scholarly journals KONTROL PENGOBATAN OPTIMAL PADA MODEL PENYEBARAN TUBERKULOSIS TIPE SEIT

2017 ◽  
Vol 6 (2) ◽  
pp. 137
Author(s):  
JONNER NAINGGOLAN
Keyword(s):  
Optimal Control ◽  
Optimal Control Theory ◽  
Infected Individual ◽  
Control Treatment ◽  
Kutta Method ◽  
Basic Reproduction Ratio ◽  
Reproduction Ratio ◽  
Tuberculosis Model ◽  
Runge Kutta Method ◽  
Number Of Individuals

A tuberculosis model of SEIT type which incorporates treatment of infectives is considered. The population is divided into four compartments, that is: S are individuals in the susceptible compartment, E are individuals in the exposed compartments, I are individuals in the infected compartment, and T are individuals in the treatment compartments. For this model, controls on treatment is incorporated to reduce the actively infected individual compartments, via application of the Pontryagins Maximum Principle of optimal control theory. Numerical calculations with the approach of the Runge-Kutta method of fourth order can be seen that, the influence of the control treatment to more effectively reduce the number of individuals in the infected compartment compared with no controls. The basic reproduction ratio with control less compared with no controls.

scholarly journals Optimal Control of the Lost to Follow Up in a Tuberculosis Model

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Yves Emvudu ◽  
Ramsès Demasse ◽  
Dany Djeudeu
Keyword(s):  
Optimal Control ◽  
Optimization Strategy ◽  
Basic Reproduction Ratio ◽  
Reproduction Ratio ◽  
Tb Control ◽  
New Class ◽  
Tuberculosis Model ◽  
African Context ◽  
Lost To Follow Up

This paper deals with the problem of optimal control for the transmission dynamics of tuberculosis (TB). A TB model that considers the existence of a new class (mainly in the African context) is considered: the lost to follow up individuals. Based on the model formulated and studied in the work of Plaire Tchinda Mouofo, (2009), the TB control is formulated and solved as an optimal control theory problem using the Pontryagin's maximum principle (Pontryagin et al., 1992). This control strategy indicates how the control of the lost to follow up class can considerably influence the basic reproduction ratio so as to reduce the number of lost to follow up. Numerical results show the performance of the optimization strategy.

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.

Controlling Asthma Due to Air Pollution

2020 ◽  
pp. 1-22
Author(s):  
Ankush H. Suthar ◽  
Purvi M. Pandya
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Air Pollution ◽  
Control Theory ◽  
Global Stability ◽  
Optimal Control Theory ◽  
Positive Impact ◽  
Equilibrium Points ◽  
Local And Global Stability ◽  
Number Of Individuals

The health of our respiratory systems is directly affected by the atmosphere. Nowadays, eruption of respiratory disease and malfunctioning of lung due to the presence of harmful particles in the air is one of the most sever challenge. In this chapter, association between air pollution-related respiratory diseases, namely dyspnea, cough, and asthma, is analysed by constructing a mathematical model. Local and global stability of the equilibrium points is proved. Optimal control theory is applied in the model to optimize stability of the model. Applied optimal control theory contains four control variables, among which first control helps to reduce number of individuals who are exposed to air pollutants and the remaining three controls help to reduce the spread and exacerbation of asthma. The positive impact of controls on the model and intensity of asthma under the influence of dyspnea and cough is observed graphically by simulating the model.

scholarly journals PEMODELAN MATEMATIKA DENGAN METODE RUNGE KUTTA UNTUK PENYAKIT CAMPAK MENGGUNAKAN MATLAB R2010a

2018 ◽  
Vol 4 (2) ◽  
Author(s):  
Ketut Queena Fredlina ◽  
Komang Tri Werthi
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Measles Virus ◽  
Immunization Coverage ◽  
Living Environment ◽  
Basic Reproduction Ratio ◽  
Reproduction Ratio ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
The Mathematical Model

