Pemodelan Matematika Penyebaran Penyakit Co-Infection HIV/AIDS dan Skabies Krustosa

Nisa', Kholishun (2019) Pemodelan Matematika Penyebaran Penyakit Co-Infection HIV/AIDS dan Skabies Krustosa. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Human Immunodeficiency Virus (HIV) merupakan virus yang menginfeksi sel darah putih yang menyebabkan turunnya sistem kekebalan tubuh manusia. Seseorang yang telah terinfeksi HIV akan lebih mudah terserang penyakit, bakteri, virus, dan infeksi lainnya, salah satunya yaitu penyakit Skabies Krustosa yang merupakan salah satu jenis Skabies yang berat, penyakit kulit tersebut terjadi akibat poliferasi tungau Sarcoptes Scabiei var. Hominis di kulit secara tidak terkontrol. Co-infection antara HIV/AIDS dan Skabies Krustosa terjadi ketika HIV/AIDS dan Skabies Krustosa menginfeksi manusia secara bersamaan. Pada tugas akhir dibahas analisis model matematika penyebaran penyakit co-infection HIV/AIDS dan Skabies Krustosa. Berdasarkan hasil analisis model didapatkan 4 titik setimbang, yaitu titik setimbang non endemik (E0), endemik HIV/AIDS (E0)1, endemik Skabies Krustosa (E0)2, dan endemik co-infection HIV/AIDS-Skabies Krustosa (E0)3. Dengan menggunakan metode Next Generation Matrix (NGM) diperoleh dua nilai bilangan reproduksi dasar, yaitu bilangan reproduksi dasar penyebaran penyakit HIV/AIDS (R0H) dan bilangan reproduksi dasar penyebaran penyakit Skabies Krustosa (R0S). Analisa kestabilan di sekitar 4 titik setimbang tersebut antara lain: titik setimbang non endemik stabil asimtotis lokal jika R0H<1 dan R0S<1, titik setimbang endemik HIV/AIDS stabil asimtotis lokal jika R0H>1 dan R0S<1, titik setimbang endemik Skabies Krustosa stabil asimtotis jika R0H<1 dan R0S>1, dan titik setimbang endemik co-infection HIV/AIDS-Skabies Krustosa jika R0H>1 dan R0S>1. Berdasarkan hasil simulasi numerik, diperoleh hasil bahwa faktor yang paling berpengaruh dalam dinamika penyebaran penyakit co-infection HIV/AIDS dan Skabies Krustosa adalah rate pengobatan penyakit AIDS dan peluang kesembuhan penyakit HIV setelah menjalani pengobatan.
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Human Immunodeficiency Virus (HIV) is a virus that infects white blood cells which causes a decrease in the human immune system.Someone who has been infected with HIV will be more easily to infected with virus, bacterial, and another disease. One of them is Crusted Scabies which is one of the most severe types of Scabies that occurs due to uncontrolled proliferation of Sarcoptes Scabiei var. mites on the skin. HIV/AIDS and Crusted Scabies co-infection occurs when HIV/AIDS and Crusted Scabies infect humans simultaneously. In this final project, we discuss a mathematical model of spreading HIV/AIDS and Crusted Scabies co-infection disease. Based on the analytical result of the model, there are four equilibrium, namely disease-free equilibrium (E0), HIV/AIDS endemic equilibrium (E0)1, Crusted Scabies endemic equilibrium (E0)2, and HIV/AIDS-Crusted Scabies co-infection endemic equilibrium (E0)3. By the Next Generation Matrix (NGM) method, we obtain two basic reproduction Numbers, that is basic reproduction number for spreading of HIV/AIDS (R0H) and basic reproduction number for spreading of Crusted Scabies (R0S). Stability analysis around four equilibrium points are (E0) equilibrium point is local asymptotically stable if R0H<1 and R0S<1.(E0)1 equilibrium point is exist and disposed to local asymptotically stable if R0H>1 and R0S<1.(E0)2 equilibrium point is exist and disposed to local asymptotically stable if R0H<1 and R0S>1.(E0)3 equilibrium point is exist and disposed to local asymptotically stable if R0H>1 and R0S>1. Then, the numerical simulation results show that the most influential factors for spreading of HIV/AIDS and Crusted Scabies co-infection disease are AIDS treatment rate and chance of healing for HIV after treatment.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Model Matematika, HIV/AIDS, Skabies Krustosa, Co-infection, Kestabilan
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA278.3 Structural equation modeling. Q Science > QA Mathematics > QA402 System analysis.
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	Kholishun Nisa'
Date Deposited:	10 Aug 2026 02:13
Last Modified:	10 Aug 2026 02:13
URI:	http://repository.its.ac.id/id/eprint/66274

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