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All Journal Jurnal Ilmu Dasar JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI CAUCHY: Jurnal Matematika Murni dan Aplikasi Kubik NUMERICAL (Jurnal Matematika dan Pendidikan Matematika) JURNAL ILMIAH MATEMATIKA DAN TERAPAN JTAM (Jurnal Teori dan Aplikasi Matematika) Jurnal Matematika UNAND Majalah Ilmiah Matematika dan Statistika (MIMS) KUBIK: Jurnal Publikasi Ilmiah Matematika EBAMUKAI; JURNAL PENGABDIAN ILMU PENGETAHUAN DAN TEKNOLOGI
Joko Harianto
Program Studi Matematika, Fakultas MIPA, Universitas Cendrawasih
Agriculture, Biological Sciences & Forestry Humanities Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Education Mathematics Physics Public Health Social Sciences

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Journal : NUMERICAL (Jurnal Matematika dan Pendidikan Matematika)

 1 
Effect of Population Density on the Model of the Spread of Measles Joko Harianto; Katarina Lodia Tuturop; Venthy Angelika
Numerical: Jurnal Matematika dan Pendidikan Matematika Vol. 4 No. 2 (2020)
Publisher : Institut Agama Islam Ma'arif NU (IAIMNU) Metro Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25217/numerical.v4i2.831

Abstract

This study is expected to contribute to the health sector, specifically to describe the dynamics of the measles spread through the models that have been analyzed. One of the factors that became the focus of this study was reviewing the influence of population density on measles spread. The initial step formulated the model and then determined the primary reproduction number and analyzed the stability of the model equilibrium point. The results of the analysis of this model show that there are two conditions for the value of which is a requirement that the existence of two model equilibrium points as well as local stability is needed, namely and . When , there exists a unique equilibrium point, called the non-endemic equilibrium point denoted by . Conversely, when , there are two equilibrium points, namely and the endemic equilibrium point characterized by . The results of local stability analysis show that when , the equilibrium point is stable asymptotic locally. It means that if hold, then in a long time there will not be a spread of disease in the susceptible and vaccinated sub-population, or in other words, the outbreak of the disease will stop. Conversely, when equilibrium point is stable asymptotic locally. It means that if , then measles disease is still in the environment for an infinite time with the condition of the proportions of each sub-population approach to , , and .
Co-Authors Alfonsina Lisda Puspa Dewi Anike Bowaire Denny Fitrial FEBY SERU Imam Fahcruddin Jonner Nainggolan K L Tuturop Katarina Lodia Tuturop Katarina Lodia Tuturop Katarina Lodia Tuturop Krista M. Ansanay Magrice S. Maran Mesakh Wandikbo Mira Aprilia Marcus Novana V. J. Kareth Sari, Inda Puspita Titik Suparwati Venthy Angelika Venthy Angelika Wani Tabuni Zakaria V. Kareth