Open AccessAnalisis Kestabilan dan Kontrol Optimal Model Matematika Penyebaran Penyakit Ebola dengan Penanganan Medis
Author(s) -
Sofita Suherman,
Fatmawati Fatmawati,
Cicik Alfiniyah
Publication year - 2019
Publication title -
contemporary mathematics and applications
Language(s) - English
Resource type - Journals
ISSN - 2686-5564
DOI - 10.20473/conmatha.v1i1.14772
Subject(s) - basic reproduction number , stability theory , epidemic model , population , pontryagin's minimum principle , maximum principle , optimal control , stability (learning theory) , control theory (sociology) , mathematics , mathematical optimization , virology , computer science , control (management) , biology , physics , medicine , artificial intelligence , environmental health , nonlinear system , quantum mechanics , machine learning
Ebola disease is one of an infectious disease caused by a virus. Ebola disease can be transmitted through direct contact with Ebola’s patient, infected medical equipment, and contact with the deceased individual. The purpose of this paper is to analyze the stability of equilibriums and to apply the optimal control of treatment on the mathematical model of the spread of Ebola with medical treatment. Model without control has two equilibria, namely non-endemic equilibrium (E0) and endemic equilibrium (E1) The existence of endemic equilibrium and local stability depends on the basic reproduction number (R0). The non-endemic equilibrium is locally asymptotically stable if R0 1 . The problem of optimal control is then solved by Pontryagin’s Maximum Principle. From the numerical simulation result, it is found that the control is effective to minimize the number of the infected human population and the number of the infected human with medical treatment population compare without control.