STABILITAS DAN BIFURKASI HOPF PADA MODEL EPIDEMI SIRS DENGAN LAJU PENULARAN NONLINEAR; STABILITY AND HOPF BIFURCATION OF AN SIRS EPIDEMIC MODEL WITH NONLINEAR INCIDENCE RATE

Muhammad Rais Ridwan, Lina Aryati

2013 | Disertasi | PROGRAM STUDI S2 MATEMATIKA

In this paper discussed the SIRS epidemic model with transmission rate the general nonlinear with , and .There are two types of equilibrium point is disease-free equilibrium and the point endemic equilibrium. The existence of disease-free equilibrium point is not specified by parameter and and while the endemic equilibrium point is by these parameters. Analysis of the stability of the equilibrium point epidemic models consists of local stability and globall stability. Based on the rate of transmission nonlinear in general are causing changes in local stability of disease-free equilibrium point. Analysis of Hopf bifurcation at the equilibrium point endemic. Changes in parameter values indicate changes in the stability endemic equilibrium point. Numerical simulations are given to illustrate stability of the equilibrium point.

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