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All Journal The Journal of Experimental Life Sciences (JELS) Limits: Journal of Mathematics and Its Applications Sainmatika: Jurnal Ilmiah Matematika dan Ilmu Pengetahuan Alam Jurnal Matematika Integratif
Lisa Risfana Sari
Universitas Internasional Semen Indonesia
Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Chemistry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Electrical & Electronics Engineering Engineering Immunology & microbiology Mathematics Mechanical Engineering Medicine & Pharmacology Neuroscience Physics Transportation

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Studi Numerik Model Virus Hepatitis B dengan Pengaruh Penyembuhan dan Absorpsi Sari, Lisa Risfana; Andayani, Puji
Sainmatika: Jurnal Ilmiah Matematika dan Ilmu Pengetahuan Alam Vol 16, No 1 (2019): SAINMATIKA
Publisher : Faculty of Mathematics and Natural Science, Universitas PGRI Palembang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (996.667 KB) | DOI: 10.31851/sainmatika.v16i1.3124

Abstract

The phenomenon of Hepatitis B outbreak almost occurs in all developing countries including Indonesia. Hepatitis B infection can develop into acute or chronic. In the chronic stage, the infection can cause liver complications such as liver cirrhosis or liver cancer or even death. Mathematical modeling have been widely used to study the Hepatitis B virus infection. In this study a mathematical model is constructed by considering non-cytolytic immune response and pathogen absorption. The model is analyzed by determining the equilibrium point of the model, determining the existence of the equilibrium point, and analyzing the stability of the equilibrium point of the model with numerical simulation. In this case, numerical analysis is used to illustrate the conditions of infection-free and infected. Furthermore, the relation of the stability requirements of each equilibrium point is studied. The results show that there are two equilibrium points, uninfected and infected equilibrium point. Both of the uninfected equilibrium point and infected equilibrium point is asymptotically stable if a certain condition are met. Based on these results, the causes of a persistent infection are studied.
Model Matematika Pemanenan Ikan dengan Kebijakan Panen Selektif Lisa Risfana Sari
Limits: Journal of Mathematics and Its Applications Vol 17, No 1 (2020)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v17i1.6753

Abstract

Pengelolaan sumber daya perikanan termasuk sebagai aspek penting yang dipertimbangkan oleh negara maritim. Kelimpahan sumber daya ikan dapat dipertahankan dengan strategi penangkapan ikan yang tepat, salah satunya adalah kebijakan panen selektif. Dalam studi ini, dinamika kepadatan populasi ikan dipelajari menggunakan model predator-prey yang dimodifikasi. Proses panen selektif yang memperhitungkan usia atau ukuran ikan siap panen dinyatakan sebagai penundaan waktu dalam proses panen. Analisis model dilakukan dengan menentukan titik kesetimbangan model dan stabilitas titik keseimbangan model. Ada empat titik keseimbangan model, yang mewakili kondisi trivial, kepunahan prey, kepunahan predator, dan eksistensi predator-prey. Perilaku dinamis model diilustrasikan melalui simulasi numerik dengan beberapa skenario. Hasil simulasi numerik menunjukkan bahwa waktu tunda mempengaruhi stabilitas beberapa titik setimbang, sehingga menghasilkan dinamika populasi yang lebih beragam.
Studi Numerik Model Virus Hepatitis B dengan Pengaruh Penyembuhan dan Absorpsi Lisa Risfana Sari; Puji Andayani
Sainmatika: Jurnal Ilmiah Matematika dan Ilmu Pengetahuan Alam Vol. 16 No. 1 (2019): Sainmatika : Jurnal Ilmiah Matematika dan Ilmu Pengetahuan Alam
Publisher : Universitas PGRI Palembang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (996.667 KB) | DOI: 10.31851/sainmatika.v16i1.3124

Abstract

The phenomenon of Hepatitis B outbreak almost occurs in all developing countries including Indonesia. Hepatitis B infection can develop into acute or chronic. In the chronic stage, the infection can cause liver complications such as liver cirrhosis or liver cancer or even death. Mathematical modeling have been widely used to study the Hepatitis B virus infection. In this study a mathematical model is constructed by considering non-cytolytic immune response and pathogen absorption. The model is analyzed by determining the equilibrium point of the model, determining the existence of the equilibrium point, and analyzing the stability of the equilibrium point of the model with numerical simulation. In this case, numerical analysis is used to illustrate the conditions of infection-free and infected. Furthermore, the relation of the stability requirements of each equilibrium point is studied. The results show that there are two equilibrium points, uninfected and infected equilibrium point. Both of the uninfected equilibrium point and infected equilibrium point is asymptotically stable if a certain condition are met. Based on these results, the causes of a persistent infection are studied.
Comparing Vector-host and SEIR models for Zika Virus Transmission Puji Andayani; Rizal Dian Azmi; Lisa Risfana Sari
The Journal of Experimental Life Science Vol. 8 No. 3 (2018)
Publisher : Postgraduate School, Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (987.978 KB) | DOI: 10.21776/ub.jels.2018.008.03.05

Abstract

Some mathematical models to describe Zika virus transmissions have been analyzed. In this study, we construct two models of Zika virus transmission. The first one is the vector-host model. It considers the human population as host and mosquito's population as the vector. The second model is where there is only infected human population who act as transmitter without the existence of infected mosquitoes in the population. The impact of modeling assumption of Zika virus is studied by analyzed the reproduction number using Next Generation Matrix (NGM) method. Formerly, we compare the dynamics of the two models by interpreting the reproduction number of each model. Biologically, the two models cause a similar effect. If the reproduction number is less than one, then the disease is extinct. Otherwise, an endemic condition exists. The numerical simulation also used to explain the comparison of two models. The recovery and the transmission period are solved to compare these two cases. Keywords: comparison, mathematical model, reproduction number, SEIR, Zika Virus.
Model Matematika Infeksi Virus Hepatitis B dengan Adsorpsi Lisa Risfana Sari
Jurnal Matematika Integratif Vol 13, No 2: Oktober, 2017
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (544.58 KB) | DOI: 10.24198/jmi.v13.n2.13665.123-131

Abstract

Infeksi Hepatitis B terus berlanjut menjadi masalah kesehatan global. Termotivasi hal tersebut, kami memperkenalkan model matematika infeksi virus Hepatitis B (VHB). Berangkat dari fakta bahwa hukum mass-action tidak selalu benar dalam menggambarkan interaksi virus dengan sel rentan di kehidupan nyata, maka kami menggunakan tingkat infeksi standar pada model. Fase adsorpsi dalam proses infeksi virus dipertimbangkan dalam model sebagai salah satu penyebab penurunan populasi partikel virus. Pada model, populasi partikel virus dibagi menjadi dua kompartemen yaitu, virion dan kapsid intraseluler yang mengandung DNA-VHB. Populasi sel dibagi menjadi dua kompartemen yaitu, sel rentan dan sel terinfeksi. Perilaku dinamik model dianalisis dengan menentukan titikkesetimbangan bebas infeksi dan endemik, bilangan reproduksi dasar, serta kestabilan dari titik kesetimbangan tersebut. Hasil analisis dan simulasi menunjukkan bahwa stabilitas titik kesetimbangan bebas infeksi maupun endemik bergantung pada bilangan reproduksi dasar.
Co-Authors Andayani, Puji Rizal Dian Azmi