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Kamiran
Departemen Matematika ITS Surabaya Indonesia
Computer Science & IT Mathematics

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Analisis dan Kontrol Optimal pada Model Dinamik Penyebaran Virus Zika Suhud Wahyudi; Nurani Dwi Pangestu; Kamiran
Limits: Journal of Mathematics and Its Applications Vol. 20 No. 1 (2023): Limits: Journal of Mathematics and Its Applications Volume 20 Nomor 1 Edisi Ma
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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Abstract

Zika is a virus from flaviviridae family and flavivirus genus that spread by Aedes Aegypti mosquito and that can cause serious problem disease such as Guillain Barre Syndrome (GBS) and mikrosefalus. In this paper used spreading dynamic zika virus model that consists of two population and divided to sub population Susceptible humans, sub-population Asymtomatic Infected humans, sub-population Infected humans, sub-population Recovered humans, sub-population Susceptible mosquitoes, and sub-population Infected mosquitoes. The model that anlysis by determine the basic reproduction number, the point of disease free and endemic equilibrium, and the stability of each point of equilibrium. Then, do the optimal control using Pontryagin principle with numerical solution given by Range-Kutta method. The simulation results show the decreasing sub-population of infected humans, asymptomatic infected human, and population of mosquitoes after given controls such using condom, treatment, and using indoor residual spray.
Aplikasi Metode Adams-Bashforth-Moulton Model Verhulst Pada Hasil Panen Padi di Kabupaten Jombang Lukman Hanafi; Kamiran; Sadjidon; Rizki Eko Prasetyo
Limits: Journal of Mathematics and Its Applications Vol. 21 No. 1 (2024): Limits: Journal of Mathematics and Its Applications Volume 21 Nomor 1 Edisi Ma
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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Abstract

Rice is one of the main crops produced by agricultural commodities which is staple food of most Indonesian people. The availability of rice is needed to anticipate the emergence of problems in the future such as population growth, changes in seasons, or as an export commodity. Estimation of rice availability in the future can be done by forming a mathematical model, where the mathematical model used is the Verhulst logistic model. The differential equations in the Verhulst model are first solved using Runge-Kutta method to obtain four initial solutions to be used in finding approximate values using the Adams-Bashforth-Moulton method. After obtaining an approximate solution, a comparison of the accuracy based on error is carried out. The Verhulst model with a step size and carrying capacity rice harvest at Jombang Regency limited 500,000 tons, 600,000 tons, and 700,000 tons, obtained rate error values from numerical solution of Adams-Bashforth-Moulton method is 3.35%, 3.39%, and 3.36%.
Co-Authors Lukman Hanafi Nurani Dwi Pangestu Rizki Eko Prasetyo Sadjidon Suhud Wahyudi