Computational and Mathematical Methods最新文献

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.

An outbreak of severe acute respiratory syndrome (COVID-19) killed 287,355 with 4, 257,578 cases worldwide as of May 12, 2020. In this paper, we propose an SEQI_sI_aRM deterministic mathematical model which contains compartments for both human-to-human transmission and transmission through contaminated surfaces. Without intervention, the role of symptomatic and asymptomatic cases in humans is found to be very high in the transmission of the virus. Sensitive parameters which are associated with increased transmission of the COVID-19 virus were identified. According to the sensitivity results, the most sensitive parameters were disease-induced death rates of symptomatic and asymptomatic infectious people (σ), the rate of removal of virus from surfaces and environment (ν), and the rate of infection by asymptomatic infectious people (λ₂) and symptomatic infectious people (λ₁). The numerical results of our model confirm the sensitivity results that there are more new incidences of asymptomatic cases than symptomatic cases, which escalates the transmission of the virus in the community. Combined interventions like increasing both the rate of removal of viruses from surfaces and environment and decreasing the rate of infection in asymptomatic cases can play a significant role in reducing the average number of secondary infection (R₀) to less than unity, causing COVID-19 to die out.

An N-dimensional game theory–based model for multi-actor predictive analytics is presented in this article. The proposed model expands our previous work on two-dimensional group decision model for predictive analytics. The one-dimensional models are used for the problems where actors are interacting in a single issue space only. This is less than an ideal assumption since; in most cases, players’ strategies may depend on the dynamics of multiple issues when dealing with other players. In this work, the one-dimensional model is expanded to N-dimensional model by considering different positions, and separate salience values, across different axes for the players. The model predicts an outcome for a given problem by taking into account stakeholder’s positions in different dimensions and their conflicting perspectives. To illustrate the capability of the proposed model, three case studies have been presented.

There has been several Lagrange and Hermite type interpolations of entire functions whose linear canonical transforms have compact supports in ℝ. There interpolation representations are called sampling theorems for band-limited signals in signal analysis. The truncation, amplitude, and jitter errors associated with the Lagrange type interpolations are investigated rigorously. Nevertheless, the amplitude and jitter errors arising from perturbing samples and nodes are not studied before. The aim of this work is to establish rigorous analysis of their types of perturbation errors, which is important from both practical and theoretical points of view. We derive precise estimates for both types of errors and expose various numerical examples.

This paper mainly deals on the issue of a chaotic synchronization of a master and slave systems. It is generally the requirement of the synchronization that someone needs at least one to one master and slave systems. In the current study, the authors introduce the concept of a synchronization in which there is no need of slave/response system externally. Furthermore, the synchronization has been demonstrated here within a system among the subsystems of different orders. In addition, adaptive control is chosen for the synchronization among various combinations in multiswitching manner. For demonstration purpose, Lorenz Six Dimensional Hyper Chaotic System (L6DHCS) is chosen. There are three different kinds of possible switches presented by the authors formed within the considered system. The numerical simulations are carried out to validate the effectiveness of the analytical technique using Mathematica.

In this paper, we present a new computational method based on an exponential spline for solving a class of delay differential equations with a negative shift in the differentiated term. When the shift parameter is O(ε), the proposed method works well and also controls the oscillations in the solution’s layer region. To accomplish this, we included a parameter in the proposed numerical scheme that is based on a special type of mesh, and the parameter is evaluated using the theory of singular perturbation. Maximum absolute errors and convergences of numerical solutions are tabulated to demonstrate the efficiency of the proposed computational method and to support the convergence analysis of the presented scheme.

This article suggests two new modified iteration methods called the modified Gauss-Seidel (MGS) method and the modified fixed point (MFP) method to solve the absolute value equation. Using appropriate assumptions, we examine the convergence of the given methods. Lastly, numerical examples illustrate the usefulness of the new strategies.