ANALISIS KESTABILAN MODEL EPIDEMI SVEIR DENGAN IMUNITAS PARSIAL; ( ANALYSIS OF AN SVEIR EPIDEMIC MODEL WITH PARTIAL IMMUNITY )

Hanum, Ulfi, Widodo

2016 | Disertasi | FMIPA

In this thesis we establish a SV EIR epidemic model with nonlinear incidence rate. Vaccinated class is assumed to have partial immunity. The basic reproduction number R0 obtained by using the next generation matrix. We consider the value of R0 to determined the existence and the local stability of disease-free equilibrium point and endemic equilibrium point. If R0 < 1, the disease-free equilibrium point is asymptotically stable global, it proved by determine the solution of each variable in the SV EIR model. When R0 > 1; to determine local asymptotic stability of endemic equilibrium point we used Hurwitz criteria, and for established sufficient condition of global asymptotic stability in endemic equilibrium point we used geometrical approach. To show the effect of R0 value in the equilibrium points, we simulated for measles case.

Kata Kunci : SVEIR epidemic model; equilibrium point; stability, Compound Matrix; Perron-Frobenius; measles