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All Journal SELAPARANG: Jurnal Pengabdian Masyarakat Berkemajuan EIGEN MATHEMATICS JOURNAL Journal of Research Applications in Community Services Basis : Jurnal Ilmiah Matematika Jurnal Sains Natural JMT (Jurnal Matematika dan Terapan) Journal of Mathematics, Computation and Statistics (JMATHCOS)
Raming, Indriasri
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Journal : EIGEN MATHEMATICS JOURNAL

 1 
Natural Cubic Spline Method as a Method in Constructing a Life Table in Gegelang Village West Lombok Fauzi, Andri Azmul; Ridwan, Lalu Muhammad; Agustini, Dwi; Putri, Desi Febriani; Tumilaar, Rinancy; Asmaidi, Asmaidi; Raming, Indriasri
Eigen Mathematics Journal Vol 7 No 1 (2024): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v7i1.215

Abstract

This research aims to reconstruct a life table based on real data obtained in Gegelang Village, West Lombok. The data used in this research is the population in 2016, the death rate in 2014-2018 and the birth rate in 2014-2018. The first step taken was to compile a rough life table using the partial data situation and full data situation methods. Both methods are included in the maximum likelihood method. After carrying out calculations, different life expectancy figures are obtained. The respective calculation results were 62.21 years for the partial data situation method and 73.07 years for the full data situation method. Next, a graduation is carried out using the natural cubic spline method on the life table obtained from a rough life table model calculation. The graphic model produced by the rough life table is fluctuating so it is necessary to graduate using the natural cubic spline method to obtain a monotonically decreasing graph. The life table model chosen for graduation is a life table whose life expectancy is close to the life expectancy of West Lombok Regency in 2015, namely 65.1 years. After graduation, the new life expectancy was found to be 66.92 years.
Penerapan Kendali Optimal pada Model Matematika SEITRS Penularan Tuberkulosis dengan Variabel Kendali Sosialisasi dan Terapi Rafiq, Muhammad; Wigantono, Sri; Raming, Indriasri
Eigen Mathematics Journal Vol 8 No 2 (2025): December
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v8i2.322

Abstract

Tuberculosis (TB) is an infectious disease caused by Mycobacterium tuberculosis, which remains a serious public health concern. The objective of this study is to develop, analyze, and propose an optimal control strategy for the transmission dynamics of TB using an SEITRS mathematical model. The model consists of five population compartments: Susceptible (S), Exposed (E), Infected (I), Treatment (T), and Recovered (R). The methodology involves constructing the SEITRS model, determining the equilibrium points, and analyzing their stability under different conditions of the basic reproduction number. The model has two equilibrium points, namely the non-endemic and endemic equilibrium. If the basic reproduction number is less than one and certain conditions are satisfied, the non-endemic equilibrium is locally asymptotically stable. Conversely, if the basic reproduction number is greater than one and specific conditions are met, the endemic equilibrium becomes locally asymptotically stable. Furthermore, this study provides optimal control strategies in the SEITRS model. We use two control variables in this model, namely socialization and therapy, to reduce the number of infected individuals. The sufficient conditions for the existence of optimal controls are derived using Pontryagin’s Maximum Principle. Numerical simulations are then conducted to examine the impact of applying these controls on the system. The simulation results indicate that the simultaneous implementation of socialization and therapy controls is effective in reducing the number of TB-infected individuals.
Co-Authors A'yun, Qonita Qurrota Adawiyah, Rabbiatul Agustina, Ayu Risma Aminah, Esse Ashari, Trie Andini Nur Aslina Asmaidi Asmaidi Auliya Rahman Avrilia, Mia Putri A’yun, Qonita Qurrota Cahyadi, Aldy Fradana Mahaputra Dala, Maria Alensia Deltin Dimas Raditya Dwi Agustini, Dwi Elvita, Melati Fahrezi, Korompot Naufal Fauzi, Andri Azmul Fidia Deny Tisna Amijaya Hardina Sandariria Manggiri, Itsar Meirylia, Dhita Putri Moh. Nurul Huda, Moh. Nurul Muhammad Rafiq Mulyadi, Taqriri Kamal Munfaati, Rafika Husnia Pridiptama, Raka Putra Putri, Annisa Amalia Putri, Desi Febriani Ramadhanty, Husna Novia Ridwan, Lalu Muhammad Saderisa, Saderisa Sahputra, Dimas Raditya Said Said, Said Selasih, Dian Sri Wigantono Syaripuddin Syaripuddin Syaripuddin Tumilaar, Rinancy Wasono, Wasono Wirawan, Adellia Septina Wulandari Wulandari