Analisis kestabilan dan kontrol optimal model matematika penyebaran penyakit Ebola dengan variabel kontrol berupa karantina

Erzalina Ayu Satya Megananda, Cicik Alfiniyah, Miswanto Miswanto


Ebola disease is an infectious disease caused by a virus from the genus Ebolavirus and the family Filoviridae. Ebola disease is one of the most deadly diseases for human. The purpose of the thesis is to analyze the stability of the equilibrium point and to apply the optimal control of quarantine on a mathematical model of the spread of ebola. Model without control has two equilibria, non-endemic equilibrium and endemic equilibrium. The existence of endemic equilibrium and local stability depends on the basic reproduction number (R0). The non-endemic equilibrium is asymptotically stable if R0 < 1 and endemic equilibrium tend to asymptotically stable if R0 > 1. The problem of optimal control is solved by Pontryagin’s Maximum Principle. From the numerical simulation, the result shows that control is effective enough to minimize the number of infected human population and to minimize the cost of its control.


Mathematical Model; Ebola Disease; Stability; Quarantine; Optimal Control

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World Health Organization, “Ebola virus disease,”, Beijing, accessed on March 13, 2018.

N. Dharmayanti dan I. Sendow, “Awareness of Ebola: exotic zoonotic disease,” Indonesian Bulletin of Animal and Veterinary Sciences, vol. 25, no. 1, 2015.

Centers for Disease Control and Prevention, “Ebola hemorrhagic fever,”, accessed on March 13, 2018.

S. A. Carroll, J. S. Towner, T. K. Sealy, L. K. McMullan, M. L. Khristova, F. J. Burt, R. Swanepoel, P. E. Rollin, dan S. T. Nichol, “Molecular evolution of viruses of the family Filoviridae Based on 97 whole-genome sequences,” Journal of Virology, vol. 87, no. 5, hal. 2608–2616, 2013.

F. Agusto, “Mathematical model of Ebola transmission dynamics with relapse and reinfection,” Mathematical Biosciences, vol. 283, hal. 48–59, 2017.

P. Diaz, P. Constantine, K. Kalmbach, E. Jones, dan S. Pankavich, “A modified SEIR model for the spread of Ebola in Western Africa and metrics for resource allocation,” Applied Mathematics and Computation, vol. 324, hal. 141–155, 2018.

A. Dénes dan A. B. Gumel, “Modeling the impact of quarantine during an outbreak of Ebola virus disease,” Infectious Disease Modelling, vol. 4, hal. 12–27, 2019.[8] 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.

N. Chitnis, J. M. Hyman, dan J. M. Cushing, “Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model,” Bulletin of Mathematical Biology, vol. 70, no. 5, hal. 1272–1296, 2008.

L. S. Pontryagin, V. G. Boltyanskii, G. R. V, dan E. F. Mishchenko, The mathematical theory of optimal processes. New York: Wiley, 1962.

S. Lenhart dan J. T. Workman, Optimal control applied to biological models. Chapman and Hall/CRC, 2007.


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