β
π Dokumentasi & Referensi Ilmiah
Campak Airborne Transmission Simulator β Tim PPI RSUD Dr. Moewardi / FK UNS β 2026
Semua parameter berbasis peer-reviewed literature. Simulator untuk edukasi, bukan keputusan klinis.
1. Speed & Durasi Simulasi
Slider Speed mengontrol multiplier waktu simulasi relatif terhadap waktu nyata.
| Speed | Rasio | 1 dtk real = β¦ simulasi | Cocok untuk |
|---|
| 1 | 1Γ real-time | 1 detik | Observasi detail partikel |
| 3 (default) | 3Γ | 3 detik | Keseimbangan detail & kecepatan |
| 5 | 5Γ | 5 detik | Akumulasi partikel mid-term |
| 10 | 10Γ | 10 detik | Fast-forward melihat infeksi |
Timer β± menunjukkan waktu simulasi. Pada speed=3, simulasi 10 menit memerlukan ~3,3 menit real-time. Untuk 2 jam simulasi (persistensi aerosol campak), ~40 menit real-time (speed=3) atau ~12 menit (speed=10).
Kejadian periodik: Emisi pernapasan kontinu (~12% dari burst rate). Batuk (cough burst) setiap 4 detik simulasi. Evaluasi infeksi setiap frame render.
2. Parameter Ruangan
| Parameter | Nilai | Satuan |
|---|
| Lebar Γ Kedalaman Γ Tinggi | 8 Γ 6 Γ 3.5 | meter |
| Volume | 168 | mΒ³ |
| Okupansi | 9 orang | 1 infeksius + 8 rentan |
| AC Inlet | Atas-belakang-tengah (unit 1.8m) |
| Exhaust Outlet | Bawah-depan-tengah (1.2m) |
3. Parameter Patogen
| Parameter | Campak | COVID-19 | Referensi |
|---|
| Rβ | 15 | 2.5 | Guerra et al. 2017 [1]; Li et al. 2020 |
| Quanta rate (q) | 2,345 q/h | 48 q/h | Azimi et al. 2021 [2]; Dai & Zhao 2020 [3] |
| Persistensi udara | 120 menit | 30 menit* | WHO 2025 [4]; *estimasi praktis |
| Spread factor | 1.6 | 0.9 | Kecepatan awal partikel (relatif) |
Quanta generation rate campak: Rentang literatur 128β5.580 q/h. Nilai 2.345 q/h berasal dari rata-rata kasus sekolah dasar (q=1.925) dan menengah (q=2.765) dalam Azimi et al. via model Wells-Riley yang dimodifikasi. Riley et al. (1978) menghitung 570 q/h dari outbreak klasik di sekolah.
*Persistensi COVID: Data laboratorium menunjukkan viabilitas aerosol hingga 3 jam (van Doremalen et al. 2020, NEJM). Nilai 30 menit adalah estimasi praktis untuk persistensi infeksius efektif di ruangan berventilasi.
4. Model Wells-Riley
P = 1 β exp( βI Γ q Γ p Γ t / Q )
P = probabilitas infeksi (0β1)
I = jumlah infector (= 1)
q = quanta generation rate (quanta/jam) β Campak: 2.345, COVID: 48
p = laju ventilasi paru = 0,5 mΒ³/jam (istirahat)
t = durasi paparan (jam)
Q = laju ventilasi ruangan = Volume Γ ACH (mΒ³/jam)
[Asal-usul] Riley EC, Murphy G, Riley RL (1978). "Airborne spread of measles in a suburban elementary school." Am J Epidemiol 107(5):421-432.
Contoh Perhitungan (Terkoreksi)
| Skenario | q (q/h) | ACH | t (jam) | P (%) |
|---|
| Campak, vent buruk, 1 jam | 2.345 | 2 | 1 | 97,0% |
| Campak, vent sedang, 1 jam | 2.345 | 6 | 1 | 68,8% |
| Campak, HEPA, 30 mnt | 2.345 | 24 | 0,5 | 7,1% |
| COVID, vent buruk, 1 jam | 48 | 2 | 1 | 6,9% |
| COVID, vent sedang, 1 jam | 48 | 6 | 1 | 2,4% |
5. Model Aliran Udara (Vector Field)
Aliran udara dimodelkan sebagai velocity vector field: kecepatan dihitung di setiap titik (x,y,z) berdasarkan pola sirkulasi realistis, diskalakan oleh faktor ACH/6.
| Komponen | Lokasi | Arah |
|---|
| AC Inlet Jet | Atas-belakang | ββ ke bawah & depan, decay eksponensial |
| Back Wall | Dinding belakang | β ke bawah |
| Floor Flow | Lantai | β ke depan menuju exhaust |
| Front Wall | Dinding depan | β ke atas |
| Ceiling Return | Langit-langit | β ke belakang (loop utama) |
| Central Vortex | Tengah ruangan | Rotasi YZ β traps particles |
| Exhaust Suction | Bawah-depan | Radial ke dalam, r=2.5m |
Removal oleh ventilasi: (1) Exhaust proximity removal proporsional ACH, (2) General dilution = ACH/3600 per detik, (3) Natural decay setelah persistensi maksimal. Central vortex menyebabkan partikel terjebak dan sulit mencapai exhaust β konsisten dengan temuan riset UMN (Shao et al. 2021).
