scholarly journals Kontrol Optimal pada Model Epidemik SIR Penyakit Demam Berdarah

2018 ◽  
Vol 4 (2) ◽  
pp. 110
Author(s):  
Katrina Pareallo ◽  
Wahidah Sanusi ◽  
Syafruddin Side
Keyword(s):  
Optimal Control ◽  
Yellow Fever ◽  
Aedes Albopictus ◽  
Minimum Principle ◽  
Sir Model ◽  
Distribution Model ◽  
Control Factor ◽  
System Of Differential Equations ◽  
Dengue Vaccine ◽  
Result Analysis

This study discusses about the optimal control on dengue fever distribution model using the minimum principle of Pontryagin. Dengue is a disease caused by dengue virus it transmitted by the female mosquitos species, namely Aedes aegeypti and Aedes Albopictus. Thus disease cause death if not treated seriously. The disease can be prevented by vaccine, called Chimeric Yellow Fever 17D-Tetravalent Dengue Vaccine(CYD-TDV).  The discussion starts from determining the SIR model using the controls, determining the optimal control using the minimum principle of Pontryagin , the simulation using Maple software and the result analysis. In this study obtained the system of differential equations, optimal control equations, and graphs of the SIR model without using controls and using the control. Based on the results obtained concluded that by adding control factor to SIR model can minimize the number of infected individuals.

scholarly journals Kontrol Optimal Upaya Pengobatan Penyakit Campak Menggunakan Model Endemi SIR

2019 ◽  
Vol 9 (2) ◽  
pp. 94
Author(s):  
Ida Ayu Putu Ari Utari
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Minimum Principle ◽  
System Of Differential Equations ◽  
Pontryagin Minimum Principle ◽  
Main Target ◽  
Model Determination ◽  
Efficiency Rate

Measles is an acute highly contagious disease caused by Paramyxovirus. Measles is considered as a dangerous disease because it cause complications, brain and other organs damage, lifelong disability, paralysis and even death. In the previous studies, it was known that the spread of measles highly dependent on number of infected individuals so it is necessary to control measles through treatment. In this paper, we study about the application of the optimal control theory on the system of differential equations of the SIR endemic model. Determination of the optimal control is obtained through the application of the Pontryagin minimum principle. The main target in this paper is to find a unique optimal control where the optimal control can be described as an efficiency rate of treatment in individuals infected with measles to decrease the number of infected individuals.

Pontryagin maximum principle and second order optimality conditions for optimal control problems governed by 2D nonlocal Cahn–Hilliard–Navier–Stokes equations

Analysis ◽  
2020 ◽  
Vol 40 (3) ◽  
pp. 127-150
Author(s):  
Tania Biswas ◽  
Sheetal Dharmatti ◽  
Manil T. Mohan
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stokes Equations ◽  
Minimum Principle ◽  
Immiscible Fluids ◽  
Second Order ◽  
Navier Stokes ◽  
Distributed Optimal Control ◽  
Navier Stokes Equations

AbstractIn this paper, we formulate a distributed optimal control problem related to the evolution of two isothermal, incompressible, immiscible fluids in a two-dimensional bounded domain. The distributed optimal control problem is framed as the minimization of a suitable cost functional subject to the controlled nonlocal Cahn–Hilliard–Navier–Stokes equations. We describe the first order necessary conditions of optimality via the Pontryagin minimum principle and prove second order necessary and sufficient conditions of optimality for the problem.

scholarly journals SIR Model for Dengue Disease with Effect of Dengue Vaccination

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Pratchaya Chanprasopchai ◽  
I. Ming Tang ◽  
Puntani Pongsumpun
Keyword(s):  
Mathematical Model ◽  
Mortality Rate ◽  
Dengue Virus ◽  
Numerical Solutions ◽  
Specific Treatment ◽  
Sir Model ◽  
Dengue Vaccine ◽  
Dengue Disease ◽  
Modelling Methods

