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All Journal IAES International Journal of Robotics and Automation (IJRA) CAUCHY: Jurnal Matematika Murni dan Aplikasi Kinetik: Game Technology, Information System, Computer Network, Computing, Electronics, and Control Limits: Journal of Mathematics and Its Applications PengabdianMu: Jurnal Ilmiah Pengabdian kepada Masyarakat Contemporary Mathematics and Applications (ConMathA)
Miswanto
Universitas Airlangga
Agriculture, Biological Sciences & Forestry Automotive Engineering Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Electrical & Electronics Engineering Energy Engineering Law, Crime, Criminology & Criminal Justice Materials Science & Nanotechnology Mathematics Public Health Social Sciences

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Analisis Kestabilan dan Kontrol Optimal Model Matematika Penyebaran Leptospirosis dengan Saturated Incidence Rate Miswanto; Nisrina Firsta Ammara; Windarto
Contemporary Mathematics and Applications (ConMathA) Vol. 5 No. 2 (2023)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v5i2.49379

Abstract

Leptospirosis is a disease caused by the bacteria Leptospira inchterohemorrhagiaea. Leptospirosis can attack humans and other animals, through rodents, especially rats. This research aims to analyze the stability of the equilibrium point in the mathematical model of the spread of Leptospirosis and apply optimal control variables in the form of prevention and treatment efforts. Based on the results of the mathematical model analysis of the spread of Leptospirosis, two equilibrium points were obtained, there are the non-endemic equilibrium point and the endemic equilibrium point. Local stability and the existence of an equilibrium point depend on the basic reproduction number ????0. The non-endemic equilibrium point is local asymptotically stable if ????0 < 1, while the endemic equilibrium point tends to be asymptotically stable if ????0 > 1. Next, the problem of control variables in the model is determined using Pontryagin's Maximum Principle. Numerical simulation results show that providing control in the form of prevention efforts and treatment efforts simultaneously provides effective results in minimizing the population of individuals exposed to and infected by Leptospirosis at the cost of providing optimal control.
Analisis Kestabilan Model Predator Prey Leslie Gower dengan Fungsional Respon Crowley Martin dan Adanya Prey Terinfeksi Serta Faktor Ketakutan Miswanto Miswanto; Nunik Suroiyah; Windarto Windarto
Limits: Journal of Mathematics and Its Applications Vol 20, No 3 (2023)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v20i3.18530

Abstract

Ekosistem adalah suatu sistem yang terdiri dari organisme hidup dan lingkungannya yang seringkali terjadi interaksi antara makhluk hidup dengan lingkungannya, atau makhluk hidup yang satu dengan mahkluk hidup yang lain. Sebagai contoh interaksi antara predator dengan prey, yaitu singa dengan rusa, ular dengan tikus, burung elang dengan ular dan lain-lain. Pada interaksi antara predator prey seringkali nampak adanya prey yang terinfeksi. Hal ini berdampak adanya penyebaran penyakit oleh prey terinfeksi. Penelitian ini mengkaji model predator prey Leslie Gower fungsi respon Crowley Martin dengan prey terinfeksi serta adanya faktor ketakutan. Metode yang digunakan dalam penelitian ini adalah metode analitik dan simulasi numerik. Metode analitik digunakan untuk mengkaji eksistensi titik setimbang dan analisis kestabilan titik setimbang model, sedangkan metode simulasi numerik digunakan untuk mendukung hasil metode analitik. Berdasarkan hasil analitik diperoleh dua titik setimbang yang cenderung stabil asimtotis, yaitu titik setimbang kepunahan prey terinfeksi dan predator (E1) dan titik setimbang kepunahan predator (E2) Sedangkan titik setimbang kepunahan prey terinfeksi (E3) dan titik setimbang koeksistensi (E4) tidak diperoleh secara analitik. Oleh karena analisis kestabilannya menggunakan bidang fase. Hasil simulasi numerik menunjukkan bahwa keempat titik setimbang, yaitu E1,E2, E3, dan E4 cenderung stabil asimtotis.
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 Alfiniyah, Cicik Bertha Aurellia Pamudya Fajar Biba, Farah D. Mahayana Elda Widya Er Ayu Nurafifah Fatmawati Fatmawati H Muhammad H. Muhammad Mhammad I. Pranoto I. Pranoto Khusnul Khotimah, Bain Laurensia Regina Bestari Gepak Mahayana, D Millah, Nashrul Mohammad Imam Utoyo Nisrina Firsta Ammara Nunik Suroiyah Puja Nur Audria Sentot Achmadi Windarto Windarto Windarto Windarto, Windarto Yeni Kustiyahningsih