6. Parameter Masker
| Jenis | Ξ·emisi | Ξ·inhalasi | Visual |
|---|
| Tanpa masker | 0% | 0% | β |
| Masker bedah | 50% | 35% | Kotak hijau + ear loops |
| N95 respirator | 90% | 63% | Kotak putih tebal |
Emisi efektif = emit_rate Γ (1 β Ξ·_emisi)
Paparan efektif = exposure Γ (1 β Ξ·_inhalasi Γ 0.7)
[Ref] Sickbert-Bennett EE et al. (2020). JAMA Intern Med 180(12):1607-1612. N95: >90%, bedah: 37β69%. Nilai tengah digunakan.
7. Model Vaksinasi (SEIRV All-or-Nothing)
| Dosis | Vaccine Efficacy | Mekanisme |
|---|
| 1 dosis MMR | 93% | 93% fully immune, 7% vaccine failure β tetap rentan |
| 2 dosis MMR | 97% | 97% fully immune, 3% vaccine failure β tetap rentan |
Per orang divaksinasi:
if random() < VE β IMMUNE (ungu, shield ring, tidak terinfeksi)
else β SUSCEPTIBLE-VACCINATED (hijau pucat, shield tipis, masih rentan)
Coverage β₯75% menggunakan model 2 dosis. Coverage 25-50% menggunakan model 1 dosis.
[Ref] CDC CFA (2025). "Behind the Model: Interactive Measles Outbreak Simulator." Model SEIRV stokastik, all-or-nothing vaccination.
8. Reff (Effective Reproduction Number)
R_eff = Rβ Γ (1 β vaxCoverage Γ VE) Γ (1 β Ξ·_emisi) Γ (1 β Ξ·_inhalasi)
Masker bedah: faktor = (1β0.5)Γ(1β0.35) = 0,325
N95: faktor = (1β0.9)Γ(1β0.63) = 0,037
| Skenario | Rβ | Vax | Masker | R_eff | Status |
|---|
| Campak tanpa intervensi | 15 | 0% | β | 15,0 | β οΈ Outbreak |
| Campak 95% vax 2d | 15 | 95% | β | 1,18 | β οΈ Masih >1 |
| Campak 95% vax + bedah | 15 | 95% | Bedah | 0,38 | β
Terkontrol |
| Campak N95 saja | 15 | 0% | N95 | 0,56 | β
Terkontrol* |
| COVID 75% vax 2d | 2.5 | 75% | β | 0,68 | β
Terkontrol |
*Catatan: R_eff N95 saja = 0,56 mengasumsikan kepatuhan 100% dan fit sempurna β kondisi ideal. Dalam praktik, compliance dan fit bervariasi. Kombinasi vaksinasi + masker + ventilasi memberikan perlindungan berlapis (Swiss cheese model).
9. Kontrol Kamera & Interaktif
| Aksi | Desktop | Mobile |
|---|
| Rotasi kamera | Klik kiri + drag | 1 jari swipe |
| Zoom | Scroll mouse | Pinch 2 jari |
| Pan | Klik kanan + drag | β |
| Auto orbit | Tombol π Auto/Manual |
10. Referensi Ilmiah
Model Transmisi & Wells-Riley
[1] Guerra FM et al. (2017). The basic reproduction number (Rβ) of measles: a systematic review. Lancet Infect Dis 17(12):e420βe428. β Rβ campak: 12β18.
[2] Azimi P et al. (2021). Mechanistic transmission modeling of COVID-19 on the Diamond Princess. PNAS 118(8):e2015482118. β Quanta measles avg: 2.345 q/h.
[3] Dai H, Zhao B (2020). Association of infected probability of COVID-19 with ventilation rates. medRxiv. β Quanta COVID: 14β48 q/h.
[4] WHO (2025). Measles Fact Sheet. Geneva. β Persistensi aerosol campak hingga 2 jam.
[5] Riley EC, Murphy G, Riley RL (1978). Airborne spread of measles in a suburban elementary school. Am J Epidemiol 107(5):421β432.
[6] Sze To GN, Chao CYH (2010). Review and comparison between the WellsβRiley and doseβresponse approaches. Indoor Air 20(1):2β16.
[7] Bazant MZ, Bush JWM (2021). A guideline to limit indoor airborne transmission of COVID-19. PNAS 118(17):e2018995118.
Masker & Ventilasi
[8] Sickbert-Bennett EE et al. (2020). Filtration Efficiency of Hospital Face Mask Alternatives. JAMA Intern Med 180(12):1607β1612. β N95: >90%, bedah: 37β69%.
[9] Noakes CJ et al. (2006). Mathematical models for assessing the role of airflow on airborne infection risk in hospital wards. J R Soc Interface 3:767β780.
[10] Shao S et al. (2021). Risk assessment of airborne transmission of COVID-19 by asymptomatic individuals. J Aerosol Sci 151:105661.
Vaksinasi & Epidemiologi
[11] CDC CFA (2025). Behind the Model: Interactive Measles Outbreak Simulator. β SEIRV all-or-nothing; VEβ=93%, VEβ=97%.
[12] Portnoy A et al. (2025). Impact of vaccination timing and coverage on measles near elimination dynamics. Nat Commun 16:9066.
[13] Moss WJ (2017). Measles. Lancet 390(10111):2490β2502.
[14] Wang CC et al. (2021). Airborne transmission of respiratory viruses. Science 373:eabd9149.
Immune Amnesia
[15] Mina MJ et al. (2019). Measles virus infection diminishes preexisting antibodies. Science 366(6465):599β606.
[16] Laksono BM et al. (2018). Mechanism of measles-associated immune suppression. Nat Commun 9:4944.
Simulator oleh Tim PPI β RSUD Dr. Moewardi / FK UNS β’ Three.js r128 β’ Wells-Riley Model β’ SEIRV Vaccination
Versi 5.0 β Maret 2026 β Untuk keperluan edukasi, bukan panduan keputusan klinis
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