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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.

The contributions of AI-based applications in monitoring real-time financial transactions, and detecting fraudulent activity by scrutinizing consumer behavior, transaction patterns, and other relevant measures are worth mentioning for potential threats identification in the fractional financial crime population dynamics. Leveraging these financial crime systems in terms of population dynamics with the exploitation of supervised Nonlinear Autoregressive Exogenous Networks Optimized with the Bayesian Regularization (NARX-BR) procedures for attaining sufficient accuracy and flexibility for the approximate solutions of a fractional variant of stiff Nonlinear Financial Crime Population Dynamics (NFCPDs) differential system. The population dynamics for the financial crime model are classified mainly into susceptible persons, financial criminals, individuals being prosecuted individuals under prosecution, imprisoned persons, and honest individuals by law. The acquisition of synthetic data generated with Grünwald–Letnikov (GL) fractional operator for the multi-layer structure execution of NARX-BR procedure for solving NFCPDs for varying financial crime parameters, such as influence rate, recruitment rate, conversion rate to honest people, freedom rate, financial criminal prosecution rate per capita, percentage of discharge rate from prosecution, transition rate to prison, discharge and acquittal rate from prosecutions. The estimated outcomes of NARX-BR and the calculated numerical solutions of NFCPDs consistently overlap implying that the error between the results is approximately equal to zero. The effectiveness of model performance is assessed through a variety of evaluation metrics, that include minimization of mean square error-based objective function, adaptive regulating parameters of the optimization algorithm, error distribution plots, regression studies, error endogeneity, and cross-correlation analyses. This study contributes to integrating fractional calculus with the knacks of innovative AI and open paths to provide data-driven efficient solution-based policy recommendations in the field of financial crime population dynamics.

The structure of a novel computational hyperbolic tangent sigmoid deep neural network (HTS-DNN) is presented for the numerical solutions of the hepatitis B virus model, which is based on the antibody immune response. The mathematical model is categorized as healthy and hepatocytes, capsids, antibodies and free viruses. A novel process based on the HTS-DNN is exploited by using two hidden layers with 20 and 30 numbers of neurons. The optimization is performed through Bayesian regularization, which is one of the reliable procedures used in the optimization of various problems. A dataset is obtained through the Runge–Kutta solver, which is used to reduce the mean square error by dividing the training, testing and verification data as 70%, 16% and 14%. Moreover, the statistical representations in the sense of error histogram, regression, and state transitions also approve the accuracy of the scheme.

The “hard water” factor shows the management of water in the Nusa Tenggara Timur, which shows a higher ratio based on the ion’s minerals. The incessant use of hard water presents kidney dysfunction, which produces diabetic and vascular kinds of diseases. Therefore, it is essential to recognize the influences of hard water on kidney function. A novel design of a stochastic solver using the transfer radial basis function is provided by applying the Bayesian regularization neural network for solving the model. The kidney dysfunction mathematical system is divided into humans (susceptible, infected, recovered) and water components (magnesium, calcium). Twelve numbers of neurons with the radial basis transfer function have been used in the hidden layers for solving the model. The approach performance is remarked through the results comparison and further reducible absolute error found around $10^{-06}$ to $10^{-08}$ develop the scheme’s exactness. Moreover, the statistical performances including regression coefficient performances around 1 for each case of the model validate the reliability and exactness of the scheme for solving the model.

A recurrent neural network modeling approach for software reliability prediction with respect to cumulative failure time is proposed. Our proposed network structure has the capability of learning and recognizing the inherent internal temporal property of cumulative failure time sequence. Further, by adding a penalty term of sum of network connection weights, Bayesian regularization is applied to our network training scheme to improve the generalization capability and lower the susceptibility of overfitting. The performance of our proposed approach has been tested using four real-time control and flight dynamic application data sets. Numerical results show that our proposed approach is robust across different software projects, and has a better performance with respect to both goodness-of-fit and next-step-predictability compared to existing neural network models for failure time prediction.

Using an artificial neural network and the Bayesian Regularization Technique (NNs-BRT), the stochastic method’s strength is used to analyze the differential system, illustrating a nonlinear smoke epidemic differential model (NSED). This allows for a more precise, dependable, cost-effective, dynamic calculating approach. In addition to experiments utilizing nonlinear mathematical structures through five distinct classes of differential operators-smokers contemplating quitting, infrequent smokers, regular smokers, those who have temporarily abstained from smoking, and those who have permanently quit smoking the NSED framework has been established. By allocating 25% of the data for testing and validation and 75% for training, the proposed NNs-BRT can determine the estimated solutions of five different examples based on the numerical computation of the NSED system employing Adams techniques. To prove the accuracy of the given NNs-BRTs, a comparison of the results from the dataset obtained using the Adam method for different scenarios reflecting variance in recruitment rate, effective contact rate between C and A, natural death rate, how quickly occasional smokers become regular smokers, contact rate between smokers, and temporary quitters, number of smokers quitting, and percentage of smokers who are still leaving for good is made. The use of error histograms, mean square error, regression, correlation, and state transitions is also examined in numerical replications of the NNs-BRTs to verify their competence, dependability, accuracy, consistency, and proficiency.