Analisis Kestabilan dan Kontrol Optimal pada Model Dinamik Penyebaran Penyakit Malaria

Purwanti, Retna Shely (2019) Analisis Kestabilan dan Kontrol Optimal pada Model Dinamik Penyebaran Penyakit Malaria. Undergraduate thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

suatu penyakit yang disebabkan oleh parasit Plasmodium yang ditularkan oleh gigitan nyamuk Anopheles betina. Hampir separuh populasi dunia hidup dalam risiko penyakit ini dengan lebih dari 300 juta orang terjangkit malaria setiap tahun. Dalam tugas akhir ini, digunakan model penyebaran penyakit malaria yang terdiri dari dua populasi. Populasi tersebut dibagi menjadi beberapa sub-populasi antara lain sub-populasi manusia Susceptible, sub-populasi manusia Exposed, sub-populasi manusia Infected, sub-populasi manusia Recovered, sub-populasi nyamuk Susceptible, sub-populasi nyamuk Exposed, dan sub-populasi nyamuk Infected. Model penyebaran penyakit malaria dianalisis kestabilannya dengan menentukan titik kesetimbangan bebas penyakit dan endemik, yang selanjutnya dicari kestabilan dari setiap titik kesetimbangan. Model penyebaran penyakit malaria dengan kontrol optimal dari Prinsip Maksimum Pontryagin agar dapat meminimumkan sub-populasi manusia dan sub-populasi nyamuk yang terinfeksi. Selanjutnya disimulasikan dengan menggunakan Matlab. Hasil simulasi menunjukan menurunnya sub-populasi manusia dan populasi nyamuk yang terinfeksi parasit Plasmodium setelah adanya pemberian kontrol penyemprotan insektisida dan pengobatan.
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Malaria is a disease caused by the Plasmodium parasite which is transmitted by the bite of a female Anopheles mosquito. Nearly half of the world's population lives at risk of this disease with more than 300 million people contracting malaria every year. In this final project, the model of the spread of malaria is used which consists of two populations. The population is divided into several sub-populations including the Susceptible human, sub-population, the human sub-population Exposed, the human sub-population Infected, the Recovered human sub-population, the Susceptible mosquito sub-population, the Exposed mosquito sub-population, and the sub-population Infected mosquitoes. The model of the spread of malaria is analyzed for its stability by determining disease-free and endemic equilibrium points, which then look for stability from each equilibrium point. The model of the spread of malaria with optimal control of Pontryagin's Maximum Principle in order to minimize the human sub-population and sub-populations of infected mosquitoes. Then simulated using Matlab. The simulation results show a decrease in the human sub-population and the population of mosquitoes infected with the Plasmodium parasite after giving control of insecticide spraying and treatment.

Item Type:	Thesis (Undergraduate)
Additional Information:	RSMa 616.979 2 Pur a-1 2019
Uncontrolled Keywords:	Model penyebaran penyakit malaria, Kestabilan, Kontrol Optimal, Prinsip Maksimum Pontryagin
Subjects:	Q Science Q Science > QA Mathematics > QA402 System analysis.
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	RETNA SHELY PURWANTI
Date Deposited:	13 Dec 2021 08:21
Last Modified:	13 Dec 2021 08:21
URI:	http://repository.its.ac.id/id/eprint/61827

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