Analisis Model Matematika Penularan Campak dengan Vaksinasi dan Rawat Inap Menggunakan Bifurkasi Transkritikal

Authors

Dimaz Wahyu Adipradana Institut Teknologi Sepuluh Nopember

DOI:

Abstract

Measles as one of notifable disease gets serious concern worldwide since it was first found in ninth century. The implementation of vaccines for controlling measles transmission since 1963 up to nowadays requires various studies regarding the efectiveness of the vaccines. The studies of modeling of measles virus transmission has been done by many researchers in Mathematics. In this study, three different models of measles virus transmission that include hospitalization compartment. In the first model, the population is constant, while in the second model, the population dependent by time. The last model, the infected population respect to Holling type II functional response. The model divided the population into Susceptibles ( ), Infectives ( ), Hospitalized ( ), and Recovered ( ) or called SIHR model. The analysis started with determining the the equilibria and their stability based on Basic Reproduction Number ( ). Futhermore, we do bifurcation analysis on those models and find a transcritical bifurcation.

Keywords: Basic Reproduction Number, Equilibrium, Hospitalized, Measles, Transcritical Bifurcation, Vaccination

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