Kontrol Optimal Penyebaran Bakteri Patogen Menggunakan Prinsip Minimum Pontryagin

Dwiningrum, Desy Wahyu (2021) Kontrol Optimal Penyebaran Bakteri Patogen Menggunakan Prinsip Minimum Pontryagin. Undergraduate thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Kualitas lingkungan yang kurang baik memicu mikroorganisme untuk bermutasi, salah satunya yaitu bakteri. Bakteri dapat bertahan dan tumbuh dalam jumlah besar pada kondisi lingkungan yang buruk, seperti air yang tercemar. Kurangnya kesadaran menjaga lingkungan dapat menjadi salah satu faktor akan munculnya bibit penyakit. Sebagian penyakit dapat ditularkan melalui beberapa media, salah satunya air. Penyakit yang dapat ditularkan penyebarannya melalui media air diantaranya diare, kolera, disentri, dan demam tifoid/tifus. Penyebaran penyakit tersebut disebabkan oleh adanya bakteri patogen. Jika penyakit dianggap remeh dan tidak mendapatkan penanganan yang tepat maka dapat mengakibatkan kematian. Salah satu contohnya diare, yang menjadi penyebab utama kasus kematian anak di Indonesia. Oleh karena itu, diperlukan langkah-langkah pengendalian guna menurunkan laju penyebaran bakteri patogen. Dalam Tugas Akhir ini, digunakan model matematika yang terbentuk dari adanya interaksi antara sub-populasi manusia Suspectible dan sub-populasi manusia Infected dengan mempertimbangkan kepadatan konsentrasi bakteri patogen. Dari model tersebut dimodifikasi dengan menambahkan dua variabel kontrol untuk mengurangi banyaknya individu infected. Kemudian dilakukan pembentukan desain kontrol optimal menggunakan Prinsip Minimum Pontryagin dan diselesaikan secara numerik dengan metode Runge Kutta Orde 4. Input kontrol yang digunakan merepresentasikan tindakan pencegahan berupa sanitasi dan pengobatan individu infected. Hasil simulasi numerik menunjukkan bahwa dengan pemberian kontrol pengobatan efektif untuk mengoptimalkan jumlah manusia yang terinfeksi bakteri patogen, karena angka yang dihasilkan mendekati nol di akhir hari ke-30, artinya hampir tidak didapati individu infected dalam populasi tersebut. ==================================================================================================================== Poor environmental quality triggers microorganisms to mutate, one of which is bacteria. Bacteria can survive and grow in large quantities in poor environmental conditions, such as polluted water. Lack of awareness of protecting the environment can be one of the factors in the emergence of disease seeds. Some diseases can be transmitted through several media, one of which is water. Diseases that can be transmitted through water media include diarrhea, cholera, dysentery, and typhoid. The spread of the disease is caused by the presence of pathogenic bacteria. If the disease is underestimated and does not get proper treatment then it can result in death. One example is diarrhea, which is the cause of child death in Indonesia. Therefore, control measures are needed to reduce the rate of spread of pathogenic bacteria. In this Final Project, a mathematical model is used that is formed from the interaction between the Suspectible human sub-population and the Infected human sub-population taking into account the density of the concentration of pathogenic bacteria. The model was modified by adding two control variables to reduce the number of individuals. Then the formation of the optimal control design using the Minimum Pontryagin Principle and completed numerically with the Runge Kutta Orde 4 method. The control input used represents preventive measures in the form of sanitation and treatment of infected individuals. Numerical simulation results show that by administering effective treatment controls to optimize the number of humans infected with pathogenic bacteria, as the resulting number is close to zero at the end of the 30th day, meaning that there are hardly any individuals infected in the population.

Item Type: Thesis (Undergraduate)
Uncontrolled Keywords: Bakteri Patogen, Kontrol Optimal, Prinsip Minimum Pontryagin, Runge Kutta, Pathogenic Bacteria, Optimal Control, Minimum Pontryagin Principle, Runge Kutta
Subjects: Q Science > QA Mathematics > QA278.3 Structural equation modeling.
Q Science > QA Mathematics > QA371 Differential equations--Numerical solutions
Q Science > QA Mathematics > QA372.B9 Differential equations--Numerical solutions. Runge-Kutta formulas--Data processing.
Q Science > QA Mathematics > QA614.8 Differentiable dynamical systems
Divisions: Faculty of Mathematics and Science > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User: Desy Wahyu Dwiningrum
Date Deposited: 30 Aug 2021 02:05
Last Modified: 30 Aug 2021 02:05
URI: https://repository.its.ac.id/id/eprint/90530

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