Model matematika pada interaksi virus HIV-1 dan respon sel CD4+T

Prihatno, Imam (2019) Model matematika pada interaksi virus HIV-1 dan respon sel CD4+T. Diploma thesis, UIN Sunan Gunung Djati Bandung.

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Abstract

Virus HIV merupakan masalah penting dalam kehidupan karena mempunyai dampak yang buruk untuk kesehatan masyarakat. Virus HIV dapat ditularkan melalui hubungan seksual, penggunaan jarum suntik, serta seorang ibu yang menderita HIV. Upaya pencegahan yang berkelanjutan tidak dapat mengurangi jumlah orang yang menderita HIV dari tahun ke tahun yang selalu meningkat. Dalam tugas akhir ini, penyebaran HIV dinyatakan dalam bentuk model matematika dengan berfokus pada interaksi virus HIV dan respon sel CD4+T. Model telah dibangun sebagai sistem persamaan diferensial nonlinier. Eksistensi dan kestabilan titik equilibrium dianalisis secara lokal dengan melihat tanda nilai eigen dari matriks Jacobi dari sistem persamaan diferensial nonlinier yang telah dibangun. Kriteria Routh-Hurwitz juga digunakan dalam analisis kestabilan pada titik equilibrium endemik karena nilai eigen yang kompleks dari matriks Jacobi. Nilai ambang atau disebut juga sebagai Basic Reproduction Number (R0) diperoleh dengan menggunakan teori next generation matrix. Pengaruh dalam mengubah nilai parameter pada solusi juga dianalisis setiap saat menggunakan metode analisis sensitivitas lokal. Pada akhirnya, simulasi numerik dilakukan sebagai konfirmasi hasil analisis serta interpretasi biologis. The HIV virus is an important problem in life because it has a bad impact on public health. The HIV virus can be transmitted through sexual intercourse, the use of syringes, and a mother with HIV. Continued prevention efforts cannot reduce the number of people with HIV disease from year to year which is always increasing. In this paper, the spread of HIV is expressed in the form of a mathematical model by focusing on the interaction of the HIV virus and the CD4+T cells response.The model has been built as a nonlinear system of differential equations. The existence and stability of equilibrium points are analyzed locally by looking at the eigenvalue sign from the Jacobi matrix of the nonlinear system of differential equations that have been constructed. The Routh Hurwitz criteria are also used in the stability analysis at the endemic equilibrium point due to the complexity of the eigenvalues of the Jacobi matrix. The threshold value or commonly referred to as the Basic reproduction number is obtained using the theory of the next generation matrix. The effect of changing the parameter values on the solution is also analyzed at all times using the local sensitivity analysis method. Finally, numerical simulations are carried out as confirmation of analytical results as well as biological interpretations.

Item Type: Thesis (Diploma)
Uncontrolled Keywords: HIV (Human Immunodeficiency Virus); Sel CD4+T; Model Matematika; Fungsi Respon Holling; Sistem Persamaan Diferensial; Titik Equilibrium; Next Generation Matrix (NGM); Nilai Eigen; Kestabilan; Kriteria Kestabilan Routh-Hurwitz; Metode Runge-Kutta
Subjects: Mathematics > Data Processing and Analysis of Mathematics
Mathematics > Dictionaries and Encyclopedia of Mathematics
Analysis, Theory of Functions > Differential Calculus and Equations
Diseases > Diseases of Immune System
Divisions: Fakultas Sains dan Teknologi > Program Studi Matematika
Depositing User: Imam Prihatno
Date Deposited: 15 Nov 2019 03:25
Last Modified: 15 Nov 2019 03:25
URI: http://digilib.uinsgd.ac.id/id/eprint/26362

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