amirul hakam dan covid-19...endah rm putri amirul hakam departemen matematika institut teknologi...
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ENDAH RM PUTRI AMIRUL HAKAM
www.its.ac.id
DEPARTEMEN MATEMATIKA INSTITUT TEKNOLOGI SEPULUH
NOPEMBER (ITS) Surabaya - Indonesia
MATEMATIKA DAN COVID-19
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www.its.ac.id
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www.its.ac.id
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Sebaran COVID-19 di Dunia
https://www.worldometers.info/coronavirus/country
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https://www.worldometers.info/coronavirus/country http://infocovid19.jatimprov.go.id/
Sebaran COVID-19 di Indonesia
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Untuk Apa Pemodelan Matematika ??
https://www.worldometers.info/coronavirus/country
Model Prediksi dan Evaluasi
Perumusan, Implementasi , dan Evaluasi Kebijakan
input
feedback
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Existing Research Overview
Model Kompartemen SIRD
Estimasi parameter: GA
Profil sebaran individu di tiap kompartemen
(terinfeksi, sembuh, mati)
Data Analytic Ensemble-SVR
COVID-19
Estimasi variabel: EKF
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DATA ANALYTIC (ENSEMBLE-SVR)
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1. Susceptible • Individu yang rentan terinfeksi
2. Infected • Individu yang terinfeksi dan
bisa menginfeksi individu lain 3. Recovered
• Individul yang sembuh setelah terinfeksi
4. Death • Individu yang meninggal setelah
terinfeksi
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Model Kompartemen
Model Kompartemen SIRD
Susceptible Infected
Recovered
Death
r
a
d
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Model Matematika SIRD
• r = laju infeksi • a = laju kesembuhan • d = laju kematian
𝒅𝒅𝒅𝒅
= −𝒓𝒅𝒓
𝒅𝒓𝒅𝒅
= 𝒓𝒅𝒓 − 𝒂 + 𝒅 𝒓
𝒅𝒅𝒅𝒅
= 𝒂𝒓 𝒅𝒅𝒅𝒅
= 𝒅𝒓
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Model Kompartemen GA-SIRD (PENDEKATAN GENETIC ALGORITHM)
23 Jan 2020 - 08 April 2020 Lockdown
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www.its.ac.id
Model Kompartemen GA-SIRD (PENDEKATAN GENETIC ALGORITHM)
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Model Kompartemen GA-SIRD (PENDEKATAN GENETIC ALGORITHM)
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Perubahan peak seiring pertambahan data
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Perubahan peak seiring pertambahan data (update)
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MODEL SIRD (PENDEKATAN
EXTENDED KALMAN FILTER)
Predict
1. Predict the state ahead 2. Predict the error covariance
ahead
𝑥𝑘+1− = 𝑓 𝑥𝑘 𝑃𝑘+1− = 𝐴𝑃𝑘𝐴𝑇 + 𝐺𝐺𝐺𝑇
𝐴 =𝜕𝑓𝜕𝑥
Update
1. Compute the Kalman gain 2. Update the estimate with
measurement 3. Update the error covariance
𝐾𝑘+1 = 𝐼 − 𝐾𝐾 𝑃𝑘+1− 𝑃𝑘+1 = 𝑃𝑘+1− 𝐾𝑇 𝐾𝑃𝑘+1− 𝐾𝑇 + 𝑅 −1 𝑥𝑘+1 = 𝑥𝑘+1− + 𝐾 𝑧𝑘+1 − ℎ 𝑥𝑘+1−
Inisialisasi dengan optimisasi GA Pengukuran aktual
Titik setimbang : (𝑆,𝐼,𝑅,𝐷)=((𝑎+𝑑)/𝑟,0,0,0)
Model non-linier diskrit: 𝑆𝑘+1 = −𝑟𝑘𝑆𝑘𝐼𝑘Δ𝑡 + 𝑆𝑘 𝐼𝑘+1 = 𝑟𝑘𝑆𝑘𝐼𝑘 − 𝑎𝑘 + 𝑑𝑘 𝐼𝑘 Δ𝑡 + 𝐼𝑘 𝑅𝑘+1 = 𝑎𝑘𝐼𝑘Δ𝑡 + 𝑅𝑘 𝐷𝑘+1 = 𝑑𝑘𝐼𝑘Δ𝑡 + 𝐷𝑘
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Model Kompartemen SIRD-EKF (PENDEKATAN EXTENDED KALMAN FILTER)
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Model Kompartemen SIRD-EKF (PENDEKATAN EXTENDED KALMAN FILTER)
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Model Kompartemen SIRD-EKF (PENDEKATAN EXTENDED KALMAN FILTER)
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Model Kompartemen GA-SIRD (PENDEKATAN GENETIC ALGORITHM)
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Model Kompartemen SIRD-EKF (PENDEKATAN EXTENDED KALMAN FILTER)
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Apa selanjutnya ?
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www.its.ac.id
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www.its.ac.id
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ONGOING RESEARCH
• REPRODUCTION NUMBER ECONOMIC RISK MODEL OF PANDEMIC
• APPLICATION OF CONTROL SYSTEM ON PANDEMIC MODEL
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Anggota tim:
• Departemen Matematika: • Muhammad Lutfi Shahab, Imam Mukhlash, Mohammad Iqbal, Endah RM Putri, Helisyah
N Fadhillah, Erna Apriliani, Didik Khusnul Arif • SimcovID:
• Hadi Susanto, Venansius Ryan T, Hengky Kurniawan, Amirul Hakam, Endah RM Putri, dan lain-lain.
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Terima Kasih