Nonlinear stochastic modeling plays a significant role in disciplines such as psychology, finance, physical sciences, engineering, econometrics, and biological sciences. Dynamical consistency, positivity, and boundedness are fundamental properties of stochastic modeling. A stochastic coronavirus model is studied with techniques of transition probabilities and parametric perturbation. Well-known explicit methods such as Euler Maruyama, stochastic Euler, and stochastic Runge-Kutta are investigated for the stochastic model. Regrettably, the above essential properties are not restored by existing methods. Hence, there is a need to construct essential properties preserving the computational method. The non-standard approach of finite difference is examined to maintain the above basic features of the stochastic model. The comparison of the results of deterministic and stochastic models is also presented. Our proposed efficient computational method well preserves the essential properties of the model. Comparison and convergence analyses of the method are presented.
Intrusion Detection System (IDS) plays a crucial role in detecting and identifying the DoS and DDoS type of attacks on IoT devices. However, anomaly-based techniques do not provide acceptable accuracy for efficacious intrusion detection. Also, we found many difficulty levels when applying IDS to IoT devices for identifying attempted attacks. Given this background, we designed a solution to detect intrusions using the Convolutional Neural Network (CNN) for Enhanced Data rates for GSM Evolution (EDGE) Computing. We created two separate categories to handle the attack and non-attack events in the system. The findings of this study indicate that this approach was significantly effective. We attempted both multiclass and binary classification. In the case of binary, we clustered all malicious traffic data in a single class. Also, we developed 13 layers of Sequential 1-D CNN for IDS detection and assessed them on the public dataset NSL-KDD. Principal Component Analysis (PCA) was implemented to decrease the size of the feature vector based on feature extraction and engineering. The approach proposed in the current investigation obtained accuracies of 99.34% and 99.13% for binary and multiclass classification, respectively, for the NSL-KDD dataset. The experimental outcomes showed that the proposed Principal Component-based Convolution Neural Network (PCCNN) approach achieved greater precision based on deep learning and has potential use in modern intrusion detection for IoT systems.
The current effort is devoted to investigating and exploring the stochastic nonlinear mathematical pandemic model to describe the dynamics of the novel coronavirus. The model adopts the form of a nonlinear stochastic susceptible-infected-treated-recovered system, and we investigate the stochastic reproduction dynamics, both analytically and numerically. We applied different standard and nonstandard computational numerical methods for the solution of the stochastic system. The design of a nonstandard computation method for the stochastic system is innovative. Unfortunately, standard computation numerical methods are time-dependent and violate the structure properties of models, such as positivity, boundedness, and dynamical consistency of the stochastic system. To that end, convergence analysis of nonstandard computational methods and simulation with a comparison of standard computational methods are presented.
Pneumonia is a highly transmissible disease in children. According to the World Health Organization (WHO), the most affected regions include south Asia and sub-Saharan Africa. Worldwide, 15% of pediatric deaths can be attributed to pneumonia. Computing techniques have a significant role in science, engineering, and many other fields. In this study, we focused on the efficiency of numerical techniques via computer programs. We studied the dynamics of the pneumonia-like infections of epidemic models using numerical techniques. We discuss two types of analysis: dynamical and numerical. The dynamical analysis included positivity, boundedness, local stability, reproduction number, and equilibria of the model. We also discuss well-known computing techniques including Euler, Runge Kutta, and non-standard finite difference (NSFD) for the model. The non-standard finite difference (NSFD) technique shows convergence to the true equilibrium points of the model for any time step size. However, Euler and Runge Kutta do not work well over large time intervals. Computing techniques are the suitable tool for crosschecking the theoretical analysis of the model.
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