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All Journal Epsilon: Jurnal Matematika Murni dan Terapan Jurnal Fisika FLUX Jurnal Matematika Sains dan Teknologi Desimal: Jurnal Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Tropical Wetland Journal Bubungan Tinggi: Jurnal Pengabdian Masyarakat Jurnal Abdimas Prakasa Dakara
Yuni Yulida
Program Studi Matematika FMIPA Universitas Lambung Mangkurat
Agriculture, Biological Sciences & Forestry Humanities Chemical Engineering, Chemistry & Bioengineering Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Energy Engineering Materials Science & Nanotechnology Mathematics Mechanical Engineering Medicine & Pharmacology Physics Social Sciences Transportation Other

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MODEL SEIDR DALAM STUDI PENYEBARAN TUBERKULOSIS: ANALISIS INTERVENSI DIAGNOSIS DAN DAMPAKNYA TERHADAP DINAMIKA INFEKSI Sila Rizqina; Muhammad Afief Balya; Yuni Yulida; Muhammad Ahsar Karim; Hermei Lissa
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 1 (2025)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v19i1.15641

Abstract

Pulmonary Tuberculosis (TB) is a contagious infectious disease caused by Mycobacterium tuberculosis. A person with tuberculosis serves as a source of transmission to the surrounding population. One way to minimize the transmission is through the implementation of effective diagnostic intervention. One approach to understanding the dynamics of TB spread is through the SEIDR epidemiological mathematical model, which includes susceptible, exposed, infectious, diagnosed, and recovered individuals. This study begins by explaining the construction of the SEIDR model, followed by determining the disease-free equilibrium point, the basic reproduction number, local stability analysis of the disease-free equilibrium, and sensitivity analysis. The final step involves conducting numerical simulations and interpreting the results obtained. There are two equilibrium points derived from the model: the disease-free equilibrium and the endemic equilibrium. The disease-free equilibrium point is asymptotically stable if the basic reproduction number is less than one, while the endemic equilibrium point is determined through simulation. Based on the simulation, it is found that the system experiences an outbreak when the basic reproduction number is greater than one. Sensitivity analysis shows that the birth rate has the highest positive influence on the basic reproduction number, while the natural death rate has the highest negative influence on the basic reproduction number. Numerical simulation results show that when transmission is high, the number of diagnosed individuals increases sharply, while the susceptible and exposed populations decrease drastically; conversely, if transmission is suppressed, active cases decline until they are completely eliminated. Therefore, effective interventions are crucial to reduce transmission and to strengthen diagnostic systems in order to achieve TB elimination at the population level
Co-Authors Abdul Hadi Ahsar Karim, Muhammad Aji Wiratama Akhmad Yusuf Ana Rizki Mahmudah Andi Tri Wardana Annisa Rahayu Arie Wijaya Arif, Alya Hanifah Azkia Khairal Jamil Azkia Khairal Jamil Azkia Khairal Jamil Balya, Muhammad Afief Bizaini Bizaini DEWI ANGGRAINI Dewi Sri Susanti Dipo Aldila Edy Sarwo Agus Wibowo Faisal Faisal Faisal Faisal Faisal Faisal Faisal Faisal Farohatin Na'imah Firman Nurrobi Firmansyah, Audinta Sakti Fitri Nor Annisa Fitriani Fitriani Friska Erlina Gabriel Henokh Gultom Gian Septiansyah Gian Septiansyah Haidir Ahsana Helfa Oktafia Afisha Herlyn Basrina Hermei Lissa Hijriati, Naimah Lestia, Aprida Siska Miftahul Jannah Miftahul Jannah Muhammad Afief Balya Muhammad Afief Balya Muhammad Ahsar Karim Muhammad Mahfuzh Shiddiq Muhammad Mahfuzh Shiddiq Munaira, Hanna Mursyidah Pratiwi Mustika Khadijah Noor Fakhriani Noorul Wakhdah Nur Wahidiyatil Jannah Nurmaini Puspitasari Nurrobi, Firman Nurul huda Oni Soesanto Pardi Affandi Rahayu, Annisa Rahmi Hidayati Raihan Nooriman Rezky Putri Rahayu Riska Fitria Riska Fitria Rizky Purnama Wulandari Rosyadi, Gusti Muhammad Sila Rizqina Sinar Ismaya Sofia Faridatun Nisa Thresye Thresye Tiara Amaliya Tri Puspa Lestari Vika Astuti Wiranto, Agung Setyo Wuri Setyana Sari Yogi Apriyanto