R. N. Andima, W. N. Mutuku, A. S. Oke, N. Farai, K. Awuor, B. A. Juma

Blindness, stroke, and amputations are some of the consequences of diabetes on humans. The fact that over 500 billion USD is spent on diabetes diagnosis, care, and treatment each year demonstrates its massive impact on the global economy. In Kenya, the incidence rate of diabetes and the number of death from diabetes and diabetes-related infections keep rising. At this rate, healthcare facilities and resources would undoubtedly become overloaded. The impact of a constant hospitalization rate on the trajectory of diabetes is explored in this study. A system of ordinary differential equations is developed to describe the dynamics of diabetes with a constant hospitalization rate. The model is shown to be well-posed, positive, and bounded, and the requirements for the local stability of the equilibrium points are established. The next generation matrix is used to calculate the reproduction number. The model is numerically solved using the explicit Runge-Kutta 4th order and the results are graphed. Improvement in lifestyle quality among the susceptible class reduces the migration from the susceptible subpopulation to the diabetic population.

]]>Sebastian Mbugri Akudugu, Douglas Kwasi Boah

Some banks in Ghana suffer low returns and sometimes incur losses when they give out loans. In this study, the concept of linear programming has been successfully used to examine the loan policy of a bank in Upper West Region of Ghana. Based on collected data and information from the bank, an optimal loans model has been developed for the bank using linear programming to help maximize its profits or returns accrued from giving out loans. Also, the effects of variations of some selected key parameters on the developed model has been performed by means of sensitivity analysis. Moreover, duality analysis has been performed on the developed model to know the effect of an increase or decrease in an available resource on the optimal solution or profit. The study recommends that, the bank under consideration should use the developed model as a guide when giving out loans in order to maximize its profits or returns. Also, other banks and financial institutions should take a cue from the developed model when giving out loans in order to maximize their profits or returns.

]]>Syed Md Omar Faruk

In this paper we consider the problem of identifying a limited amount of nodes from a given graph in order to minimize some measure of the connectivity of the surviving graph. These nodes are commonly referred to as critical nodes. In particular, we look at the problem of identifying important nodes in a path graph whose removal optimizes the connectedness of the given path. We analyze four variants of the critical node detection problem on paths and present a closed-form solution for the objective function's optimality.

]]>Md. Shajib Ali

In this article we study two numerical solutions of first order explicit upwind difference scheme (EUDS) and second order Lax-Wendroff difference scheme (LWDS) for a system of first order non-linear PDEs. The numerical simulation of a 10 km highway of three lanes is performed for 6 minutes using both the numerical schemes based on artificial initial and boundary data. The computed simulation result satisfies some verified qualitative figures of numerical solution and also the numerical solution converges for smaller temporal and spatial grid sizes.

]]>Nzerem Francis Egenti, Ukamaka Cynthia Orumie

Sources and sinks are phenomena of interest. Biological systems have their share of the inherent benefits derivable from them. One of such systems is the Autorhythmic Volume Conduction System (AVCS). Autorhythmicity is typical of electrically active cells that demonstrate rhythmic activity without being driven by external stimulation. It is a unique attribute of cardiac cells. Here, specialized nodal cells act as sources and sinks, with the conduction pathways maintaining the integrity of ionic flow. The edge-nodal system is a network. Feasible network flow of ionic current is often achieved by the synergy between edge-nodal appurtenances. A veritable way of analyzing network systems is the mathematical graph theory. Therefore, this was done here. Much as the AVCS has its idiosyncrasy in terms of current flow through edge-nodal structures, the analysis of electrical flow as evinced by source and sink phenomena is a clue to a better understanding of the conduction system of the heart.

]]>Tiryono Ruby, Machudor Yusman

This paper constructs a mathematical model of a hybrid electric energy system based on renewable energy sources and the reliability of photocell efficiency control strategies, motion sensor and or wi-fi switches in response to fluctuating demand loads. By combining these models and strategies, it is hoped that they can accommodate the phenomenon of the electricity supply system and fluctuations in demand loads that must be met together so that the actual optimal conditions in system operation can be achieved. Thus the system design information obtained from this study can be more accurate and precise so that in making decisions on the procurement of a hybrid system unit, the required power source equipment can be of higher quality and more accurate, especially in this pandemic era.

]]>Abonongo John, Ida Anuwoje L. Abonongo

Loss reserving for non-life insurance involves forecasting future payments due to claims. Accurately estimating these payments are vital for players in the insurance industry. This paper examines the applicability of the Mack Chain Ladder and its related bootstrap predictions to real non-life insurance claims in the case of auto-insurance claims from Bolgatanga State Insurance Company branch. The results showed that, the mean IBNR and Ultimate reserves from the bootstrap technique produced results that are close to that in the Mack model. The prediction errors from the bootstrap technique are higher than that of the Mack model. It was realized that, the cdf of the IBNR claims follow a log-normal distribution; this distribution was fitted from the bootstrapping with 999 replications. Also, 75%, 90%, 95% and 99.5% were the quantiles used in measuring the IBNR VaR and it was realized that 2016 recorded the highest IBNR VaR. The prediction errors from the bootstrap technique are higher than that of the Mack model. It was realized that, the cdf of the IBNR claims follow a log-normal distribution. This distribution was fitted with mean of 14.030 and standard deviation of 0.293 from bootstrapping with 999 replications. Also, the accident year (2016) recorded the highest VaR estimates.

]]>Dorrah Azis, Agus Sutrisno, Desfan Hafifullah, Subian Saidi

Generally, the order of integral and derivative are connected with the real numbers, such as the first, second, third and more order of integral and derivative. This study aims to develop a theory of an integral or derivative which has order in a 5^{th} order function and exponential function by using Riemann and Liouville method. The result of this study showed that the fractional derivative of order in the 5^{th} Order Function using Riemann-Liouville Method is the same as the form of a third derivative, which means that the value of this derivative will be the same as the result of three times the fractional integral or vice versa. In addition the fractional derivative of the exponential function using the Riemann-Liouville Method is equal to in the form of multiplication of the incomplete gamma function upper limit with exponential function.

Ameha Tefera Tessema

Let such that then Where p=2t+1 for all p odd Natural numbers(N), p=2t+2 for all p even natural numbers(N).

]]>Munyabugingo Valens

There are many fascinating things that can be described by differential equations. This paper analyzes an epidemic model created from first order differential equations to describe how the Ebola virus potentially ravage a population in Congo and Uganda. Using epidemic modelling, data from two well documented website [5], [10] and Matlab packages, we present the solutions graphically. Using SIR model, it is possible to simulate Ebola outbreaks in Congo and Uganda. The dynamics of this model is determined by the per-capital death rate of infected individuals and the per-capital effective contact rate of an individual contracting the disease. The results of these outbreak simulations equip scientists with information that may enable them to minimize potential deaths caused by Ebola outbreak.

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