Analisis Dan Kontrol Optimal Pada Model Dinamik Penyebaran Virus Zika

Pangestuti, Nurani Dwi (2018) Analisis Dan Kontrol Optimal Pada Model Dinamik Penyebaran Virus Zika. Undergraduate thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Virus zika adalah sejenis virus dari keluarga flaviviridae dan genus flavivirus yang disebarkan oleh nyamuk Aedes Aegypti yang dapat menyebabkan masalah serius seperti penyakit Guillain Barre Syndrome (GBS) dan mikrosefalus. Dalam tugas akhir ini, digunakan model penyebaran virus zika yang terdiri dari dua populasi yang dibagi menjadi beberapa sub-populasi antara lain sub-populasi manusia Susceptible, sub-populasi manusia Asymtomatic Infected, sub-populasi manusia Symtomatic Infected, sub-populasi manusia Recovered, sub-populasi nyamuk Susceptible, dan sub-populasi nyamuk Infected. Model dianalisis dengan menentukan bilangan reproduksi dasar, titik kesetimbangan bebas penyakit dan endemik, serta kestabilan dari setiap titik kesetimbangan. Kemudian dilakukan kontrol optimal menggunakan Prinsip Maksimum Pontryagin yang disimulasikan secara numerik menggunakan metode Range-Kutta. Hasil simulasi menunjukan menurunnya sub-populasi manusia yang terinfeksi virus zika dan menurunnya populasi nyamuk setelah adanya pemberian kontrol berupa penggunaan kondom, pengobatan, dan penyemprotan insektisida, dengan nilai fungsi objektif sebesar 1,0586. ================================================================================ Zika is a virus from flaviviridae family and flavivirus genus that spread by Aedes Aegypti mosquito and that can cause serious problem disease such as Guillain Barre Syndrome (GBS) and mikrosefalus. This final project used spreading dynamic zika virus mode l that consists of two population and divided to sub - population Susceptible humans, sub - population Asymtomatic Infected humans, sub - population Infected humans, sub - population Recovered humans, sub - population Susceptible mosquitoes, and sub - population Infec ted mosquitoes. The model that anlysis by determine the basic reproduction number, the point of disease free and endemic equilibrium, and the stability of each point of equilibrium. Then, do the optimal control using Pontryagin principle with n umerical solut ion given by Range - Kutta method. The simulation results show the decreasing sub - population of infected humans , asymptomatic infected human, and popu lation of mosquitoes after given controls such using condom, treatment, and using indoor residual spray with value of objective function is 1.0586.

Item Type: Thesis (Undergraduate)
Uncontrolled Keywords: Model penyebaran virus zika, Kestabilan, Kontrol Optimal, Prinsip Pontryagin, Metode Runge-Kutta
Subjects: Q Science > QA Mathematics > QA402 System analysis.
Divisions: Faculty of Mathematics, Computation, and Data Science > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User: Pangestuti Nurani Dwi
Date Deposited: 05 Jul 2021 10:24
Last Modified: 05 Jul 2021 10:24
URI: https://repository.its.ac.id/id/eprint/56485

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