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

Ebola disease is an infectious disease caused by a virus from the genus Ebolavirus and family Filoviridae. Ebola disease is one of the most deadly diseases for human. The purpose of thesis is to analyze the stability of equilibrium point and to apply the optimal control of quarantine on 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 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 result show that control is effective enough to minimize the number of infected human population and to minimize cost of its control.