Analisis dinamik model SVEIR pada penyebaran penyakit campak

Sitty Oriza Sativa Putri Ahaya, Emli Rahmi, Nurwan Nurwan


In this article, we analyze the dynamics of measles transmission model with vaccination via an SVEIR epidemic model. The total population is divided into five compartments, namely the Susceptible, Vaccinated, Exposed, Infected, and Recovered populations. Firstly, we determine the equilibrium points and their local asymptotically stability properties presented by the basic reproduction number R0. It is found that the disease free equilibrium point is locally asymptotically stable if satisfies R0<1 and the endemic equilibrium point is locally asymptotically stable when R0>1. We also show the existence of forward bifurcation driven by some parameters that influence the basic reproduction number R0 i.e., the infection rate α or proportion of vaccinated individuals θ. Lastly, some numerical simulations are performed to support our analytical results.


Mathematical Modeling; Measles; Equilibrium Point; Local Stability; Vaccination

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Kementerian Kesehatan RI Pusat Data dan Informasi., “Situasi campak dan rubella di Indonesia,” Tech. Rep., 2018.

CDC, “Measles (Rubeola),”, 2020, [Online; diakses 5 November 2020].

WHO, “Measles,”, 2019, [Online; diakses 5 November 2020].

M. Z. Ndii, Pemodelan matematika. Yogyakarta: Penerbit Deepublish, 2018.

H.W. Hethcote, “Three basic epidemiological models,” Biomathematics, vol. 18, 1989.

W. Kermack dan A. G. McKendrick, “A contribution to the mathematical theory of epidemics,” Proceedings of the Royal Society of London, vol. Part A 115 (772), hal. 700–721, 1927.

A. A. Momoh, M. O. I. Ibrahim, I. J. Uwanta, dan S. B. Manga, “Mathematical model for control of measles epidemiology,” International Journal of Pure and Applied Mathematics, vol. 67, hal. 707–718, 2013.

S. Edward, K. Raymond E., K. Gabriel T., F. Nestory, M. Godfrey G., dan M. Arbogast P., “A mathematical model for control and elimination of the transmission dynamics of measles,” Applied and Computational Mathematics, vol. 4, no. 6, hal. 396, 2015.

D. Aldila dan D. Asrianti, “A deterministic model of measles with imperfect vaccination and quarantine intervention,”

Journal of Physics: Conference Series, vol. 1218, hal. 012044, 2019.

M. Fakhruddin, D. Suandi, Sumiati, H. Fahlena, N. Nuraini, dan E. Soewono, “Investigation of a measles transmission

with vaccination: A case study in Jakarta, Indonesia,” Mathematical Biosciences and Engineering, vol. 17, no. 4, hal. 2998–3018, 2020.

P. van den Driessche dan J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for

compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, no. 1-2, hal. 29–48, 2002.

A. Suryanto, Metode numerik untuk persamaan diferensial biasa dan aplikasinya dengan Matlab. Malang: Penerbit UNM,


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