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All Journal Journal of Tropical Life Science : International Journal of Theoretical, Experimental, and Applied Life Sciences Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai-Nilai Islami)
Trisilowati Trisilowati, Trisilowati
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Agriculture, Biological Sciences & Forestry Arts Humanities Environmental Science Mathematics

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Kontrol Optimal pada Model Epidemi SEIQR dengan Tingkat Kejadian Standar Zulaikha, Zulaikha; Trisilowati, Trisilowati; Fadhilah, Intan
Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai-Nilai Islami) Vol 1 No 1 (2017): Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai Islami )
Publisher : Mathematics Department

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (749.077 KB)

Abstract

Penelitian ini dilakukan dengan modifikasi model epidemik SEIQR dengan tingkat kejadian standar dan kontrol optimal. Kontrol optimal dilakukan dengan menambahkan dua variabel kontrol yaitu usaha pengontrolan kontak langsung antara populasi rentan dengan populasi terinfeksi, dan pemberian obat pada populasi terinfeksi. Tujuan penelitian ini adalah untuk meminimumkan jumlah subpopulasi yang terinfeksi, jumlah subpopulasi laten, jumlah biaya edukasi dan biaya pemberian obat. Kondisi kontrol optimal pada penelitian ini diperoleh dengan menggunakan prinsip minimum Pontryagin. Selanjutnya, simulasi numerik dilakukan dengan metode Sweep Maju-Mundur untuk menunjukkan bagaimana pengaruh adanya kontrol terhadap model epidemik. Hasil penelitian yang dilakukan menunjukkan bahwa dengan adanya kontrol terlihat efektif dalam menekan jumlah pertumbuhan subpopulasi terinfeksi dengan subpopulasi laten.
Dynamics of a Fractional Order Eco-Epidemiological Model Nugraheni, Kartika; Trisilowati, Trisilowati; Suryanto, Agus
Journal of Tropical Life Science Vol 7, No 3 (2017)
Publisher : Journal of Tropical Life Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11594/jtls.07.03.09

Abstract

In this paper, we propose a fractional order eco-epidemiological model. We considere the existence of time memory in the growth rate of the three populations. We observed the dynamical behaviour by analysing with fractional order and then simulateing using Grünwald-Letnikov approximation to support analytical results. It found that the model has five equilibrium points, namely the origin, the survival of susceptible prey, the predator free equilibria, the infected prey free equilibria, the interior equilibria. Numerical simulations show that the existence of fractional order  is a factor which affects the behaviour of solutions. 
A Dynamical Analysis on a Tumour Virotherapy Model with Standard Incident Rate Ikawati, Deasy Sandhya Elya; Kusumawinahyu, Wuryansari Muharini; Trisilowati, Trisilowati
Journal of Tropical Life Science Vol 7, No 1 (2017)
Publisher : Journal of Tropical Life Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11594/jtls.07.01.03

Abstract

This paper discusses a dynamical analysis on a model that governs the growth of tumour cell under a therapy by using oncolytic viruses, on the standard incident rate. The model is a modification of the similar one by replacing the bilinear incident rate with the standard one. The conducted dynamical analysis consists of the determination of equilibrium points and their existence conditions, followed by local as well as global stability analysis of the equilibrium points. The analytical result shows that there are two equilibrium points, namely uninfected and the endemic point, which needs a condition to exist. Stability analysis shows that there is a dimensionless basic reproduction number that marks the existence as well as the stability of equilibrium points. When basic reproduction number is less than one, there is only the uninfected equilibrium, which is global asymptotically stable. On the other hands, both of equilibrium points exist when the basic reproduction number is more than one, but the uninfected point is not stable anymore, while the endemic one is local asymptotically stable under a condition. Some numerical simulations are performed to illustrate the analytical result. Numerically, it can also be demonstrated that there is a set of parameters which indicates that tumour can be fully removed.  
Co-Authors Ikawati, Deasy Sandhya Elya Intan Fadhilah, Intan Kartika Nugraheni M.Pd S.T. S.Pd. I Gde Wawan Sudatha . Wuryasari Muharini Kusumawinahyu Zulaikha Zulaikha