ABSTRAK ANALISIS MODEL DINAMIK INFEKSI HIV SEL

ABSTRAK
ANALISIS MODEL DINAMIK INFEKSI HIV SEL
LANGERHANS DAN SEL T CD4+ MELALUI MUKOSA
SELAMA INFEKSI HIV-1 AWAL
Oleh
Sutimin
NIM: 30111012
(Program Studi Doktor Matematika)
Infeksi HIV melalui hubungan seksual menyerang sel-sel target awal di mukosa
genital, yaitu sel Langerhans dan sel T CD4+ . Pada tahap infeksi HIV-1 awal terjadi
respon yang kuat sel-sel Langerhans dan T CD4+ terhadap patogen HIV, dan terjadi
peningkatan penyebaran virus oleh sel-sel Langerhans dan T CD4+ menuju infeksi
sistemik.
Penelitian ini membangun suatu model matematika yang menjelaskan infeksi HIV
sel-sel Langerhans dan T CD4+ dan implikasinya terhadap dinamika infeksi HIV-1
awal. Studi selanjutnya mengembangan model dengan menggabungkan efek terapi
antiretroviral kombinasi RTI (reverse transcriptase inhibitors) dan PI (protease
inhibitors), berdasarkan konsep farmakokinetik obat di dalam tubuh.
Analisis model dilakukan untuk menunjukkan eksistensi solusi tak negatif dan
terbatas. Analisis model mengungkap parameter rasio yang menentukan tingkat
keendemikan infeksi HIV-1 dinyatakan oleh rasio reproduksi alternatif, <1 , yang
ekivalen dengan rasio reproduksi dasar <0 . Analisis perilaku kestabilan titik
equilibrium dinyatakan dalam <1 . Perilaku keendemikan infeksi HIV dianalisis
melalui <1 terhadap efek laju kematian lisis pada sel T CD4+ dan terhadap efek
pengobatan kombinasi RTI dan PI.
Hasil studi menyatakan bahwa peningkatan laju kematian lisis sel T CD4+
menaikan tingkat infeksi HIV-1. Pengobatan antiretroviral pada individu terinfeksi
HIV-1 lebih efektif jika dilakukan dengan terapi kombinasi obat RTI dan PI. Faktor
ketidakpatuhan dalam berobat dan resitensi obat menyebabkan peningkatan jumlah
virus.
Kata Kunci: HIV-1, rasio reproduksi alternatif, sel Langerhans, sel T CD4+ , RTI,
PI.
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ABSTRACT
ANALYSIS OF DYNAMICAL MODEL OF LANGERHANS
AND CD4+ T CELLS HIV INFECTION THROUGH MUCOSA
DURING EARLY HIV-1 INFECTION
by
Sutimin
NIM: 30111012
(Doctoral Study Program of Mathematics)
HIV infection through sexual intercourse attacks target cells in the genital mucosa,
namely Langerhans cells and CD4+ T cells. At the stage of early HIV-1 infection,
strong response of Langerhans cells and CD4+ T occurs against pathogens HIV,
and the increase in the spread of the virus by the Langerhans cells and CD4+ T
leads to the systemic infection.
A mathematical model that captures the infection of Langerhans cells and CD4+ T
cells and its implication to early HIV infection within the host is developed. The
model is developed to explain the effects of the combined RTI (reverse transcriptase
inhibitors) and PI (protease inhibitors) therapy based on drug pharmacokinetics
model.
The existence of non-negative and boundedness solutions is analyzed. Mathematical analysis reveals alternative basic reproduction ratio, <1 , a ratio parameter
that represents the endemicity of HIV-1 infection, which is equivalent to the
biological basic reproduction ratio <0 . The stability of the equilibrium points is
analyzed with respect to <1 . The endemic behavior is also analyzed from <1 with
respect to viral lysis in cells T CD4+ and the effect of RTI and PI treatments.
The results suggest that the increase of the lysis death rate of CD4+ T cells is
associated with the increase of progression of HIV infection. The effectiveness of
the treatments requires a combination of RTI and PI therapy, other results show
that imperfect adherence and drugs resistance lead to an increase in viral load in
the absence of virus mutation.
Keywords: HIV-1, alternative reproduction ratio, Langerhans, T CD4+ cells, RTI,
PI.
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