scholarly journals Optimal control for SIR Model with The Influence of Vaccination, Quarantine and Immigration factor

2020 ◽  
Vol 16 (3) ◽  
pp. 311
Author(s):  
Susi Agustianingsih ◽  
Rina Reorita ◽  
Renny Renny
Keyword(s):  
Optimal Control ◽  
Minimum Cost ◽  
Sir Model ◽  
Human Populations ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Simulation Results ◽  
The Mathematical Model ◽  
Susceptible Group ◽  
Minimum Costs

The SIR model is one of the mathematical model which describes the characteristic of the spread of infectious disease in differential equation form by dividing the human populations into three groups. There are individual susceptible group, individual infective group, and individual recovered group. This model involves vaccination, quarantine, and immigration factors. Vaccination and quarantine must be given as much as it needs, so a control is required to minimize infection of disease and the number of individual infective with a minimum costs. In this research, optimal control of SIR model with vaccination, quarantine, and immigration factor is solved by using Pontryagin maximum principle and numerically simulated by using Runge-Kutta method. Numerical simulation results show optimal control of treatment, citizen of vaccination, immigrant of vaccination, and quarantine will accelerate the decline of infected number with the minimum cost, compared with the optimal control of SIR model without quarantine factor.

Enhancement the Solar Still Performance Using Chimney Exhaust Gases

2021 ◽  
Author(s):  
Hamdy Hassan
Keyword(s):  
Mathematical Model ◽  
Theoretical Study ◽  
Saline Water ◽  
Kutta Method ◽  
Solar Still ◽  
Climate Conditions ◽  
Exhaust Gases ◽  
Runge Kutta Method ◽  
The Impact ◽  
The Mathematical Model

Abstract In this paper, a theoretical study is presented on enhancement of the solar still performance by using the exhaust gases passing inside a chimney under the still basin. The impact of the exhaust gases temperature on the solar still temperature, productivity, and efficiency are considered. The performance of solar still with chimney is compared with that of conventional solar still. The study is carried out under the hot and climate conditions of Upper Egypt. A complete transient mathematical model of the physical model including the solar still regions temperatures, productivity, and heat transfer between the solar still and the exhaust gases are constructed. The mathematical model is solved numerically by using fourth-order Runge-Kutta method and is programmed by using MATLAB. The mathematical model is validated using an experimental work. The results show that the solar still saline water temperature increases and productivity with using and rising the exhaust gases. Furthermore, the impact of using exhaust gases on the still performance in winter is greater than in summer. using chimney exhaust gases at 75 °C and 125 °C enhances the daily freshwater yield of the conventional still by more than three times and about six times in winter, respectively, and about two and half times and more than three times in summer, respectively.

scholarly journals Dynamics of the mobile platform with four wheel drive

2019 ◽  
Vol 254 ◽  
pp. 03006
Author(s):  
Anna Jaskot ◽  
Bogdan Posiadała
Keyword(s):  
Theoretical Model ◽  
Mobile Platform ◽  
Kutta Method ◽  
Friction Forces ◽  
Runge Kutta Method ◽  
Wheel Drive ◽  
Motion Parameters ◽  
Simulation Results ◽  
Four Wheel Drive ◽  
Unsteady Conditions

The dynamics problem of motion of the mobile platform with four wheel drive under the unsteady conditions have been formulated and analysed. The mobile platform prototype have been equipped with four independently driven and steered electric drive units.The theoretical model have been formed for the proposed design concept of the platform. The relations between friction forces in longitudinal and transverse directions in reference to the active forces have been considered. The analysis of the motion parameters for different configurations of the wheel positions has been included. The formulated initial problem has been numerically solved by using the Runge-Kutta method of the fourth order. The sample simulation results for different configurations of the platform elements during its motion have been included and the conclusions have been formulated.

scholarly journals Analisis Kontrol Optimal Pada Model Matematika Penyebaran Pengguna Narkoba Dengan Faktor Edukasi

