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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan Jurnal Abadimas Adi Buana Jurnal Penamas Adi Buana PengabdianMu: Jurnal Ilmiah Pengabdian kepada Masyarakat Contemporary Mathematics and Applications (ConMathA) Jambura Journal of Biomathematics (JJBM) Jurnal Abdiraja
Alfiniyah, Cicik
Departemen Matematika, Fakultas Sains Dan Teknologi, Universitas Airlangga
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MATHEMATICAL MODELLING OF SMOKING BEHAVIOR: TREATMENT AND PREVENTION OPTIMAL CONTROL Noersena, Ananda; Fatmawati, Fatmawati; Alfiniyah, Cicik; Abidemi, Afeez
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp2003-2016

Abstract

Smoking remains a critical global public health challenge, with both traditional tobacco use and the rising prevalence of e-cigarettes contributing to significant morbidity and mortality. This study introduces a novel mathematical model that captures the dynamics of smoking behavior by explicitly integrating two smoker populations: traditional tobacco users and e-cigarette users. The model incorporates optimal control strategies aimed at prevention, via public health campaigns, and cessation, through smoking cessation treatments. The smoking model without control has two basic reproduction numbers for tobacco smokers and e-cigarette smokers, and . The extinction smoker’s equilibrium is locally asymptotically stable if and . The extinction tobacco smokers equilibrium is locally asymptotically stable if and . The endemic equilibrium tends to be asymptotically stable whenever and . Simulations demonstrate that implementing control strategies significantly reduces smoking prevalence, with the combined two strategies achieving the most substantial reduction.
MATHEMATICAL MODEL OF DENGUE HEMORRHAGIC FEVER SPREAD WITH DIFFERENT LEVELS OF TRANSMISSION RISK Herdicho, Faishal Farrel; Hakim, Nabil Azizul; Fatmawati, Fatmawati; Alfiniyah, Cicik; Akanni, John Olajide
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1649-1666

Abstract

Dengue Haemorrhagic Fever (DHF) is a vector-borne disease caused by the dengue virus, transmitted to humans through the bite of an infected female Aedes aegypti mosquito. DHF is prevalent in tropical regions, necessitating mathematical modeling to better understand its dynamics and predict its spread. This study develops and analyzes a mathematical model for DHF transmission that incorporates seven compartments to reflect different transmission risk levels. Stability analysis of the disease-free and endemic equilibria was conducted, with the basic reproduction number used to classify the conditions under which DHF transmission is controlled or endemic . Key model parameters were estimated using DHF case data from East Java in 2018, employing a genetic algorithm (GA) to optimize the estimation process. The GA approach achieved a mean absolute percentage error (MAPE) of , ensuring high accuracy in parameter values. Furthermore, the basic reproduction number was determined to be , which is greater than one, confirming that DHF remains endemic in East Java. Sensitivity analysis identified the mosquito biting rate , mosquito mortality rate , and transmission rates as the most critical factors influencing . Numerical simulations demonstrated the effects of these key parameters on both and the symptomatic human population . An increase in , , or significantly amplified and , while a rise in had the opposite effect, reducing both transmission and infections. These results underscore the critical role of vector control strategies, such as increasing mosquito mortality and reducing breeding sites, in mitigating DHF outbreaks. This study highlights the utility of combining mathematical modeling with genetic algorithm-based parameter estimation to provide accurate insights into disease dynamics and inform effective control measures.
FRACTIONAL-ORDER MODEL OF THE DRUG USER TRANSMISSION Izzati, Indah Nurun; Fatmawati, Fatmawati; Alfiniyah, Cicik
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 1 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss1pp511-524

Abstract

Drug abuse poses significant challenges to public health and socio-economic stability worldwide. Narcotics, which are psychotropic compounds, are typically used for treating specific medical conditions. Currently, many individuals abuse drugs outside of the function of treatment. This misuse leads to central nervous system disorders, resulting in significant mental and behavioral health issues. In this article, we discuss a fractional-order mathematical model for the transmission of drug users with fractional-order α∈ (0,1]. We employ fractional-order differential equations using the Caputo derivative approach to model the transmission dynamics. We analyze the local stability of drug-free and endemic equilibrium points and calculate the basic reproduction number (). Our analysis indicates that the drug-free equilibrium is locally asymptotically stable when , while the endemic equilibrium is stable when . We implement a numerical scheme to simulate the fractional-order model, illustrating the theoretical findings.
Co-Authors Abdul Faliq Anwar Abidemi, Afeez Ahmadin Ahmadin Akanni, John Olajide Anisa Puspitasari Asri Bekti Pratiwi, Asri Bekti Auli Damayanti Dinda Ariska Putri Elda Widya Erzalina Ayu Satya Megananda Fatmawati Fatmawati Fatmawati, Fatmawati Fatmawati, Fatmawati Hakim, Nabil Azizul Herdicho, Faishal Farrel Inna Kuswandari Izzati, Indah Nurun Jaelani, Abdulloh Laurensia Regina Bestari Gepak Millah, Nashrul Miswanto Muhammad Abdurrahman Rois Muhammad Iqbal Abdi Farchan Nanda Amalia Rahma Nashrul Millah Noersena, Ananda Riris Nur Patria Putri Sofita Suherman Windarto