ABSTRACT<br />Mathematical models have important roles in various fields of science. By using several assumptions, problems that exist in the living environment can be transformed in mathematical models. From the existing mathematical model, the parameters that affect the model can then be analyzed. An epidemic is an event that can be transformed into a mathematical model. Epidemic events are the occurrence of the spread or outbreak of an illness in a region. Measles is one of the causes of death in developing countries caused by the measles virus, the Paramixovirus group. In 1982 a measles immunization program in Indonesia was conducted. Based on data from the 2015 Ministry of Health, Indonesia has a medium immunization coverage in Southeast Asia, which is 84%. In 2020 Indonesia has a target rate of measles immunization coverage of 95%. Measles is a concern of the Bali Provincial Health Office because the spread of this disease is always high. Specifically in this study we will discuss mathematical models for the incidence of measles epidemics. The problem is how to construct the model and what parameters are the most significant influences in the mathematical model of measles. In making mathematical models for the spread of measles, the population is divided into 3 parts: Susceptible, Infectious, and Recovered. Furthermore, analyze the parameters and determine the basic reproduction ratio (𝑹𝟎), then numerical simulations were carried out using the Order 4 Runge Kutta method.<br />Keywords : Mathematics , Measles, basic reproduction ratio (𝑹𝟎), Runge-Kutta Methods<br />ABSTRAK<br />Model matematika memiliki peran yang cukup penting dalam berbagai bidang ilmu. Dengan menggunakan beberapa asumsi, permasalahan yang ada dalam lingkungan kehidupan dapat ditransformasikan dalam model matematika. Dari model matematika yang ada selanjutnya dapat dianalisis parameter-parameter yang mempengaruhi model tersebut. Kejadian epidemi merupakan salah satu kejadian yang dapat ditransformasikan dalam model matematika. Kejadian epidemi adalah kejadian penyebaran atau mewabahnya suatu penyakit dalam suatu wilayah. Penyakit campak merupakan salah satu penyakit penyebab kematian penduduk di negara-negara berkembang yang disebabkan oleh virus campak golongan Paramixovirus. Pada tahun 1982 program imunisasi campak di Indonesia telah dilakukan. Berdasarkan data dari Departemen Kesehatan 2015, Indonesia memiliki cakupan imunisasi kategori sedang di Asia Tenggara yakni 84%. Pada tahun 2020 Indonesia memiliki target angka cakupan imunisasi campak sebesar 95%. Penyakit campak menjadi perhatian Dinas Kesehatan Profinsi Bali karena penyebaran penyakit ini selalu ada. Secara khusus dalam penelitian ini akan membahas model matematika untuk kejadian epidemi penyakit campak. Yang menjadi permasalahan adalah bagaimana mengontruksi model dan parameter apakah yang berpengaruh paling signifikan dalam model matematika penyakit campak. Dalam pembuatan model matematika untuk penyebaran penyakit campak, populasi manusia dibagi menjadi 3 bagian yaitu : Susceptible, Infectious, dan Recovered. Selanjutnya menganalisis parameter dan menentukan nilai basic reproduction ratio (R0), kemudian dilakukan simulasi numerik dengan metode Runge Kutta Orde 4.<br />Kata kunci : model matematika, campak, basic reproduction ratio (𝑹𝟎),metode Runge-Kutta

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.

scholarly journals Modeling the Dynamics of an Epidemic under Vaccination in Two Interacting Populations

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Ibrahim H. I. Ahmed ◽  
Peter J. Witbooi ◽  
Kailash Patidar
Keyword(s):  
Optimal Control Theory ◽  
Equilibrium Points ◽  
Vaccination Strategy ◽  
Kutta Method ◽  
Sir Epidemic ◽  
Runge Kutta Method ◽  
Interacting Populations ◽  
Group Population ◽  
The Stability ◽  
Disease Free

We present a model for an SIR epidemic in a population consisting of two components—locals and migrants. We identify three equilibrium points and we analyse the stability of the disease free equilibrium. Then we apply optimal control theory to find an optimal vaccination strategy for this 2-group population in a very simple form. Finally we support our analysis by numerical simulation using the fourth order Runge-Kutta method.

Sign in / Sign up

Export Citation Format

Share Document