The dengue disease is caused by dengue virus, and there is no specific treatment. The medical care by experienced physicians and nurses will save life and will lower the mortality rate. A dengue vaccine to control the disease is available in Thailand since late 2016. A mathematical model would be an important way to analyze the effects of the vaccination on the transmission of the disease. We have formulated an SIR (susceptible-infected-recovered) model of the transmission of the disease which includes the effect of vaccination and used standard dynamical modelling methods to analyze the effects. The equilibrium states and their stabilities are investigated. The trajectories of the numerical solutions plotted into the 2D planes and 3D spaces are presented. The main contribution is determining the role of dengue vaccination in the model. From the analysis, we find that there is a significant reduction in the total hospitalization time needed to treat the illness.

scholarly journals Safety Follow-up of a Dengue Vaccine When Administered Concomitantly with a Yellow Fever Vaccine in Healthy Toddlers in Colombia

2018 ◽  
Vol 37 (11) ◽  
pp. 1190-1191 ◽  
Author(s):  
Margarita Cortés ◽  
Pio López ◽  
Viviana Márquez ◽  
Carlos Cortes ◽  
Elizabeth Toro ◽  
...  
Keyword(s):  
Yellow Fever ◽  
Yellow Fever Vaccine ◽  
Dengue Vaccine

scholarly journals Optimal Control of a Dengue-Dengvaxia Model: Comparison Between Vaccination and Vector Control

2021 ◽  
Vol 9 (1) ◽  
pp. 198-212
Author(s):  
Cheryl Q. Mentuda
Keyword(s):  
Optimal Control ◽  
Vector Control ◽  
Basic Reproduction Number ◽  
Human Population ◽  
Model Comparison ◽  
Reproduction Number ◽  
Control Strategies ◽  
Minimum Principle ◽  
Transmitted Disease ◽  
The Basic Reproduction Number

Abstract Dengue is the most common mosquito-borne viral infection transmitted disease. It is due to the four types of viruses (DENV-1, DENV-2, DENV-3, DENV-4), which transmit through the bite of infected Aedes aegypti and Aedes albopictus female mosquitoes during the daytime. The first globally commercialized vaccine is Dengvaxia, also known as the CYD-TDV vaccine, manufactured by Sanofi Pasteur. This paper presents a Ross-type epidemic model to describe the vaccine interaction between humans and mosquitoes using an entomological mosquito growth population and constant human population. After establishing the basic reproduction number ℛ0, we present three control strategies: vaccination, vector control, and the combination of vaccination and vector control. We use Pontryagin’s minimum principle to characterize optimal control and apply numerical simulations to determine which strategies best suit each compartment. Results show that vector control requires shorter time applications in minimizing mosquito populations. Whereas vaccinating the primary susceptible human population requires a shorter time compared to the secondary susceptible human.

scholarly journals Application and benchmarking of a direct method to optimize the fuel consumption of a diesel electric locomotive

2018 ◽  
Vol 232 (9) ◽  
pp. 2272-2289 ◽  
Author(s):  
V Macian ◽  
C Guardiola ◽  
B Pla ◽  
A Reig
Keyword(s):  
Optimal Control ◽  
Direct Method ◽  
Minimum Principle ◽  
Optimization Technique ◽  
Direct Methods ◽  
Optimization Methods ◽  
Computational Time ◽  
Electric Locomotive ◽  
Pontryagin Minimum Principle ◽  
A Direct Method

This paper addresses the optimal control of a long-haul passenger train to deliver minimum-fuel operations. Contrary to the common Pontryagin minimum principle approach in railroad-related literature, this work addresses this optimal control problem with a direct method of optimization, the use of which is still marginal in this field. The implementation of a particular direct method based on the Euler collocation scheme and its transcription into a nonlinear problem are described in detail. In this paper, this optimization technique is benchmarked with well-known optimization methods in the literature, namely dynamic programming and the Pontryagin minimum principle, by simulating a real route. The results showed that the direct methods are on the same level of optimality compared with other algorithms while requiring reduced computational time and memory and being able to handle very complex dynamic systems. The performance of the direct method is also compared to the real trajectory followed by the train operator and exhibits up to 20% of fuel saving in the example route.

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