ANALISIS KESTABILAN LOKAL TITIK EKUILIBRIUM MODEL EPIDEMI SEIV DENGAN PERTUMBUHAN LOGISTIK

Abstract

The SEIV model uses population growth which is assumed to follow logistical growth. The model is studied then analyzed. The analysis shows that the non-endemic (disease-free) equilibrium point is locally asymptotically stable when the basic reproduction number less than one, while the endemic equilibrium point is locally asymptotically stable when the basic reproduction number greater than one. Then a numerical simulation was carried out using Maple software to support the results of the local stability analysis of the equilibrium point. Based on numerical simulations, it shows that a disease will disappear from the population when the basic reproduction number less than one and for a long time a disease will remain in the population (still an epidemic) when the basic reproduction number greater than one.
Keywords: SEIV model, logistical growth, equilibrium point, basic reproduction number
MSC2020: 92C60