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The Effect of Virotherapy, Chemotherapy, and Immunotherapy to Immune System: Mathematical Modelling Approach Sa'adah, Aminatus; Prihantini, Prihantini; Masulah, Bidayatul
KUBIK Vol 8, No 2 (2023): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Jurusan Matematika, Fakultas Sains dan Teknologi, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v8i2.29521

Abstract

Medical research and therapeutic interventions continue to evolve, and one interesting area of study is the complex interaction among virotherapy, chemotherapy, and the immune system. Each treatment has its own advantages and disadvantages. In this study, a mathematical model was developed to describe how the immune system, tumor cells, and normal cells interact when all three types of therapy are used to treat cancer patients. To determine the effectiveness of various treatments, numerical simulations of eight different treatment strategies were performed. These simulations measured how much the concentration of immune cells, tumor cells, and normal cells decreased as a result of the treatment. Based on the numerical simulations performed, the application of the three types of therapy provided the greatest reduction (99%) in the concentration of tumour cells but also provided a significant reduction (68%) in the concentration of immune cells in the body.
Simulation of Quantum Tunnelling in Semiconductors: Analysis of Barrier Thickness Variation through the High Order FDTD Method Firdaus, Rohim Aminullah; Kurniawan, Ananda Rossy; Latifah, Eny; Saputra, Yohanes Dwi; Masulah, Bidayatul; Winarno, Nanang
POSITRON Vol 14, No 2 (2024): Vol. 14 No. 2 Edition
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam, Univetsitas Tanjungpura

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26418/positron.v14i2.82415

Abstract

The time-dependent Schrödinger equation is fundamental to quantum mechanics, describing the temporal evolution of quantum systems. This research presents a High-Order Finite-Difference Time-Domain (HO-FDTD) method, employing Taylor series expansion to solve the equation with enhanced efficiency and accuracy. By advancing beyond traditional methods like first-order Taylor series (Crank-Nicolson, forward or backward Euler) or computationally intensive Runge-Kutta schemes, the HO-FDTD method leverages higher-order Taylor expansion for the time evolution operator while simultaneously refining the Laplacian operator. This dual improvement enhances precision, allowing for accurate modeling of complex quantum phenomena. Focusing on quantum tunneling, a critical process where electrons traverse potential barriers despite insufficient classical energy, the study examines tunneling probabilities and electron behavior across barriers of varying thickness in semiconductors. The simulations reveal that thicker barriers reduce tunneling probabilities, amplify deviations in electron positions, and indicate energy transfer during interactions, with increased resistance lowering kinetic energy and raising potential energy. These findings emphasize the significant influence of barrier thickness on quantum tunneling and highlight the HO-FDTD method"™s capability to capture intricate quantum dynamics, establishing it as a robust tool for advancing research and applications in quantum mechanics.