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All Journal Jurnal Matematika Journal of Mathematical and Fundamental Sciences Jurnal Penelitian Pendidikan IPA (JPPIPA) JMPM: Jurnal Matematika dan Pendidikan Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Jambura Journal of Mathematics ComTech: Computer, Mathematics and Engineering Applications MES: Journal of Mathematics Education and Science Indonesian Journal of Electrical Engineering and Computer Science Jambura Journal of Biomathematics (JJBM) Milang Journal of Mathematics and Its Applications Aceh International Journal of Science and Technology Journal of Mathematics, Computation and Statistics (JMATHCOS) MILANG Journal of Mathematics and Its Applications
Paian Sianturi
Department Of Mathematics, Bogor Agricultural University, Jl. Meranti, Kampus IPB Dramaga, Bogor 16680, Indonesia
Agriculture, Biological Sciences & Forestry Astronomy Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry 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 Physics Transportation

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Journal : JTAM (Jurnal Teori dan Aplikasi Matematika)

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Mathematical Model of COVID-19 Spread with Vaccination in Mataram City Hattamurrahman, Muhammad Putra Sani; Sianturi, Paian; Sumarno, Hadi
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 4 (2024): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i4.23113

Abstract

The COVID-19 pandemic has had a significant impact on public health worldwide.. Mathematical modeling is considered an alternative tool for understanding real-life problems, including the dynamics of COVID-19 spread. This is an applied research that purpose adds vaccination to Zeb et al. (2020) SEIQR model of COVID-19 spread and examines the dynamic of COVID-19 spread in Mataram City. First, we construct the new model by making assumptions. The fixed point and basic reproduction number (R_0 ) are then used to analyze the model using the next-generation matrix method. The next-generation matrix method is utilized to estimate the R_0 in a compartmental disease model. Two fixed points are acquired, specifically the disease-free fixed point, which is locally asymptotically stable under the condition R_0<1 determined by the Routh Hurwitz criterion via linearization using the Jacobi matrix. And the disease-endemic fixed point, which is locally asymptotically stable under the condition R_0>1 indicated by Lyapunov function. The population dynamics when R_0<1 and R_0>1 can also be observed through numerical simulation. The results of a numerical simulation indicate that giving the proportion of number vaccinated 62 per cent is effective in suppressing the number of infections. 
Sensitivity Analysis of SEIRS Model with Quarantine on the Spread of Covid-19 Hardianti, Wiwik Tri; Sumarno, Hadi; Sianturi, Paian
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 4 (2022): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i4.9627

Abstract

Since the Covid-19 pandemic, various mathematical models have been developed to describe its spread using the compartment model. The purpose of this research was to construct a new model of Covid-19. This formulated model is an application of SEIRS epidemic model by Zhang & Teng (2007) and a modification of the Covid-19 model by Chatterjee et al. (2020) by adding variations of quarantine. The model is analyzed by determining the disease-free fixed point and basic reproduction number 〖(R〗_0) through the next generation matrix method. The next step is to analyze the sensitivity to find out the parameters that have the most influence on the spread of Covid-19. The disease will not spread in the population if the value of R_0<1, while the disease will spread if the value of R_0>1. The result of the sensitivity analysis stated the parameters that can be controlled and have the most significant effect, respectively, are the transmission rate from symptomatic infected individuals (β_2 ),transmission rates from asymptomatic infected individuals (β_1 ), quarantine rates for symptomatic infected individuals (θ_3), and quarantine rates for asymptomatic infected individuals (θ_2). Parameters β_2 and β_1 have a negative index, while θ_3 and θ_2 have a negative index. It means decreasing the transmission rate from infected individuals and increasing the quarantine rate for infected individuals can decrease the spread of Covid-19. Therefore there will not be an outbreak in the long term. 
Co-Authors Abdur Rohman Abdur Rohman Akmal Taufik Ali Kusnanto Annisa, Mutia Ardana, N K Kutha Ardana, N. K. Kutha Ardana, Ngakan Komang Kutha Arindria Sekar Putri Valentinna Asmaidi Asmaidi Budi Suharjo D. Ananda Osferi Dian Grace Ludji Dini Dessya Luthfiani Eliska, Nur Endar Hasafah Nugrahani Endar Nugrahani Fahren Bukhari Fatimatuzzahroh Hadi Sumarno Hadi Sumarno Hardianti, Wiwik Tri Hattamurrahman, Muhammad Putra Sani Ilmi, Salsabilla Fitri Jaharuddin Julianto, MT Luthfiani, Dini Dessya Mutia Annisa N. K. Kutha Ardana N. K. Kutha Ardana Nabila, Nabila NGAKAN KOMANG KUTHA ARDHANA Niswah Yanfa Nabilah Syams Nugrahani, Endar Nur Azizah Nurul Qorima Putri Praptaningsih, Anggun Putri, Nurul Qorima Rauf, Nurul Maqfirah Resmawan Resmawan Riza Rusdiani Taufik, Akmal Toni Bakhtiar Valentinna, Arindria Sekar Putri Yomi Kharisma Septika