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All Journal HAYATI Journal of Biosciences CAUCHY: Jurnal Matematika Murni dan Aplikasi Jurnal Matematika & Sains Journal of Mathematical and Fundamental Sciences Jurnal Daya Matematis Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai-Nilai Islami) Communication in Biomathematical Sciences Jurnal Sains Dirgantara
Nuning Nuraini
Department of Mathematics, Institut Teknologi Bandung
Agriculture, Biological Sciences & Forestry Arts Humanities Astronomy Chemistry Earth & Planetary Sciences Education Mathematics Physics Social Sciences

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A Simple Modelling of Microscopic Epidemic Process with Two Vaccine Doses on a Synthesized Human Interaction Network Seprianus; Nuraini, Nuning; Saputro, Suhadi Wido
Communication in Biomathematical Sciences Vol. 7 No. 1 (2024)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2024.7.1.6

Abstract

In this study, we illustrate the incorporation of two vaccine doses into a discrete SIR model to aid in the decision-making process for optimal vaccination strategies. We present a basic model of a human interaction network synthesized to depict social contacts within a population, taking into account the number of connections and the level of interaction among individuals. Under a limited number of available vaccine doses, we explore various vaccination scenarios considering factors such as the distribution of vaccines, the proportion of vaccinated individuals, and the timing of vaccination commencement. Our research demonstrates that the most effective vaccination strategy, which focuses on re-characterized hubs or redefining the individual who has high connectivity, will cover fewer individuals and result in the smallest total number of infected individuals.
A Sinusoidal-Based Mathematical Model for Psychotherapy Effects in Bipolar Disorder Type 2 Patients Nursuprianah, Indah; Anggriani, Nursanti; Nuraini, Nuning; Rosandi, Yudi
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.33537

Abstract

Bipolar Disorder (BD) is a mental disorder characterized by recurrent manic and depressive episodes. This study aims to build a mathematical model that models mood changes in BD type 2 before and after psychotherapy. Daily mood data were collected for more than 3 months from one BD patient, then divided into seven terms of 14 days each. The analysis was carried out through a sinusoidal function fitting process and numerical simulation based on the Van der Pol differential equation. The results showed that before psychotherapy, the mood amplitude reached 1.99632, the frequency was 0.4926, and the moment of inertia was 4.121081. After undergoing routine psychotherapy 9 times, the amplitude decreased to 0.635, the frequency increased to 1.052, and the moment of inertia decreased to 0.903584. The average mood was controlled at 6.492, within the normal mood range. The decrease in amplitude and moment of inertia indicated that BD mood became more stable and less easily affected by the environment, while the increase in frequency indicated a faster recovery of emotional rhythm. Conclusion: Routine psychotherapy is effective in quantitatively stabilizing the mood of BD type 2.
Analysis of Diarrheal Disease Transmission in Bandung City Using the SIS Mathematical Model. Ulfa, Rezky Maya; Shaumi, Nurina Fadlila; Nuraini, Nuning
Daya Matematis: Jurnal Inovasi Pendidikan Matematika Vol 13, No 2 (2025): Juli
Publisher : Universitas Negeri Makassar

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26858/jdm.v13i2.72375

Abstract

Diarrhea remains a public health issue in developing countries around the world. It is categorized as an environmentally-based disease and occurs in nearly all geographic regions globally. The purpose of this study is to apply mathematical modeling of the spread of diarrhea in Bandung City using the SIS model, then to model the relationship between the number of rivers and the quantity of E. coli in each district in Bandung City with the number of diarrhea cases, as well as to analyze the influence of river presence and E. coli quantity in each district on the number of diarrhea cases in Bandung City. The model development began by creating a flow diagram of the spread of diarrhea using the SIS model. The results revealed an equilibrium point, specifically the endemic equilibrium point. The basic reproduction ratio in each district showed values closely aligned with mortality rates, indicating that mortality rates from the disease could serve as a useful indicator for predicting transmission rates and the impact of diarrhea within the population. The higher the mortality rate, the lower the likelihood of disease transmission, and vice versa.
Mathematical Model for the Growth of Mycobacterium Tuberculosis Infection in the Lungs: Dewanti, Retno Wahyu; Widianto, Wisnu Prasojo; Apri, Mochamad; Nuraini, Nuning; Fakhruddin, Muhammad
Communication in Biomathematical Sciences Vol. 8 No. 1 (2025)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2025.8.1.8

