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

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.