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STABILITY AND THE EFFECT OF HARVESTING IN A BUDWORM POPULATION MODEL
GUL ZAMAN,YONG HAN KANG,IL HYO JUNG 한국산업응용수학회 2010 Journal of the Korean Society for Industrial and A Vol.14 No.3
In this work, we consider a nonlinear budworm model by a system of three ordinary differential equations originally created by Ludwig et al. in 1978. The nonlinear system describes the dynamics of the interaction between a budworm and a fir forest. We introduce stability techniques to analyze the dynamical behavior of this nonlinear system. Then we use constant effort harvesting techniques to control the budworm population. We also give numerical simulations of the population model with harvest and without harvest.
Optimal vaccination and treatment in the SIR epidemic model
Gul Zaman,Yong Han Kang,Il Hyo Jung 한국산업응용수학회 2007 한국산업응용수학회 학술대회 논문집 Vol.3 No.2
Mathematical epidemiological models for the dynamics of infections that induce lifelong immunity have been extensively developed. In this work, we consider a nonlinear SIR model given by a nonlinear system describing the dynamics of the interaction between susceptible and infective individuals in population. We analyze the dynamical behavior of the nonlinear system and then use two types of control vaccination and treatment to reduce the susceptible and infective individuals and increase the number of recovered individuals. The optimality system is derived and then solved numerically using an iterative method with Runge-Kutta fourth order scheme.
Optimal Campaign Strategies in Fractional-Order Smoking Dynamics
Zeb, Anwar,Zaman, Gul,Jung, Il Hyo,Khan, Madad Verlag der Zeitschrift für Naturforschung 2014 Zeitschrift für Naturforschung. A, A journal Vol.69 No.5
<P>This paper deals with the optimal control problem in the giving up smoking model of fractional order. For the eradication of smoking in a community, we introduce three control variables in the form of education campaign, anti-smoking gum, and anti-nicotive drugs/medicine in the proposed fractional order model. We discuss the necessary conditions for the optimality of a general fractional optimal control problem whose fractional derivative is described in the Caputo sense. In order to do this, we minimize the number of potential and occasional smokers and maximize the number of ex-smokers. We use Pontryagin’s maximum principle to characterize the optimal levels of the three controls. The resulting optimality system is solved numerically by MATLAB.</P>
Khan, Amir,Zaman, Gul,Jung, Il Hyo Marcel Dekker, Inc 2017 JOURNAL OF POROUS MEDIA Vol.20 No.7
<P>This article presents some new exact solutions corresponding to unsteady magnetohydrodynamic flow of generalized Jeffrey fluid in a rectangular duct, filled with a porous medium oscillating parallel to its length. The exact solutions are established by means of the double finite Fourier sine transform and discrete Laplace transform. The series solution of velocity field, associated shear stress, and volume flow rate in terms of Fox H-function, satisfying all imposed initial and boundary conditions, have been obtained. Also, the obtained results are analyzed graphically through various pertinent parameters.</P>
APPROXIMATE SOLUTIONS TO MHD SQUEEZING FLUID FLOW
S. Islam,Murad Ullah,Gul Zaman,M. Idrees 한국전산응용수학회 2011 Journal of applied mathematics & informatics Vol.29 No.5
In this paper, a steady axisymmetric MHD flow of two dimensional incompressible fluids is studied under the influence of a uniform transverse magnetic field. The governing equations are reduced to nonlinear boundary value problem by applying the integribility conditions. Optimal Homotopy Asymptotic Method (OHAM) is applied to obtain solution of reduced fourth order nonlinear boundary value problem. For comparison, the same problem is also solved by Variational Iteration Method (VIM).
APPROXIMATE SOLUTIONS TO MHD SQUEEZING FLUID FLOW
Islam, S.,Ullah, Murad,Zaman, Gul,Idrees, M. The Korean Society for Computational and Applied M 2011 Journal of applied mathematics & informatics Vol.29 No.5
In this paper, a steady axisymmetric MHD flow of two dimensional incompressible fluids is studied under the influence of a uniform transverse magnetic field. The governing equations are reduced to nonlinear boundary value problem by applying the integribility conditions. Optimal Homotopy Asymptotic Method (OHAM) is applied to obtain solution of reduced fourth order nonlinear boundary value problem. For comparison, the same problem is also solved by Variational Iteration Method (VIM).
Presentation of Malaria Epidemics Using Multiple Optimal Controls
Lashari, Abid Ali,Aly, Shaban,Hattaf, Khalid,Zaman, Gul,Jung, Il Hyo,Li, Xue-Zhi Hindawi Limited 2012 Journal of applied mathematics (JAM) Vol.2012 No.-
<P>An existing model is extended to assess the impact of some antimalaria control measures, by re-formulating the model as an optimal control problem. This paper investigates the fundamental role of three type of controls, personal protection, treatment, and mosquito reduction strategies in controlling the malaria. We work in the nonlinear optimal control framework. The existence and the uniqueness results of the solution are discussed. A characterization of the optimal control via adjoint variables is established. The optimality system is solved numerically by a competitive Gauss-Seidel-like implicit difference method. Finally, numerical simulations of the optimal control problem, using a set of reasonable parameter values, are carried out to investigate the effectiveness of the proposed control measures.</P>