Developing supply chain strategy plays an essential role to retain competition among companies. This paper investigates the decision about which items to make to stock and which ones to make to order based on a mathematical model minimize the difference between the costs of the two approaches. The production environment is characterized by multiple activities such as purchasing, manufacturing, subassembly, and finished assembly. Through some numerical experiments the effect of different demand quantitates, customer delivery time and capacity limit are identified. The analysis provides an insight into the relationship between the supply chain costing and the strategic decision making.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Dynamical Systems and Applications.

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Effects of Slip Velocity and Hall Currents on Peristaltic Transport of Bingham-Papanastasiou Fluid with Heat Transfer

Nabil T.M. Eldabe , Hamida M. Shawky , Amira S. Awaad

Mathematics Department, Faculty of Education, Ain-Shams University.

Department of Mathematics, Faculty of Science (Grils), AL- Azhar University.

Department of Mathematics, Faculty of Science (Grils), AL- Azhar University.

ABSTRACT

In this work, we investigated the effects of slip boundary condition and Hall currents on peristaltic motion of a non-Newtonian fluid which is obeying Bingham-Papanastasiou model, with heat transfer taking into account the thermal radiation and heat generation, through an asymmetric channel. This phenomena is modeled mathematically by a system of governing equations which are continuity, momentum and heat equations. These equations are solved analytically under low Reynolds number condition and long wavelength approximation. The stream function and temperature distribution are obtained as functions of physical parameters of the problem. The effects of the parameters on these solutions are discussed numerically and illustrated graphically through a set of figures. It is found that the physical parameters played important roles to control the velocity and temperature distribution.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Dynamical Systems and Applications.

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6

On the Solutions of a System of Difference Equations

Elmetwally M. M. Elabbasy , Hamdy A. El-Metwally

Math. Dept. Faculty of Science, Mansoura University

Math. Dept. Faculty of Science, Mansoura University

ABSTRACT

In this paper, we investigate the dynamical behavior of the positive solutions of the following system of difference equations
u_{n+1}=((au_{n})/(b+cv_{n-1}^{p})) ,v_{n+1}=((dv_{n})/(e+fw_{n-1}^{q})) ,w_{n+1}=((gw_{n})/(h+Iu_{n-1}^{r}))
where the initial conditions u_{-i},v_{-i},w_{-i} (i=0,1,2,3) are non-negative real numbers and the parameters a,b,c,d,e,f,g,h,I,p,q,r, are positive real numbers, by extending some results in the literature.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Dynamical Systems and Applications.

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Mathematical Model for Hepatocytic-Erythrocytic Dynamics of Malaria

Titus Okello Orwa , Rachel Waema Mbogo , Livingstone Luboobi

Strathmore University

Strathmore University

Strathmore University

ABSTRACT

Human malaria remains a major killer disease worldwide, with nearly half (3.2 billion) of
the world’s population at risk of malaria infection. The infectious protozoan disease is
endemic in tropical and subtropical regions, with an estimated 212 million new cases and
429,000 malaria-related deaths in 2015. An in-host mathematical model of malaria that
describes the dynamics and interactions of malaria parasites with the host’s liver cells, the
red blood cells and macrophages is reformulated. By a theoretical analysis, an in-host basic
reproduction number R_0 is derived. The disease free equilibrium is shown to be locally and
globally asymptotically stable. Sensitivity analysis reveal that the erythrocyte invasion rate
β_r , the average number of merozoites released per bursting infected erythrocyte K and the
proportion of merozoites that cause secondary invasions at the blood phase ζ, are the most
influential parameters in determining the malaria infection outcomes. Numerical results show
that intervention during malaria infection should focus on minimizing the density of and the
rates of merozoite invasion on healthy erythrocytes at the blood stage.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Dynamical Systems and Applications.

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6

DYNAMICS OF A NON-AUTONOMOUS DIFFERENCE EQUATION

Hamdy A. El-Metwally , Elmetwally M. M. Elabbasy , Amna Eshtiba

Faculty of Science, Mansoura University

Faculty of Science, Mansoura University

Faculty of Education, Tripoli University, Libya

ABSTRACT

In this paper we investigate the boundedness, the periodicity character and the global behavior of the positive solutions of the difference equation
x_{n+1}=a_{n}+((x_{n}^{p})/(x_{n-1}^{p})), n=0,1,...,
where {a_{n}} is a sequence of nonnegative real numbers and the initial conditions x₋₁,x₀ are arbitrary positive real numbers.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Dynamical Systems and Applications.

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Modelling Optimal control of in-host HIV Dynamics
using different control strategies

Purity Ngina , Dr. Rachel Waema , Prof. Livingstone S. Luboobi

Strathmore University, Kenya

Strathmore University, Kenya

Strathmore University, Kenya

ABSTRACT

HIV is a major cause of deaths especially in Sub-Sahara Africa. In this paper
an in-vivo deterministic model of differential equations is presented and analyzed
for HIV dynamics. Optimal control theory is applied to investigate the key roles
played by the various HIV treatment strategies. In particular, we wish to establish
the optimal strategies for controlling the infection using three treatment regimes
as the system control variables. We apply the Pontryagin’s maximum principle in
characterizing the optimality control, which is then solved numerically by applying
the Runge-Kutta forth order scheme. The numerical results indicate that an optimal
controlled treatment strategy would ensure significant reduction in viral load and
also in HIV transmission. It is also evident from the results that protease inhibitor
plays a key role in virus suppression; this is not to underscore the benefits accrued
when all the three drugs regimes are used in combinations.