Analisis model sirs penyebaran demam berdarah dengue dengan metode runge-kutta dan algoritma genetika = Analysis of the sirs model of the spread of dengue hemorrhagic fever using runge-kutta method and genetic algorithm

Tjioenata, Melyssa Mentari (2020) Analisis model sirs penyebaran demam berdarah dengue dengan metode runge-kutta dan algoritma genetika = Analysis of the sirs model of the spread of dengue hemorrhagic fever using runge-kutta method and genetic algorithm. Bachelor thesis, Universitas Pelita Harapan.

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Abstract

Demam Berdarah Dengue adalah salah satu penyakit menular yang sering terjadi di Indonesia. Demam Berdarah Dengue disebabkan oleh Virus Dengue yang memiliki empat serotipe, DEN-1, DEN-2, DEN-3 dan DEN-4. Seumur hidupnya seseorang dapat terkena penyakit Demam Berdarah Dengue sebanyak 4 kali, masing-masing sekali untuk setiap serotipe. Setelah sembuh dari salah satu serotipe, seseorang mendapatkan kekebalan seumur hidup terhadap Demam Berdarah Dengue serotipe tersebut. Dalam skripsi ini akan dibuat suatu model untuk memodelkan penyebaran Demam Berdarah Dengue dengan asumsi hanya ada dua serotipe saja, yakni DEN-1 dan DEN-2. Model dibentuk berdasarkan kepada Model SIR (Susceptible, Infected, Recovered) dan Model SIRS (Susceptible, Infected, Recovered, Susceptible). Pada model ini perubahan jumlah populasi setiap kelompok terhadap waktu dimodelkan dalam bentuk sistem persamaan diferensial. Sistem persamaan diferensial tersebut kemudian digunakan untuk melakukan analisis titik kesetimbangan. Solusi numerik untuk sistem persamaan diferensial dicari dengan menggunakan Metode Runge-Kutta. Algoritma Genetika digunakan untuk menemukan nilai parameter pada model yang tidak diketahui. Dilakukan serangkaian simulasi untuk mendapatkan kombinasi yang menghasilkan sistem Algoritma Genetika yang akan menghasilkan solusi aproksimasi terbaik. Kombinasi mencakup ukuran populasi, nilai selection, nilai crossover dan nilai mutation. Kombinasi terbaik ini kemudian akan menghasilkan solusi aproksimasi dengan error terkecil. / Dengue Hemorrhagic Fever is a contagious disease that often occurs in Indonesia. Dengue Hemorrhagic Fever, caused by the Dengue Virus, has four serotypes : DEN-1, DEN-2, DEN-3 and DEN-4. Someone can be infected four times, once for each serotype. After recovering from one serotype, a person gets a lifetime of immunity against that serotype. In this thesis a model will be created for modeling the spread of Dengue Hemorrhagic Fever with assumption there are only two serotypes, namely DEN-1 and DEN-2. Model formed based on SIR Model (Susceptible, Infected, Recovered) and SIRS Model (Susceptible, Infected, Recovered, Susceptible). The changes in populations over time are written into a system of differential equations. The system of differential equations is then used to do an equilibrium point analysis. The numerical solution for the system of differential equations can be found using the Runge-Kutta Method. Genetic Algorithm are used to find the values of parameters in the model that are unknown. A series of simulations are performed to get the combination that produces the Genetic Algorithm system that will produce the best approximation solution. The combination includes population size, selection value, crossover value and mutation value. This best combination then will produce an approximation solution with the smallest error.

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