Intelligent Bayesian Neural Networks for Stochastic SVIS Epidemic Dynamics: Vaccination Strategies and Prevalence Fractions with Wiener Process

Real-time forecasting of infectious diseases is crucial for effective public health management, particularly during outbreaks. When infectious disease predictions are based on mechanistic models, they can guide resource allocation and help evaluate the potential effects of different interventions. However, accurately parametrizing these models in real time presents a challenge, as timely information on behavioral shifts, interventions and transmission pathways is often lacking. This investigation leverages the artificial neural networks with the Bayesian regularization (BR-ANN) backpropagation approach to examine the dynamical pathogen spread with Wiener process incorporation. The stochastic differential model is structured into susceptible, vaccinated, infectious and susceptible (SVIS) compartments. The Kloeden-Platen-Schurz (KPS) computing paradigm for the stochastic differential system is utilized to generate synthetic datasets by applying transformations to key factors, including the population recruitment ratio, transmission ratio of vulnerable individuals, natural death rate of the population, vaccination rate of vulnerable individuals, total population size, immune loss ratio of susceptible individuals, recovery rate and mortality rate from the disease among infected individuals. Random selection from the generated datasets is exploited for the training and testing procedures for constructing the BR-ANN networks. The significance of the proposed scheme for various stochastic SVIS system scenarios is endorsed by the comprehensive assessments of the BR-ANN approach that are conducted by means of extensive experimentations and comparison with the reference KPS solutions of the SVIS system in terms of MSE optimal performance plots, absolute errors, autocorrelation analysis, regression indices and error histograms.