Analisis Kestabilan dan Kontrol Optimal pada Model Matematika Penyebaran Penyakit Mumps

Miswanto Miswanto, Farah Biba, Windarto Windarto

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.

Keywords


Mumps, Equilibrium Point, Stability, Basic Reproduction Number, Optimal Control

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References


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DOI: http://dx.doi.org/10.12962/limits.v21i1.20053

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Limits: Journal Mathematics and its Aplications by Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
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