Judul: Optimal Control Model for the Spread of Ebola Disease
Abstrak: Karya ilmiah ini membahas masalah pengendalian penyakit Ebola. Pengendalian penyebaran penyakit ebola dirumuskan dalam model SIR yang dimodifikasi. Tiga variabel kontrol diperkenalkan ke dalam model. Pertama adalah usaha untuk menjaga individu yang rentan akan virus Ebola agar tidak terinfeksi dengan cara edukasi, public campaign, dsb. Kedua adalah usaha untuk mengidentifikasi individu yang telah terpapar virus Ebola tapi belum sampai terinfeksi sehingga segera mendapat perawatan. Ketiga adalah pengobatan serta pengawasan individu yang terinfeksi virus Ebola. Prinsip maksimum Pontryagin diterapkan agar mendapatkan kondisi optimalitas untuk dipenuhi oleh variabel kontrol. Penyelesaian metode numerik dari kontrol optimum akan diselesaikan menggunakan metode Runge-Kutta orde empat. Hasil dari solusi numerik menunjukkan bahwa penerapakan ketiga variabel kontrol terbukti dapat menekan jumlah individu yang terinfeksi dibandingkan sebelum diterapkan ketiga variabel kontrol. Penerapan ketiga variabel kontrol juga lebih baik dalam menekan jumlah individu terinfeksi dibandingkan hanya menerapkan kontrol variabel pertama saja maupun hanya menerapkan variabel kontrol pertama dan kedua saja. Kata kunci: kontrol optimum, metode Runge-Kutta orde empat, prinsip maksimum Pontryagin, Ebola., This thesis addresses the issues of controlling the Ebola disease. Controlling of the spread of Ebola disease is formulated in a modified SIR model. Three control variables are introduced into the model. The first is an attempt to prevent individuals who are susceptible to the Ebola virus from being infected by education, public campaigns, etc. The second is an attempt to identify individuals who have been exposed to the Ebola virus but have not yet been infected so that they receive treatment immediately. The third is the treatment and monitoring of individuals infected with the Ebola virus. Pontryagin's maximum principle is applied in order to obtain optimal conditions to be performed by the control variable. The numerical method of the optimum control will be solved by using the fourth-order Runge-Kutta method. The results of the numerical solution showed that the application of the three control variables was proven to be able to reduce the number of infected individuals compared to before the application of the three control variables. The application of the three control variables is also better in overcoming the number of infected individuals compared to applying the first control variable only or applying the first and second control variables. Keywords: optimum control, fourth-order Runge-Kutta method, Pontryagin's maximum principles, Ebola.
Keyword: ebola, optimum control, fourth-order Runge-Kutta method, Pontryagin's maximum principles

Judul: Analyzing the Solutions of Mathematical Models on the Spread of the Ebola Virus Disease
Abstrak: Penyakit virus Ebola adalah penyakit yang disebabkan oleh infeksi virus Zaire ebolavirus yang termasuk dalam filovirus. Model matematika penyebaran penyakit virus Ebola yang dikembangkan oleh Li et al. (2015) melibatkan 4 kompartemen, yaitu Susceptible (S), Exposed (E), Infected (I), dan Treated (T). Pengamatan atas dinamika populasi dan analisis sensitivitas dilakukan terhadap model yang sudah dinondimensionalkan. Pemeriksaan kestabilan dengan menggunakan kriteria Routh-Hurwitz menunjukkan bahwa titik tetap bebas penyakit (ketika Ro < 1) maupun titik tetap endemik (ketika Ro > 1) keduanya bersifat stabil asimtotik lokal. Dari sejumlah parameter yang terdapat dalam model, interaksi antara S dan E (ẞ20) adalah salah satu parameter yang berpengaruh besar terhadap Ro. Simulasi numerik dilakukan dengan menggunakan metode Runge- Kutta orde 4 dan 5, serta metode Runge-Kutta Fehlberg. Ketiga metode menghasilkan solusi numerik yang relatif sama. Namun, metode Runge-Kutta Fehlberg memiliki runtime yang lebih singkat dibandingkan metode Runge-Kutta orde 4 dan 5.
Keyword: Ebola, numerical simulations, population dynamics, Runge-Kutta, sensitivity analysis

Judul: Characterizations of low alloy steel sae 4422  plated with chromic acid (Cro3)
Abstrak: Characterizations of low alloy steel SAE 4422 plated with chromic acid (CrOrO3) was use Optical Microscopy (OM), Scanning Electron Microscopy (SEM), X-Ray Diffraction (XRD), RD),Energy Dispersive Analysis of X-Ray (EDAX), Hardness Test and Roughness Test. Microstructures analysis exhibits cracks and grain boundaries microcracks as a characteristics of chrome metal found at plating metal. Perlite and Ferrite as grains of steel found at base metal with grain boundaries around it. Phase analysis of plating metal appropriate to chrome metal with lattice constant (a) is 2.559 Å and phase analysis of base metal appropriate to iron ferrite with lattice constant (a) is 3.318 Å. Both plating and base metal have cubic system. Chemical analysis of plating metal at surface section exhibits that cracks area have highest value of carbon element compare with grains and grains boundaries area. While chemical analysis of base metal at cross section exhibits that perlite have highest value of carbon element compare with ferrite and grain boundaries. The hardness value of plating metal at surface section and cross section are 753 and 637 VHN. While, the hardness value of base metal and interface area at cross section are 205 and 373 VHN. The roughness value at measurement points of chrome surface for as received sample are 0.445 μm. Observation used Optical Microscopy and Scanning Electron Microscopy exhibits surface irregularities combine to form surface texture of plating metal at surface section.
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