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Melisa Melisa
Universitas Islam Darul 'Ulum Lamongan
Computer Science & IT Education Mathematics

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ANALISIS KESTABILAN PADA MODEL DINAMIKA PENULARAN TUBERKULOSIS SATU STRAIN DAN DUA STRAIN Melisa Melisa; Widodo Widodo
Unisda Journal of Mathematics and Computer Science (UJMC) Vol 1 No 01 (2015): Unisda Journal of Mathematics and Computer Science
Publisher : Mathematics Department of Mathematics and Natural Sciences Unisda Lamongan

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1626.767 KB) | DOI: 10.52166/ujmc.v1i01.433

Abstract

In this paper, two mathematical models are given, those are basic model of tuberculosis transmission and transmission model of tuberculosis with the problem of drug resistance. The problem of drug resistance due to the decient compliance with treatment schedules so causes treatment failure. The basic model of tuberculosis transmission incorporates slow and fast progression, efective chemoprophylaxis and therapeutic treatments. If the basic reproduction ratio R0 less than 1, then the disease-free equilibrium is globally asymptotically stable and if R0 > 1, an endemic equilibrium exists and is locally asymptotically stable. Next, transmission model of tuberculosis with the problem of drug resistance as acompetition between two types of strains of Mycobacterium tuberculosis: those are drug-sensitive strain called the regular TB (strain 1) and drug-resistant strain called the resistant TB (strain 2). If R0s less than 1 and R0r less than 1, then the disease-free equilibrium is globally asymptotically stable. If R0r > 1, an endemic equilibrium where only resistant strain exists. If R0s > 1 and R0s > R0r, endemic equilibrium where both types of strains are present and can spread in a population. Numerical simulation with the certain parameters is given to illustrate stability of equilibrium.
ANALISIS PERMAINAN EMPAT BILANGAN Melisa Melisa
Unisda Journal of Mathematics and Computer Science (UJMC) Vol 2 No 1 (2016): Unisda Journal of Mathematics and Computer Science
Publisher : Mathematics Department of Mathematics and Natural Sciences Unisda Lamongan

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (895.497 KB) | DOI: 10.52166/ujmc.v2i1.445

Abstract

The four-number game starts from 4-tuple (a; b; c; d) of nonnegative numbers a, b, c, d. In this game, the next 4-tuple is (|a-b|; |b-c|; |c-d|; |d-a|) and similar rule of changes of the subsequent 4-tuples is imposed until the game reaches the zero 4-tuple (0, 0, 0, 0). The winner of this game is the one who chooses the initial 4-tuple leading to the longest game. In this paper analyzes the game length based on the following criteria imposed on the four numbers of the 4-tuple: nonnegative integers, nonnegative rationals and nonnegative reals. The results shows that everyfour-number game with nonnegative integers or rational integers has nite length. Despite of this fact, for every positive integer m, there is an initial 4-tuple based on Tribonacci sequence that leads to four-number game with length greater than m. For the game with real integers, although the game generally has nite length, there are (innite number of) initial 4-tuples that leads to innite length games.
Co-Authors Widodo Widodo