Rabu, 18 Maret 2020 - 06:15:16 WIB

Lockdown dan Corona

Diposting oleh : Administrator
Kategori: Nasional - Dibaca: 1103 kali

[suluh.co.id] Jakarta, 18 Maret 2020

 

Kalau kita tidak serius, puncak COVID-19 di Indonesia bisa sekitar 2 bulan lagi, di bulan Ramadan
=================
 
Versi PDF dari post ini ada di web http://hadisusanto.net/paper2/covid19.pdf
 
Kemarin senior saya, Mbak Nuning Nuraini, dan tim (Kamal Khairudin dan Kang Apri) [1], melaporkan penelitian mereka yang langsung viral. Menggunakan metode pencocokan kurva (curve fitting), Mbak Nuning dkk. menemukan kalau data lapangan di Indonesia yang ada saat ini cocok dengan dinamika pertambahan infeksi di awal-awal outbreak corona di Korea Selatan. Dengan menggunakan kurva yang dicocokkan tadi, Mbak Nuning dkk mengekstrapolasi kalau puncak penyakit Corona di Indonesia akan terjadi di akhir bulan ini. Sekitar 15 hari lagi. Karena menggunakan curve fitting, artinya prediksi ini berkaitan dengan asumsi penting bahwa pemerintah Indonesia akan melakukan tindakan pencegahan dengan efektivitas yang serupa dengan yang dilakukan pemerintah Korea Selatan. Mbak Nuning dkk. mengambil posisi optimis.
 
Beberapa hari yang lalu, saya juga membuat hitung-hitungan sederhana. Tapi saya berada pada posisi pesimis. Saya mengasumsikan pemerintah me-lockdown satu daerah pandemik, tapi orang-orangnya masih berinteraksi seperti biasa: masih bisa pergi ke Puncak rame-rame, nonton bioskop, rapat akbar, dll. Saya menggunakan populasi Jakarta (~10 juta penduduk) dan mengasumsikan data kasus di Indonesia saat ini semuanya dari Jakarta.
 
Seperti tulisan di post saya sebelumnya, saya menggunakan model SI: hanya ada proporsi orang sehat (S) dan proporsi orang terinfeksi (I). Perpindahan dari kelompok sehat ke kelompok terinfeksi hanya lewat interaksi dengan efektivitas alpha. Dengan demikian model matematikanya adalah
 
S_t=-alpha*S*I … (1)
I_t=+alpha*S*I … (2).
 
Detil perhitungan ada di kotretan terlampir.
 
Dari [2], pada 2/3/2020, yang saya jadikan saat t=0, terdapat 2 orang terinfeksi. Berarti I(0)=2/10^7.
 
Dari [2], pada 15/3/2020, yaitu t=13, terdapat total 117 orang terinfeksi. Berarti I(13)=117/10^7.
 
Mengikuti detil hitungan seperti di kotretan, saya dapatkan alpha=0.313.
 
Berikutnya kita integralkan model (1)-(2). Perbandingan hasil simulasi dan data kasus lapangan untuk waktu antara t=0 sampai t=13 terlampir.
 
Selanjutnya saya plot hasil simulasi (1) dan (2) untuk waktu yang lebih lama seperti di gambar terlampir dan saya dapatkan puncak dI/dt ada di sekitar 50 hari sejak 2 Maret 2020. Berarti di bulan Ramadan. :(
 
Prediksi ini dengan asumsi “lockdown”, yang saya artikan orang luar tidak bisa masuk dan orang dalam tidak bisa keluar. Kalau tidak lockdown, model (1)-(2) menjadi:
 
S_t=M-alpha*S*I … (3)
I_t=+alpha*S*I … (4),
 
dengan M banyaknya pertambahan orang masuk ke dalam. Kalau seperti ini, pandemik tidak ada puncaknya, alias jumlah orang sakit akan naik terus!
 
Ini prediksi pesimistis saya dengan model matematika yang sangat sederhana. Dan tentu saja saya berharap saya salah total.
 
Btw, bersama Mbak Nuning, kami sedang mencoba membuat model yang lebih representatif dengan memperhitungkan, misalnya, faktor interfensi dari pemerintah.
 
Referensi:
 
 
 
 
 
 
 
 
 
Hadi Susanto - FB



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Isi Komentar :
  • Hari ini 12 juni, tahun 1964 Nelson Mandela divonis penjara seumur hidup
  • Concorde melakukan penerbangan perdananya (24 Mei 1976) dari London ke Washington, D.C ...
  • Pembalap rockie Yamaha, Vinales, menyabet gelar pertamanya di seri MotoGP perdana 2017 di Qatar
  • Ferrari akhirnya memecah kebuntuan setelah pembalapnya Vettel menjuarai GP perdana di musim 2017
  • Hari ini (21/2), 41 tahun silam Presiden Soekarno Umumkan Reshuffle Kabinet Dwikora pada thn 1966

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