Computational and Mathematical Methods

A directed Toeplitz graph with vertices , , , is a directed graph whose adjacency matrix is a Toeplitz matrix. In this paper, we investigate the Hamiltonicity in directed Toeplitz graphs with and .

The data on SARS-CoV-2 (COVID-19) in South Africa show seasonal transmission patterns to date, with the peaks having occurred in winter and summer since the outbreaks began. The transmission dynamics have mainly been driven by variations in environmental factors and virus evolution, and the two are at the center of driving the different waves of the disease. It is thus important to understand the role of seasonality in the transmission dynamics of COVID-19. In this paper, a compartmental model with a time-dependent transmission rate is formulated and the stabilities of the steady states analyzed. We note that if , the disease-free equilibrium is globally asymptotically stable, and the disease completely dies out; and when , the system admits a positive periodic solution, and the disease is uniformly or periodically persistent. The model is fitted to data on new cases in South Africa for the first four waves. The model results indicate the need to consider seasonality in the transmission dynamics of COVID-19 and its importance in modeling fluctuations in the data for new cases. The potential impact of seasonality in the transmission patterns of COVID-19 and the public health implications is discussed.

In this paper, we present a nonlinear deterministic mathematical model for malaria transmission dynamics incorporating climatic variability as a factor. First, we showed the limited region and nonnegativity of the solution, which demonstrate that the model is biologically relevant and mathematically well-posed. Furthermore, the fundamental reproduction number was determined using the next-generation matrix approach, and the sensitivity of model parameters was investigated to determine the most affecting parameter. The Jacobian matrix and the Lyapunov function are used to illustrate the local and global stability of the equilibrium locations. If the fundamental reproduction number is smaller than one, a disease-free equilibrium point is both locally and globally asymptotically stable, but endemic equilibrium occurs otherwise. The model exhibits forward and backward bifurcation. Moreover, we applied the optimal control theory to describe the optimal control model that incorporates three controls, namely, using treated bed net, treatment of infected with antimalaria drugs, and indoor residual spraying strategy. The Pontryagin’s maximum principle is introduced to obtain the necessary condition for the optimal control problem. Finally, the numerical simulation of optimality system and cost-effectiveness analysis reveals that the combination of treated bed net and treatment is the most optimal and least-cost strategy to minimize the malaria.

In recent years, the developments of new families of probability distributions have received greater attention as a result of desirable properties they exhibit in the modelling of data sets. The Harmonic Mixture Weibull-G family of distributions was developed in this study. The statistical properties were comprehensively presented and five special distributions developed from the family. The hazard functions of the special distributions were shown to exhibit various forms of monotone and nonmonotone shapes. The applications of the developed family to real data sets in medical studies revealed that the special distribution (Harmonic mixture Weibul Weibull distribution) provided a better fit to the data sets than other competitive models. A location-scale regression model was developed from the family and its application demonstrated using survival time data of hypertensive patients.

Many applications in applied sciences and engineering can be considered as the convex minimization problem with the sum of two functions. One of the most popular techniques to solve this problem is the forward-backward algorithm. In this work, we aim to present a new version of splitting algorithms by adapting with Tseng’s extragradient method and using the linesearch technique with inertial conditions. We obtain its convergence result under mild assumptions. Moreover, as applications, we provide numerical experiments to solve image recovery problem. We also compare our algorithm and demonstrate the efficiency to some known algorithms.

The compressors used in today’s natural gas production industry have an essential role in maintaining the production line operational. Each of the compressors’ components has routine maintenance tasks to avoid sudden failures. Hence, the significant advantages and benefits of performing preventative maintenance tasks in time are decreasing equipment downtime, saving additional costs, and improving the safety and reliability of the whole system. In this paper, anomaly classification and detection methods based on a neural network hybrid model named Long Short-Term Memory (LSTM)-Autoencoder (AE) is proposed to detect anomalies in sequence pattern of audio data, collected by multiple sound sensors deployed at different components of each compressor system for predictive maintenance. In research methodology, this paper has conducted experiments that employed different RNN architectures such as GRU, LSTM, Stacked LSTM, and Stacked GRU with various functions to create a baseline for model evaluation. Each architecture used audio signals dataset received from the compressor system for experiments to consider each neural network model’s performance. According to performance results, an optimal model for anomaly detection with the best performance scores has been proposed in this research. Experiments combined one-dimensional raw audio signal features using SC and Mel spectrogram features were fed to deep learning models to evaluate performance. Hence, such hybrid methods can effectively detect normal and anomaly audio signals collected from a compressor system, increasing the compressor system’s reliability and the sustainability of the gas production line. The combination of multiple-resource features in the proposed hybrid model showed a 100% score in all four-evaluation metrics such as accuracy, precision, recall, and F1 in LSTM-based autoencoder in both test and train results.