Open Access Method Article

A Novel Dynamic Grey Action Quantity GM(1,1,b) Model and Its Application

Lang Yu

Asian Research Journal of Mathematics, Page 1-11
DOI: 10.9734/arjom/2019/v13i430113

The classical GM(1,1) model treats the grey action quantity as an invariant constant, but changes have occurred within the system as time and space change. If the fixed grey action quantity is still used for modeling, the model will have errors. Aiming at this shortcoming, this paper proposes a GM(1,1,b) model in which the grey action quantity can be dynamically changed. Starting from the background value formula, the model solves the grey action quantity at different time points by the development coefficient, and fits the sequence with the DGM(1,1) model, then brings the obtained time response sequence into the classical GM (1, 1) to replaces the grey action quantity constant, so as to establish a GM(1,1,b) model with dynamic change of grey action quantity. Finally, the model is applied to the example of China's rural residents' consumption index. The numerical example shows that the GM(1,1,b) model proposed in this paper effectively improves the prediction accuracy of the model and verifies the effectiveness and practicability of the improved model.

Open Access Method Article

A Novel Method for Optimizing Fractional Grey Prediction Model

Lang Yu

Asian Research Journal of Mathematics, Page 1-15
DOI: 10.9734/arjom/2019/v13i430115

Aiming at the shortcoming that the classical FGM(1,1) model regards the gray action quantity as a fixed constant, the DGM(1,1) model is used to dynamically simulate and predict the gray action quantity, so that the gray action quantity can change dynamically with time. On this basis, a new FGM(1,1,b) model with dynamic gray quantity change with time is proposed, and the total primary energy consumption in the Middle East is taken as a numerical example for simulation prediction. The results show that the prediction accuracy of the dynamic FGM(1,1,b) model proposed in this paper is higher than that of the classical FGM(1,1) model, and the practicability and effectiveness of the FGM(1,1,b) model are verified. At the same time, it also provides relevant theoretical basis for the study of world energy development.

Open Access Original Research Article

Open Access Original Research Article

Mathematical Modeling of Yellow Fever Transmission Dynamics with Multiple Control Measures

Tunde T. Yusuf, David O. Daniel

Asian Research Journal of Mathematics, Page 1-15
DOI: 10.9734/arjom/2019/v13i430112

Yellow-fever disease remains endemic in some parts of the world despite the availability of a potent vaccine and effective treatment for the disease. This necessitates continuous research to possibly eradicate the spread of the disease and its attendant burden. Consequently, a deterministic
model for Yellow-fever disease transmission dynamics within the human and vector population is considered. The model equilibrium solutions are obtained while the criteria for their existence and stability are investigated. The model is solved numerically using the forth order Runge- Kunta scheme and the results are simulated for different scenarios of interest. Findings from the simulations show that the disease will continue to be prevalent in our society (no matter how small) as long as the immunity conferred by the available vaccine is not lifelong and the Yellowfever infected mosquitoes continue to have unhindered access to humans. Thus, justifying the wisdom behind the practice of continuous vaccination and the use of mosquito net in areas of high Yellow-fever endemicity. However, it was equally found that the magnitude of the Yellowfever outbreak can be remarkably reduced to a negligible level with the adoption of chemical or biological control measures which ensure that only mosquitoes with minimal biting tendency thrive in the environment.

Open Access Original Research Article

Hypergeometric Functions on Cumulative Distribution Function

Pooja Singh

Asian Research Journal of Mathematics, Page 1-11
DOI: 10.9734/arjom/2019/v13i430114

Exponential functions have been extended to Hypergeometric functions. There are many functions which can be expressed in hypergeometric function by using its analytic properties. In this paper, we will apply a unified approach to the probability density function and corresponding cumulative distribution function of the noncentral chi square variate to extract and derive hypergeometric functions.