Article of the Year 2020
Mathematical Modelling and Analysis of Transmission Dynamics of Lassa FeverRead the full article
Journal of Applied Mathematics publishes original research papers and review articles in all areas of applied, computational, and industrial mathematics.
Chief Editor, Professor Theodore E. Simos, is based at Ulyanovsk State Technical University, Russia. His main research interest is the numerical analysis of differential equations.
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On the Upper Bounds of Test Statistics for a Single Outlier Test in Linear Regression Models
A bewildering large number of test statistics have been found for testing the presence of an outlier in multiple linear regression models. Exact critical values of these test statistics are not available, and approximate ones are usually obtained by the first-order Bonferroni upper bound or large-scale simulations. In this paper, we show that the upper bound values of two of these test statistics are algebraically the same. An application to real data for multiple linear regression is used to demonstrate the procedure.
Assessing the Performance of DWT-PCA/SVD Face Recognition Algorithm under Multiple Constraints
Many architectures of face recognition modules have been developed to tackle the challenges posed by varying environmental constraints such as illumination, occlusions, pose, and expressions. These recognition systems have mainly focused on a single constraint at a time and have achieved remarkable successes. However, the presence of multiple constraints may deteriorate the performance of these face recognition systems. In this study, we assessed the performance of Principal Component Analysis and Singular Value Decomposition using Discrete Wavelet Transform (DWT-PCA/SVD) for preprocessing face recognition algorithm on multiple constraints (partially occluded face images acquired with varying expressions). Numerical evaluation of the study algorithm gave reasonably average recognition rates of 77.31% and 76.85% for left and right reconstructed face images with varying expressions, respectively. A statistically significant difference was established between the average recognition distance of the left and right reconstructed face images acquired with varying expressions using pairwise comparison test. The post hoc analysis using the Bonferroni simultaneous confidence interval revealed that the significant difference established through the pairwise comparison test was mainly due to the sad expressions. Although the performance of the DWT-PCA/SVD algorithm declined as compared to its performance on single constraints, the algorithm attained appreciable performance level under multiple constraints. The DWT-PCA/SVD recognition algorithm performs reasonably well for recognition when partial occlusion with varying expressions is the underlying constraint.
HIV/AIDS-Pneumonia Coinfection Model with Treatment at Each Infection Stage: Mathematical Analysis and Numerical Simulation
In the paper, we have considered a nonlinear compartmental mathematical model that assesses the effect of treatment on the dynamics of HIV/AIDS and pneumonia coinfection in a human population at different infection stages. Our model revealed that the disease-free equilibrium points of the HIV/AIDS and pneumonia submodels are both locally and globally asymptotically stable whenever the associated basic reproduction numbers ( and ) are less than unity. Both the submodel endemic equilibrium points are locally and globally asymptotically stable whenever the associated basic reproduction numbers ( and ) are greater than unity. The full HIV/AIDS-pneumonia coinfection model has both locally and globally asymptotically stable disease-free equilibrium points whenever the basic reproduction number of the coinfection modelis less than unity. Using standard values of parameters collected from different kinds of literature, we found that the numerical values of the basic reproduction numbers of the HIV/AIDS-only submodel and pneumonia-only submodel are 17 and 7, respectively, and the basic reproduction number of the HIV/AIDS-pneumonia coinfection model is . Applying sensitive analysis, we identified the most influential parameters to change the behavior of the solution of the considered coinfection dynamical system are the HIV/AIDS and pneumonia transmission rates and , respectively. The coinfection model was numerically simulated to investigate the stability of the coinfection endemic equilibrium point, the impacts of transmission rates, and treatment strategies for HIV/AIDS-only, pneumonia-only, and HIV/AIDS-pneumonia coinfected individuals. Finally, we observed that numerical simulations indicate that treatment against infection at every stage lowers the rate of infection or disease prevalence.
Hierarchical Bayesian Spatio-Temporal Modeling for PM10 Prediction
Over the past few years, hierarchical Bayesian models have been extensively used for modeling the joint spatial and temporal dependence of big spatio-temporal data which commonly involves a large number of missing observations. This article represented, assessed, and compared some recently proposed Bayesian and non-Bayesian models for predicting the daily average particulate matter with a diameter of less than 10 (PM10) measured in Qatar during the years 2016–2019. The disaggregating technique with a Markov chain Monte Carlo method with Gibbs sampler are used to handle the missing data. Based on the obtained results, we conclude that the Gaussian predictive processes with autoregressive terms of the latent underlying space-time process model is the best, compared with the Bayesian Gaussian processes and non-Bayesian generalized additive models.
The Dynamics of a Tritrophic Leslie-Gower Food-Web System with the Effect of Fear
The avoidance strategy of prey to predation and the predation strategy for predators are important topics in evolutionary biology. Both prey and predators adjust their behaviors in order to obtain the maximal benefits and to raise their biomass for each. Therefore, this paper is aimed at studying the impact of prey’s fear and group defense against predation on the dynamics of the food-web model. Consequently, in this paper, a mathematical model that describes a tritrophic Leslie-Gower food-web system is formulated. Sokol-Howell type of function response is adapted to describe the predation process due to the prey’s group defensive capability. The effects of fear due to the predation process are considered in the first two levels. It is assumed that the generalist predator grows logistically using the Leslie-Gower type of growth function. All the solution properties of the model are studied. Local dynamics behaviors are investigated. The basin of attraction for each equilibrium is determined using the Lyapunov function. The conditions of persistence of the model are specified. The study of local bifurcation in the model is done. Numerical simulations are implemented to show the obtained results. It is watched that the system is wealthy in its dynamics including chaos. The fear factor works as a stabilizing factor in the system up to a specific level; otherwise, it leads to the extinction of the predator. However, increasing the prey’s group defense leads to extinction in predator species.
Traditional Houses and Projective Geometry: Building Numbers and Projective Coordinates
The natural mathematical abilities of humans have advanced civilizations. These abilities have been demonstrated in cultural heritage, especially traditional houses, which display evidence of an intuitive mathematics ability. Tribes around the world have built traditional houses with unique styles. The present study involved the collection of data from documentation, observation, and interview. The observations of several traditional buildings in Indonesia were based on camera images, aerial camera images, and documentation techniques. We first analyzed the images of some sample of the traditional houses in Indonesia using projective geometry and simple house theory and then formulated the definitions of building numbers and projective coordinates. The sample of the traditional houses is divided into two categories which are stilt houses and nonstilt house. The present article presents 7 types of simple houses, 21 building numbers, and 9 projective coordinates.