2020 ◽  
Vol 17 (2) ◽  
pp. 238-248
Author(s):  
Resmawan ◽  
M Eka ◽  
Nurwan ◽  
N Achmad
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Optimal Control ◽  
Drug Users ◽  
Minimum Principle ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Model Drug ◽  
And Control ◽  
The Mathematical Model

ABSTRACT This paper discusses the mathematical model of drug users with education. Optimal control theory was used on this model with education as a control to achieve the goal of minimizing the number of drug users. The optimal control problem was analyzed using Pontryagin’s minimum principle and performed numerical simulation by using a 4th-order Runge-Kutta method. Based on the numerical simulation, there was a change in the number in each population which caused the population with education to increase, and control with education resulted in the reduced number of drug users. Keywords: Optimal control; mathematical model; drug users; education   ABSTRAK Artikel ini membahas tentang model matematika penyebaran pengguna narkoba dengan faktor edukasi. Teori kontrol optimal diterapkan pada model ini dengan pemberian kontrol berupa edukasi dengan tujuan untuk meminimumkan jumlah pengguna narkoba. Kontrol optimal dianalisis menggunakan Prinsip Minimum Pontryagin dan dilakukan simulasi numerik dengan menggunakan metode Runge-Kutta orde 4. Berdasarkan simulasi diperoleh bahwa terjadi perubahan jumlah di tiap populasi dan mengakibatkan jumlah populasi dengan edukasi bertambah, serta pemberian kontrol dengan edukasi mengakibatkan jumlah pengguna narkoba berkurang. Kata kunci       : Kontrol optimal; model matematika; pengguna narkoba; edukasi

scholarly journals Modeling and Optimal Control on the Spread of Hantavirus Infection

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1192 ◽  
Author(s):  
Fauzi Mohamed Yusof ◽  
Farah Aini Abdullah ◽  
Ahmad Izani Md. Ismail
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control System ◽  
Maximum Principle ◽  
Optimal Control Theory ◽  
Necessary Condition ◽  
Hantavirus Infection ◽  
Kutta Method ◽  
Rodent Population ◽  
Runge Kutta Method

In this paper, optimal control theory is applied to a system of ordinary differential equations representing a hantavirus infection in rodent and alien populations. The effect of the optimal control in eliminating the rodent population that caused the hantavirus infection is investigated. In addition, Pontryagin’s maximum principle is used to obtain the necessary condition for the controls to be optimal. The Runge–Kutta method is then used to solve the proposed optimal control system. The findings from the optimal control problem suggest that the infection may be eradicated by implementing some controls for a certain period of time. This research concludes that the optimal control mathematical model is an effective method in reducing the number of infectious in a community and environment.

scholarly journals A Differential Algebraic Method to Approximate Nonsmooth Mechanical Systems by Ordinary Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Xiaogang Xiong ◽  
Ryo Kikuuwe ◽  
Motoji Yamamoto
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Dry Friction ◽  
Differential Inclusions ◽  
Mechanical Systems ◽  
Algebraic Method ◽  
Unilateral Contact ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Simulation Results

Nonsmooth mechanical systems, which are mechanical systems involving dry friction and rigid unilateral contact, are usually described as differential inclusions (DIs), that is, differential equations involving discontinuities. Those DIs may be approximated by ordinary differential equations (ODEs) by simply smoothing the discontinuities. Such approximations, however, can produce unrealistic behaviors because the discontinuous natures of the original DIs are lost. This paper presents a new algebraic procedure to approximate DIs describing nonsmooth mechanical systems by ODEs with preserving the discontinuities. The procedure is based on the fact that the DIs can be approximated by differential algebraic inclusions (DAIs), and thus they can be equivalently rewritten as ODEs. The procedure is illustrated by some examples of nonsmooth mechanical systems with simulation results obtained by the fourth-order Runge-Kutta method.

