Analisis Model Stokastik Birth-Death pada Populasi Bakteri Esherichia coli dengan Kematian di Bawah Tekanan Antibiotik
DOI:
https://doi.org/10.31004/innovative.v5i3.19442Keywords:
Birth-Death, Escherichia coli, Minimum Inhibitory Concentration (MIC), Populasi BakteriAbstract
Penelitian membahas model stokastik dinamika populasi bakteri Escherichia coli pada kondisi tekanan antibiotik, khususnya pada konsentrasi Minimum Inhibitory Concentration (MIC), menggunakan proses birth-death linier sebagai kerangka dasar. Dinamika sistem dianalisis melalui master equation untuk memperoleh distribusi probabilitas waktu-ke-waktu, distribusi stasioner, serta waktu rata-rata kepunahan (Mean Time to Extinction) dan probabilitas first-passage time. Pendekatan stokastik mengintegrasikan model berbasis widget pada tingkat sel individu, di mana setiap sel direpresentasikan sebagai unit molekuler minimum. Ketika jumlah widget mencapai ambang batas, sistem mengalami kematian atau pembelahan, masing-masing dengan distribusi binomial simetris. Analisis dilakukan secara teoritis melalui simulasi Monte Carlo berbasis Python. Hasil menunjukkan bahwa meskipun rata-rata populasi tampak stasioner pada kondisi, sistem mengalami fluktuasi stokastik signifikan yang memicu aktivitas mikroskopik intens. Varians populasi meningkat terhadap waktu, menandakan instabilitas tersembunyi. Simulasi menunjukkan bahwa waktu rata-rata kepunahan meningkat subeksponensial terhadap ukuran populasi awal.
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Copyright (c) 2025 Farhan Anshari, Puspa Arinda Ginting, Anggi Pasha Aritonang, Elizabeth Hutasoit, Oliver Juan Gery Manihuruk, Sudianto Manullang, Alvi Sahrin Nasution
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