# PEMODELAN MATEMATIKA EPIDEMI INFLUENZA DENGAN MEMPERHATIKAN PELUANG KEBERHASILAN VAKSINASI DAN KEKEBALAN TETAP

• Nisa Aulia Universitas Negeri Semarang
• Muhammad Kharis Universitas Negeri Semarang
• Supriyono Supriyono Universitas Negeri Semarang
Keywords: Influenza Epidemic Model; Vaccination; Analysis of Stability; Equilibrium Point

### Abstract

This study reviews about a mathematical model for influenza epidemic. The mathematical model used is in the form of SIR epidemic models.This model considerates the factors of vaccination as a prevention of influenza diseases spread and immunity remains of each person who has recovered from the disease. In this research, it is conducted the study concerning the mathematical model of influenza epidemics by considering the chances of vaccination success and immunity remains, analysis of equilibrium and stability of the model, as well as model simulation and interpretation of model behavior. The method used is literature review, laboratory studies and analysis. The first step in this research is to determine the problem, formulate the problem, literature review, analysis and problem solving as well as the conclusion. As the results, it is obtained a model with four variable and nine parameters. From the model obtained an equilibrium point that is disease free equilibrium point which is stable asymptotically on R0 < 1 and unstable on R0 > 1. Furthermore, It is concluded that there is no possibility of widespreadoutbreaks and a geometric overview is given in the form of simulation with Maple 12 program.

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Published
2017-02-27
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