Analisis model epidemi SEIV dengan laju penularan nonlinear

HIKMAH, Nurul, Prof. Dr. Widodo, M.S

2009 | Tesis | S2 Matematika

Diberikan model epidemi SEIV dengan laju penularan non linier. Model ini menjelaskan efek psikologis dari perubahan perilaku individu yang rentan ketika jumlah individu yang sakit meningkat dan untuk menentukan eksistensi dan kestabilan titik ekuilibrium bebas penyakit dan endemik. Didefinisikan angka reproduksi dasar (rumus), dengan (simbol) jumlah individu yang direkrut ke dalam kelas rentan, (simbol) proporsi individu rentan yang diberi vaksin, (simbol) laju kontak perkapita, (simbol) laju individu yang telah sembuh, (simbol) laju perpindahan individu dari kelas (simbol) ke kelas (simbol) yang bernilai konstan, (simbol) laju kematian alami yang bernilai konstan, dan (simbol) laju berkurangnya vaksin. Jika (simbol)(simbol)(simbol) 1 maka titik ekuilibrium bebas penyakit stabil asimtotik global dan jika (simbol)(simbol)(simbol) 1, maka titik ekuilibrium endemik stabil global.

We consider a SEIV epidemic model with non linear incidence rate. The model describes the psychological effect of the behavioral change of susceptible individuals when the number of infectious individuals increases as well as determining the existence and stability of disease-free equilibrium and endemic equilibrium points. The basic reproduction number is defined by (formula), where (symbol) is the recruitment rate individuals into the susceptible population, p is the fraction of recruited individuals who are vaccinated,(symbol) is the rate at which susceptible individuals become infectious, (symbol) is the rate at which infected individuals are treated or recovered, (symbol) is the rate at which exposed individuals become infectious, (symbol) is the natural date rate, and (symbol) is the rate at which vaccine wanes. It is shown that if the basic reproduction number (symbol) (symbol) (symbol) 1, then the disease-free equilibrium is globally asymptotically stable and if (symbol) (symbol) (symbol) 1, then the endemic equilibrium is globally stable.

Kata Kunci : SEIV,Titik ekuilibrium,Kestabilan, SEIV, Equilibrium point , Stability