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All Journal Limits: Journal of Mathematics and Its Applications
Windarto, Windarto
Department of Mathematic, Airlangga University
Mathematics

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Analisis Kestabilan dan Kontrol Optimal pada Model Matematika Penyebaran Penyakit Mumps Miswanto, Miswanto; Biba, Farah; Windarto, Windarto
Limits: Journal of Mathematics and Its Applications Vol 21, No 1 (2024)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v21i1.20053

Abstract

Mumps is an acute disease in children and adults, caused by paramyxovirus. In this thesis, a mathematical model analysis of the spread of mumps disease was carried out and the application of optimal control, namely prevention by giving vaccinations and treatment. Based on the analysis of the model without control obtained a non-endemic equilibrium point and an endemic equilibrium point. The non-endemic equilibrium point is local asymptotic stable if the basic reproduction number is less than one while the endemic equilibrium point tends to be local asymptotic stable if the basic reproduction number is more than one . Optimal control on the mathematical model of the spread of mumps disease was carried out using the Pontryagin’s Maximum Principle. The results of numerical simulations show that the provision of control, namely prevention and treatment, is simultaneously considered the most effective and efficient to minimize the number of individual populations infected with mumps disease with minimum cost.
Co-Authors Biba, Farah Miswanto