Kestabilan Model SIRS dengan Pertumbuhan Logistik dan Non-monotone Incidence Rate

Mohammad soleh (Jurusan Matematika Fakultas Sains dan Teknologi UIN Suska Riau)
Syamsuri Syamsuri (Jurusan Matematika Fakultas Sains dan Teknologi UIN Suska Riau)

Seminar Nasional Teknologi Informasi Komunikasi dan Industri
2015: SNTIKI 7

This paper discussed about mathematical modeling on the spread of infectious diseases by SIRS model. Most research about SIRS models is using exponential growth, so we propose SIRS model with logistic growth. This model has two equilibrium states: disease-free equilibrium and endemic state. Both equilibrium state are determined by solving the equations in the model. Each equilibrium state tested stability criteria eigen values. Our result obtained that if then a free equilibrium state is asymptotically stable, otherwise if then an endemic state is asymptotically stable.Keywords : Asymptotically Stable, Equilibrium State, Exponential Growth, Logistic Growth, SIRS Model.