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

In this thesis, two mathematical models are given, those are a basic transmission model of tuberculosis and transmission model of tuberculosis with the problem of drug resistance. The problem of drug resistance due to the deficient compliance with treatment schedules so causes treatment failure. The basic model of tuberculosis infection that incorporate slow and fast progression, effective chemoprophylaxis and therapeutic treatments. If the basic reproduction ratio R0 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 that are drug-sensitive strain called the regular TB (strain 1) and drug-resistant strain called the resistant TB (strain 2). If R0s 1 and R0r 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 can spread in a population. Numerical simulation with the certain parameters is given to illustrate stability of equilibrium