FUNGSI LYAPUNOV DAN STABILITAS GLOBAL UNTUK MODEL EPIDEMIOLOGI SIR DAN SIRS DENGAN TRANSMISI NON-LINIER; LYAPUNOV FUNCTIONS AND GLOBAL STABILITY FOR SIR AND SIRS EPIDEMIOLOGICAL MODELS WITH NON-LINEAR TRANSMISSION

Hasriani Ishak, L ina Aryati

2012 | Disertasi | PROGRAM STUDI S2 MATEMATIKA

The stability of the equilibrium point of the system using Lyapunov function is discussed in this thesis. Lyapunov function is used for the global stability of dimensional compartment epidemic model with the common function f(S,I) as non linear transmission rates, with f(S,I) of characteristics is monotonically increase with respect to S and I and concave with respect to I. In this thesis, two epidemic models are discussed, those are SIR and SIRS. Two equilibrium points from SIR or SIRS are obtained using equivalent way of Lyapunov function, They must be local asymptotically stable for all appropriate parameter value. With appropriate parameter value and initial value near equilibrium points, then for along time, there are two possibilities, those are the susceptible population and infected population will be existent, or the infected population extinctand suspectible population will be existent. Furthemore, with appropriate parameter value, for a long time, all population will be existent for any initial value. Numerical simulations are given to ilustrate stability behaviour of equilibrium point

Kata Kunci : FUNGSI LYAPUNOV; STABILITAS GLOBAL; MODEL EPIDEMIOLOGI SIR DAN SIRS; TRANSMISI NON-LINIER