| Summary: | 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.
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