Karunia, Rosa (2024) Penerapan Kontrol Optimal Pada Penyebaran Penyakit Leptospirosis Menggunakan Prinsip Minimum Pontryagin. Other thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Penyakit leptospirosis tergolong sebagai penyakit zoonosis atau penyakit yang bersumber dari hewan kemudian ditularkan ke manusia. Leptospirosis banyak tersebar di negara tropis, seperti Indonesia. Bakteri Leptospira merupakan penyebab utama dari penyakit ini. Bakteri Leptospira dapat berasal urin hewan terinfeksi penyakit leptospirosis. Hewan yang dapat menularkan diataranya hewan ternak, tikus, hewan peliharaan, dan sebagainya. Manusia dapat tertular leptospirosis apabila melakukan kontak dengan air atau lingkunagan yang telah tercemar bakteri Leptospira. Manusia dapat terpapar bakteri Leptospira melalui luka terbuka dan melalui makanan yang sudah tercemar. Leptospirosis dapat menyebabkan beberapa efek samping, dari mulai demam ringan hingga infeksi akut yang mengakibatkan kegagalan pada organ manusia. Jika sudah terjadi infeksi akut, maka bisa berakibat kematian. Penelitian ini mengembangkan model penyebaran penyakit leptospirosis dengan menambahkan kontrol berupa pembasmian tikus (u1) dan pengobatan pada manusia (u2). Model penyebaran penyakit leptospirosis yang dibahas adalah SIR-SI. Penyelesaian untuk kontrol optimal didapatkan dengan Prinsip Minimum Pontryagin serta untuk simulasi numeriknya dengan metode Runge Kutta Orde-4. Analisis model penyebaran penyakit leptospirosis dilakukan di titik kesetimbangan endemik dan bebas penyakit. Hasil analisis menunjukkan bahwa model stabil pada kedua titik kesetimbangan. Dan setelah diberikan kontrol, terbukti bahwa model dapat dikontrol. Setelah dilakukan simulasi, terbukti bahwa populasi vektor terinfeksi (Ir) menurun setelah ditambahkan kontrol u1. Kemudian populasi manusia terinfeksi (Ih) juga menurun setelah ditambahkan kontrol u2, sehingga berdampak kepada bertambahnya populasi manusia yang sembuh (Rh).
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Leptospirosis is classified as a zoonotic disease or a disease that originates from animals and is then transmitted to humans. This disease is widely spread in tropical countries, such as Indonesia. Leptospira bacteria are the main cause of this disease. Leptospira bacteria can come from the urine of animals that infected with leptospirosis. Animals that can Infects include livestock, rats, pets, and so on. Humans can get
leptospirosis disease if you interact with an environment contaminated with Leptospira bacteria. Leptospira bacteria can enter the human body through wounds open and through contaminated food. Leptospirosis can cause several side effects, ranging from mild fever to acute infections that result failure in human organs. If an acute infection has
occurred, it can have consequences death. This research develops a model for the spread of leptospirosis by adding control in the form of rat extermination (u1) and treatment
on human (u2). The mathematical model of the spread of leptospirosis that used is SIR-SI. Solution for optimal control using Pontryagin’s Minimum Principle and for numerical
simulations using the Runge Kutta Order-4. Analysis of the model for the spread of leptospirosis is carried out at the equilibrium point endemic and disease free. The analysis
results show that the model is stable at both equilibrium points. And after being given control, it was proven that the model could controlled. After carrying out the simulation,
it was proven that the population of infected vector(Ir) decreased after adding control u1. Then the population of infected human (Ih) as well decreased after adding the u2 control, resulting in an increase in population recovered humans (Rh).
Item Type: | Thesis (Other) |
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Uncontrolled Keywords: | Kontrol Optimal, Leptospirosis, Prinsip Minimum Pontryagin, Optimal Control, Pontryagin Minimum Principle. |
Subjects: | Q Science > QA Mathematics > QA372.B9 Differential equations--Numerical solutions. Runge-Kutta formulas--Data processing. Q Science > QA Mathematics > QA401 Mathematical models. Q Science > QA Mathematics > QA614.8 Differentiable dynamical systems |
Divisions: | Faculty of Mathematics, Computation, and Data Science > Mathematics > 44201-(S1) Undergraduate Thesis |
Depositing User: | Rosa Karunia |
Date Deposited: | 02 Aug 2024 04:19 |
Last Modified: | 02 Aug 2024 04:19 |
URI: | http://repository.its.ac.id/id/eprint/109811 |
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