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All Journal Seminar Nasional Teknologi Informasi Komunikasi dan Industri
Mohammad soleh
Jurusan Matematika Fakultas Sains dan Teknologi UIN Suska Riau
Computer Science & IT Control & Systems Engineering Electrical & Electronics Engineering Industrial & Manufacturing Engineering Mathematics

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Kestabilan Model SIRS dengan Pertumbuhan Logistik dan Non-monotone Incidence Rate Mohammad soleh; Syamsuri Syamsuri
Seminar Nasional Teknologi Informasi Komunikasi dan Industri 2015: SNTIKI 7
Publisher : UIN Sultan Syarif Kasim Riau

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Abstract

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.
Kestabilan Model SIS dengan Non-monotone Incidence Rate & Treatment Mohammad Soleh
Seminar Nasional Teknologi Informasi Komunikasi dan Industri 2015: SNTIKI 7
Publisher : UIN Sultan Syarif Kasim Riau

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (529.627 KB)

Abstract

Our paper proposed a non monoton incidence rate, logistic growth, migration, and under treatment for SIS model. The character of originally SIS model which using bilinear insience rate will cover by new model. An existences and stabilities of free disease state and endemic are investigated to explore the characteristic of model. The existence of equilibrium point is founded by solving differential equation of the model and their stability are explored by an eigen criteria. We obtained that only one free disease state and endemic which asimtotycal stable by condition.Key words: Endemic state, Free Disease state, Non Monoton Incidence Rate, SIS Model, treatment.
Co-Authors Syamsuri Syamsuri