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All Journal Communication in Biomathematical Sciences Limits: Journal of Mathematics and Its Applications PengabdianMu: Jurnal Ilmiah Pengabdian kepada Masyarakat Contemporary Mathematics and Applications (ConMathA)
Windarto
Departemen Matematika, Universitas Airlangga
Agriculture, Biological Sciences & Forestry Economics, Econometrics & Finance Law, Crime, Criminology & Criminal Justice Materials Science & Nanotechnology Mathematics Public Health Social Sciences

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Journal : Limits: Journal of Mathematics and Its Applications

 1 
Pendekatan Numerik pada Model Penyebaran SARS dengan Method of Lines Patria Arif Bijaksana; Windarto Windarto; Fatmawati Fatmawati
Limits: Journal of Mathematics and Its Applications Vol 15, No 1 (2018)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (430.006 KB) | DOI: 10.12962/limits.v15i1.3489

Abstract

Pada paper ini dikaji pendekatan numerik model matematika penyebaran SARS dengan adanya suku difusi. Suku difusi pada model tersebut mengilustrasikan penyebaran SARS berdasarkan lokasi. Solusi numerik dilakukan dengan menggunakan Method of Lines. Selanjutnya dibandingkan hasil simulasi numerik antara model penyebaran SARS tanpa suku difusi dan dengan adanya suku difusi. Hasil simulasi dari model penyebaran penyakit SARS tanpa suku difusi hanya menunjukkan terjadinya penyebaran SARS secara periodik waktu. Berdasarkan hasil simulasi pada model SARS dengan adanya suku difusi dapat diketahui bahwa penyebaran SARS dapat ditinjau dari titik awal penyebaran SARS secara spasial dan juga perodik waktu. Lebih lanjut, dari hasil simulasi menunjukkan bahwa semakin jauh dari pusat penyebaran SARS, laju penyebaran penyakit SARS akan semakin kecil
Analisis Kestabilan dan Kontrol Optimal pada Model Matematika Penyebaran Penyakit Mumps Miswanto Miswanto; Farah Biba; 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 Abdul Faliq Anwar Adiluhung Setya Pambudi Alfiniyah, Cicik Bertha Aurellia Pamudya Fajar Dinda Ariska Putri Eridani Farah Biba Fatmawati Fatmawati Fatmawati, Fatmawati Inna Kuswandari Jaelani, Abdulloh Miswanto Nanda Amalia Rahma Nisrina Firsta Ammara Patria Arif Bijaksana Riris Nur Patria Putri Utami Dyah Purwati