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ANALISIS KESTABILAN PADA MODEL DINAMIKA PENULARAN TUBERKULOSIS SATU STRAIN DAN DUA STRAIN

Unisda Journal of Mathematics and Computer Science (UJMC)

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ISSN 2579-907X
2460-3333
 
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Title Statement ANALISIS KESTABILAN PADA MODEL DINAMIKA PENULARAN TUBERKULOSIS SATU STRAIN DAN DUA STRAIN
 
Added Entry - Uncontrolled Name Melisa, Melisa
Widodo, Widodo
Universitas Islam Darul 'Ulum Lamongan
Universitas Gadjah Mada
 
Summary, etc. 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 a competition 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.
 
Publication, Distribution, Etc. Mathematics Department of Mathematics and Natural Sciences Unisda Lamongan
 
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http://e-jurnal.unisda.ac.id/index.php/ujmc/article/view/433
 
Data Source Entry Unisda Journal of Mathematics and Computer Science (UJMC); Vol 1 No 01 (2015): Unisda Journal of Mathematics and Computer Science
 
Language Note eng
 
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