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