chain. We also theoretically investigate the effect of learning stability and the choice of hidden neurons in the proposal. From a practical perspective, we compare our proposed EWNet framework with several statistical, machine learning, and deep learning models. Experimental results show that the proposed EWNet is highly competitive compared to the state-of-the-art epidemic forecasting methods.

翻译：摘要：传染病仍然是全球人类疾病和死亡的主要诱因之一，其中许多疾病会引发流行病感染浪潮。由于缺乏针对大多数流行病的特定药物和现成疫苗，这一情况愈发恶化。这迫使公共卫生官员和政策制定者依赖可靠准确的流行病预测所生成的早期预警系统。准确的流行病预测可帮助利益相关者根据实际情况调整应对措施，例如疫苗接种活动、人员调度和资源分配，从而减轻疾病的影响。然而，多数过去的流行病由于其传播波动具有季节性依赖变异性和流行病本身特性，表现出非线性和非平稳特征。我们采用基于最大重叠离散小波变换（MODWT）的自回归神经网络分析多种流行病时间序列数据集，并将其命名为EWNet模型。MODWT技术有效刻画了流行病时间序列中的非平稳行为和季节依赖性，并在所提出的集成小波网络框架中提升了自回归神经网络的非线性预测能力。从非线性时间序列的角度，我们探究了所提EWNet模型的渐近平稳性，以展示相关马尔可夫链的渐近行为。同时，我们从理论上研究了学习稳定性和隐藏神经元选择对模型的影响。从实践层面，我们将所提出的EWNet框架与多种统计模型、机器学习模型和深度学习模型进行了比较。实验结果表明，与最先进的流行病预测方法相比，所提出的EWNet模型具有高度竞争力。