Journal of Applied Mathematics

In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect of varying the parameters. It is observed that the system has a chaotic dynamics.

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This paper is aimed at presenting thermal slip flow driven by oscillatory pressure gradient in a deformable microchannel of elliptic cross-section. The fully developed flow of Newtonian fluid is considered, and Navier slip is applied on the boundary. The boundary value problem is formulated and applied to the coronary blood flow-heat transfer phenomenon during thermotherapy treatment. Its semianalytical solutions of velocity and temperature fields are carried out by the Ritz method. The effects of oscillatory wall and slip length on velocity and temperature fields of blood are investigated.

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In this research, the color system was analyzed according to the International Lighting Commission (CIE) standard by studying the theoretical aspect of the general color system according to the latest communication theories of the visual image supported by mathematical equations and illustrations supporting the relevant hypotheses and then a comparison of evolution. There is an enormous use in color spaces and systems according to their own use, where the use of colors has become in various areas including television systems; computer systems; industry and product colors; printing of all kinds of black and white and color; paint colors for buildings, houses, and cities; and many other color-related uses. The development of color spaces and systems from 1931 to the present day has expanded a lot, and this led to the emergence of new areas of color systems characterized by accuracy and beauty and became the color of the subcolors according to the desire of the customer and the quality of use. The development of color systems has an impact on visual communication such as television broadcasting systems, medical image processing, and video signal processing, as well as in the field of computer such as graphic equipment and printing.

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A collection of oscillatory basis functions generated via an integral equation is investigated here. This is a new approach in the harmonic analysis as we are able to interpret phenomena with damping and amplifying oscillations other than classical Fourier-like periodic waves. The proposed technique is tested with a data set of dengue incidence, where different types of influences prevail. An intermediate transform supported by the Laplace transform is available. It facilitates parameter estimation and strengthens the extraction of hidden influencing accumulations. This mechanistic work can be extended as a tool in signal processing that encounters oscillatory and accumulated effects.

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This paper proposes a statistical mechanical model for the energy conservation behaviour of energy users. The model was inspired by the multipopulation Curie-Weiss model and the discrete choice with social interaction model. We demonstrate that the model integrates the sociopsychological, the economic, and the energy technologist viewpoints to energy management, allowing us to subject these perspectives to an empirical study.

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This study examined the applicability of artificial neural network models in modelling univariate time series ambulance demand for short-term forecasting horizons in Zimbabwe. Bulawayo City Councils’ ambulance services department was used as a case study. Two models, feed-forward neural network (FFNN) and seasonal autoregressive integrated moving average, (SARIMA) were developed using monthly historical data from 2010 to 2017 and compared against observed data for 2018. The mean absolute error (MAE), root mean square error (RMSE), and paired sample -test were used as performance measures. Calculated performance measures for FFNN were MAE (94.0), RMSE (137.19), and the test statistic value (>0.05) whilst corresponding values for SARIMA were 105.71, 125.28, and (<0.05), respectively. Findings of this study suggest that the FFNN model is inclined to value estimation whilst the SARIMA model is directional with a linear pattern over time. Based on the performance measures, the parsimonious FFNN model was selected to predict short-term annual ambulance demand. Demand forecasts with FFNN for 2019 reflected the expected general trends in Bulawayo. The forecasts indicate high demand during the months of January, March, September, and December. Key ambulance logistic activities such as vehicle servicing, replenishment of essential equipment and drugs, staff training, leave days scheduling, and mock drills need to be planned for April, June, and July when low demand is anticipated. This deliberate planning strategy would avoid a dire situation whereby ambulances are available but without adequate staff, essential drugs, and equipment to respond to public emergency calls.

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