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"ABSTRAKPenyebaran HIV dapat dimodelkan dengan menggunakan pendekatan deterministik kedalam sistem persamaan diferensial biasa tidak linier berdimensi tujuh, pada skripsi ini dibuat model matematika penyebaran HIV dengan intervensi ART. Pada model sederhana yaitu ketika tidak dilakukan intervensi ART, titik keseimbangan bebas penyakit dan titik keseimbangan endemik dapat ditentukan secara analitik dengan basic reproduction number. Kriteria kestabilan lokal dari titik keseimbangan bebas penyakit dan titik keseimbangan endemik dapat dianalisis. Titik keseimbangan endemik ada ketika nilai basic reproduction number lebih besar dari satu. Berdasarkan analisis sensitivitas dari basic reproduction number pada model lengkap model dengan intervensi ART , dengan memperbesar laju intervensi ART pada manusia yang terinfeksi HIV akan menurunkan basic reproduction number. Simulasi numerik dilakukan untuk menganalisis pengaruh intervensi ART dalam mengurangi total manusia terinfeksi selama periode intervensi.

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ABSTRACTHIV spreads can be modeled using a deterministic approach into a seven dimensional nonlinear ordinary differential equation, in this thesis establish a mathematical model for the spread of HIV with an intervention of ART treatment. In a simplified model, when no ART treatment implemented, disease free and the endemic equilibrium points were established analytically along with the basic reproduction number. The local stability criteria of disease free equilibrium and the existing criteria of endemic equilibrium analyzed. The endemic equilibrium exists when basic reproduction number is larger than one. From the sensitivity analysis of basic reproduction number of the complete model model with ART treatment , the enlarging number of the infected human who following the ART treatment program will reduce basic reproduction number. The numerical simulation of the autonomous system to show how treatment intervention of ART impacts the reduction of the infected population during intervention time period."

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