Abstract

In this work, we develop a population dynamics model of Mycobacterium tuberculosis (Mtb), the bacteria responsible for tuberculosis (TB), to evaluate the impact of bacterial competition on infection prevalence. We consider two types of Mtb population growth: The first is caused by bacteria that grow inside each infected macrophage and is believed to be correlated with the number of infected macrophages; The second is that extracellular bacteria grow through self-replication. In this study, we modeled the immune response to Mtb bacterial infection in the lungs using a five-dimensional differential equation system. This model represents changes in the number of healthy macrophages, infected macrophages, activated macrophages cells, extracellular bacterial particles, and naive T cells. Qualitative analysis and numerical results reveal the existence of two equilibrium points: disease-free equilibrium and endemic equilibrium, which represent latent or active tuberculosis based on the number of bacteria. In addition, a sensitive analysis of the model parameters shows that macrophages are not sufficient to control the initial invasion of Mtb. The immune system must therefore employ more complex defense mechanisms to contain Mtb infection, such as recruiting various elements of immune system and forming granulomas.
Penyebaran Rumor dalam Masyarakat: Sebuah Pendekatan Pemodelan Matematika dalam Studi Kasus Pemilihan Umum Septyawan, Stefanus Raynaldo; Bunga, Esther Yolandyne; Nuraini, Nuning; Arcede, Jayrold P.
Communication in Biomathematical Sciences Vol. 7 No. 2 (2024)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2022.7.2.3

Abstract

Rumors can be defined as unverified information or statements shared by people that may be positive or negative and circulate without confirmation. Since humans naturally seek factual information for social and self-enhancement purposes, rumors become an inevitable aspect of human life, including in politics, such as elections. The complexity of the electoral process, with various factors such as individual candidates, social circumstances, and particularly the media, leads to the dynamic spread of rumors in society. Thus, it is both interesting and important to understand the dynamics of rumor spreading, particularly in the context of elections. In this article, we formulate a mathematical model of rumor spread dynamics based on different attitudes of people toward rumors. The model considers the spread of rumors about two candidates in the electoral context. From the model, we derived and investigated the basic reproductive number (R0) as a threshold for rumor spread and conducted a sensitivity analysis with respect to all the model parameters. Based on numerical experiments and simulations, it was revealed that the number of people resistant to or disbelieving in rumors increases significantly in the first ten days and remains higher than other subpopulations for at least after first seven days. Furthermore, we found that a high number of people directly affected by rumors, combined with the rumor transmission rate for both candidates being greater than each other, are necessary and sufficient conditions for rumors to circulate rapidly and remain stable in society. The results of this study can be interpreted and considered as a campaign strategy in an electoral context.
Co-Authors Anita Triska Apri, Mochamad Apri, Mochamad Arcede, Jayrold P. Bunga, Esther Yolandyne Deana Wahyuningrum Edy Soewono Edy Soewono Edy Soewono Fakhruddin, Muhammad Faraimunashe Chirove Farida Fauzi, Ilham Saiful Glenn Lahodny Jr. Hakim L. Malasan Heni Widayani Hilda Fahlena I Gusti Bagus Wiksuana Indah Nursuprianah Jafaruddin Hamid Juni Wijayanti Puspita Kamal Khairudin Kamal Khairudin Sukandar Karunia Putra Wijaya Khairudin, Kamal Kusdiantara, Rudy Lisyani Budipradigda Suromo Mharta A. Wardana Mia Siti Khumaeroh Mochamad Apri Mona Zevika Muhammad Fakhruddin Muhammad Fakhruddin Nadia Novriana Sumarti Novriana Sumarti Nursanti Anggriani Nurwijayanti Retno Wahyu Dewanti Rizqina, Sila Rudy Kusdiantara Saputro, Suhadi Wido Seprianus Septyawan, Stefanus Raynaldo Shaumi, Nurina Fadlila Sudirman Sukandar, Kamal Khairudin sutimin sutimin Syamsiar, Syamsiar Syukriyah, Yenie Tay, Chai Jian Tjandra Anggraeni Tri W. Hadi Ulfa, Rezky Maya Vania Mene Risriani Widianto, Wisnu Prasojo Widya Oktaviana Wijaya, Karunia Putra Wirdatul Aini Yenie Syukriyah Yudi Rosandi Zikri, Afdol