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All Journal Journal of Tropical Life Science : International Journal of Theoretical, Experimental, and Applied Life Sciences The Journal of Experimental Life Sciences (JELS) Journal of Innovation and Applied Technology Research Journal of Life Science Natural B Telematika Limits: Journal of Mathematics and Its Applications
Trisilowati, Trisilowati
Brawijaya University
Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Computer Science & IT Education Environmental Science Immunology & microbiology Mathematics Medicine & Pharmacology Neuroscience

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Optimal Control of Tumor Growth Model with Dendritic Cells as Immunotherapy Firmansyah Reskal Motulo; Trisilowati Trisilowati; Abdul Rouf
The Journal of Experimental Life Science Vol. 8 No. 2 (2018)
Publisher : Postgraduate School, Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1053.56 KB) | DOI: 10.21776/ub.jels.2018.008.02.06

Abstract

In this paper, optimal control of tumor growth model with dendritic cells as immunotherapy is provided. The model equation can be expressed into a nonlinear differential equation system consisting of four compartments namely, tumor cells, CTL cells, helper T cells, and dendritic cells. Dendritic cells as immunotherapy are injected to the body at time t. The aim of this optimal control is to minimize the tumor cells density as well as the cost of dendritic cells to be administered to the body.Optimal control problem is carried out based on Pontryagin's maximum principle and numerical simulation is solved by using Forward-Backward Sweep methods. Simulation results show that control strategy shrinks tumor cells density which is shown by tumor cells density graph that monotonically decreases after applying dendritic cells as immunotherapy.Keywords: immunotherapy, optimal control, Tumor cell.
Numerical Simulation of Leslie-Gower Predator-Prey Model with Stage-Structure on Predator Rima Anissa Pratiwi; Agus Suryanto; Trisilowati Trisilowati
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 (1381.092 KB) | DOI: 10.21776/ub.jels.2018.008.03.011

Abstract

In this paper, we introduce Leslie-Gower predator-prey model with a stage-structure population on the predator. This model consists of two populations, that are prey and predator populations. Here, we divide predator into two stages. Thus, we have three classes of population in this model that are prey, juvenile predator, and mature predator. The focus of this paper is to know the interaction between the population that is affected by stage-structure in predator population in the model and to study numerically the effects of stage-structure in predator population on the interaction of prey and predator. It is found that the transition rate from juvenile to mature predator is a very important parameter which may determine the long-term behavior of both prey and predator.Keywords: Leslie-Gower model, predator-prey model, stage-structure.
Sensitivity and Stability Analysis of a SEIR Epidemic Model with Information Robiatul Witari Wilda; Trisilowati Trisilowati; Moch. Aruman Imron
The Journal of Experimental Life Science Vol. 9 No. 1 (2019)
Publisher : Postgraduate School, Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1163.176 KB) | DOI: 10.21776/ub.jels.2019.009.01.08

Abstract

In this paper, the construction and stability analysis of a SEIR epidemic model with information are discussed. This model contains information about how to prevent the spread of infectious diseases which is transmitted by infected individuals to susceptible individuals. Furthermore, the dynamical analysis of the model which includes determination of equilibrium points terms of existence, stability analysis of the equilibrium points and sensitivity analysis are observed. Local stability of the equilibrium point is determined by linearizing the system around the equilibrium point and checking for the eigenvalue sign of Jacobian matrix at each equilibrium point. Sensitivity analysis is performed by using a sensitivity index to measure the relative change of basic reproduction number on each parameter. Based on the analysis result, there are two equilibrium points namely disease-free equilibrium point and endemic equilibrium point. The disease-free equilibrium point always exists and is locally asymptotically stable if the basic reproduction number is less than one. Moreover, the endemic equilibrium point exists and is locally asymptotically stable under certain conditions. From sensitivity analysis, it is found that the rate of mortality is the most sensitive parameter and the least sensitive parameter is the rate of exposed individual becomes infected individual. Finally, numerical simulation is conducted to support the analysis result.Keywords: Epidemic, information, sensitivity analysis, SEIR, stability analysis.
Co-Authors Abdul Rouf Agus Suryanto AGUS WIDODO Agus Widodo Anam, Syaiful Badria Ulfa Candra Dewi Cholifatul Maulidiah Firmansyah Reskal Motulo Hidayat, Noor Kartika Nugraheni Karunia Theda Kristanti Kristanti, Karunia Theda Lu’luul Wardah Moch. Aruman Imron Moh. Nurul Huda Muhammad Abdurrahman Rois Muna Afdi Muniroh Rima Anissa Pratiwi Suryanto, Agus Ummu Habibah Wilda, Robiatul Witari Wuryansari M. K. Wuryasari Muharini Kusumawinahyu Zuraidah Fitriah