Research on Numerical Simulation of Quad Bundle Conductor on Galloping

2013 ◽  
Vol 457-458 ◽  
pp. 23-27
Author(s):  
Xue Ping Zhan ◽  
Kuan Jun Zhu ◽  
Cao Lan Liu ◽  
Bin Liu ◽  
Jun Zhang ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Finite Element ◽  
Numerical Results ◽  
Kutta Method ◽  
Aerodynamic Parameter ◽  
Runge Kutta Method ◽  
Simulation Results ◽  
Runge Kutta ◽  
Element Method

The models of the multi-bundled conductors are constructed by finite element method in this paper. The numerical results are given by using the 4th order Runge-Kutta method considering aerodynamic parameter of sub-conductor. The simulation results are obtained on galloping of quad bundle conductors with the different span. Thus some effective numerical results of quad twin bundle conductor can provide a useful reference for anti-galloping design.

Symmetric and symplectic methods for gyrocenter dynamics in time-independent magnetic fields

2016 ◽  
Vol 07 (02) ◽  
pp. 1650008 ◽  
Author(s):  
Beibei Zhu ◽  
Zhenxuan Hu ◽  
Yifa Tang ◽  
Ruili Zhang
Keyword(s):  
Numerical Simulation ◽  
Hamiltonian System ◽  
Second Order ◽  
Symplectic Methods ◽  
Kutta Method ◽  
Numerical Accuracy ◽  
Runge Kutta Method ◽  
Simulation Results ◽  
Runge Kutta

We apply a second-order symmetric Runge–Kutta method and a second-order symplectic Runge–Kutta method directly to the gyrocenter dynamics which can be expressed as a noncanonical Hamiltonian system. The numerical simulation results show the overwhelming superiorities of the two methods over a higher order nonsymmetric nonsymplectic Runge–Kutta method in long-term numerical accuracy and near energy conservation. Furthermore, they are much faster than the midpoint rule applied to the canonicalized system to reach given precision.

scholarly journals Comparison of Numerical Simulation of Epidemiological Model between Euler Method with 4th Order Runge Kutta Method

2021 ◽  
Vol 2 (1) ◽  
pp. 37-44
Author(s):  
Rizky Ashgi
Keyword(s):  
Numerical Simulation ◽  
Numerical Methods ◽  
Sir Model ◽  
Euler Method ◽  
Kutta Method ◽  
System Of Differential Equations ◽  
Runge Kutta Method ◽  
Global Pandemic ◽  
The World ◽  
Runge Kutta

Coronavirus Disease 2019 has become global pandemic in the world. Since its appearance, many researchers in world try to understand the disease, including mathematics researchers. In mathematics, many approaches are developed to study the disease. One of them is to understand the spreading of the disease by constructing an epidemiology model. In this approach, a system of differential equations is formed to understand the spread of the disease from a population. This is achieved by using the SIR model to solve the system, two numerical methods are used, namely Euler Method and 4th order Runge-Kutta. In this paper, we study the performance and comparison of both methods in solving the model. The result in this paper that in the running process of solving it turns out that using the euler method is faster than using the 4th order Runge-Kutta method and the differences of solutions between the two methods are large.

On the Dynamics of a Rotary Compressor: Part 1 — Mathematical Modeling

1993 ◽  
Author(s):  
Sisir K. Padhy
Keyword(s):  
Experimental Validation ◽  
Sensitivity Study ◽  
Solution Procedure ◽  
Rotary Compressor ◽  
Kutta Method ◽  
Air Conditioners ◽  
Runge Kutta Method ◽  
Bearing Dynamics ◽  
The Mathematical Model ◽  
Theoretical Results

Abstract The rotary compressor has been used in room air conditioners as well as in refrigerators for many years. Although a number of published papers has been reported on rotary compressor, in the area of dynamics only a few are found. In addition only one paper describes experimental validation with some agreement with theoretical results. Again the effect of various operating pressures and temperatures, rotational speed of shaft etc. is not fully covered in any published literature. The present paper analyzes the rotary compressor dynamics in detail. The mathematical model, the solution procedure using Runge-Kutta method, and the bearing dynamics are described. The second part of this papers describes the experimental validation and sensitivity study using different variables that affect the compressor dynamics.

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