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All Journal JTAM (Jurnal Teori dan Aplikasi Matematika) Jambura Journal of Biomathematics (JJBM)
Rois, Muhammad Abdurrahman
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Computer Science & IT Decision Sciences, Operations Research & Management Mathematics

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Two isolation treatments on the COVID-19 model and optimal control with public education Rois, Muhammad Abdurrahman; Fatmawati, Fatmawati; Alfiniyah, Cicik
Jambura Journal of Biomathematics (JJBM) Volume 4, Issue 1: June 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v4i1.19963

Abstract

This study examines a COVID-19 mathematical model with two isolation treatments. We assume that isolation has two treatments: isolation with and without treatment. We also investigated the model using public education as a control. We show that the model has two equilibria based on the model without control. The basic reproduction number influences the local stability of the equilibrium and the presence of an endemic equilibrium. Therefore, the optimal control problem is solved by applying Pontryagin's Principle. In the 100th day following the intervention, the number of reported diseases decreased by 85.5% when public education was used as the primary control variable in the simulations.
Dynamic Analysis of COVID-19 Model with Quarantine and Isolation Rois, Muhammad Abdurrahman; Trisilowati, Trisilowati; Habibah, Ummu
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 5, No 2 (2021): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v5i2.5167

Abstract

This study discusses the dynamic analysis of the COVID-19 model with quarantine and isolation. The population in this model is divided into seven subpopulations: subpopulation of susceptible, exposed, asymptomatic, symptomatic, quarantine, isolated and recovered. Two equilibrium points were obtained based on the analysis results, namely the disease-free and endemic equilibrium points. The existence and local stability of the equilibrium point depends on the value of the basic reproduction number . Then, the point of disease-free equilibrium always exists, and the point of endemic equilibrium exists when it meets . The point of disease-free equilibrium is locally asymptotically stable when it satisfies  and the endemic equilibrium point is locally asymptotically stable with conditions. Furthermore, numerical simulations are carried out to determine the model's behavior using the fourth-order Runge-Kutta method. The numerical simulation obtained supports the dynamic analysis results. Finally, the graphical results are presented. The findings here suggest that human-to-human contact is a potential cause of the COVID-19 outbreak. Therefore, quarantine of susceptible and exposed subpopulations can reduce the risk of infection. Likewise, isolation of infected subpopulations can reduce the risk of spreading COVID-19.
Fractional-Order COVID-19 Model in Indonesia with Comorbidity and Immunization: PID Control, Ulam-Hyers Stability, and Biosecurity Implications Farman, Muhammad; Alfiniyah, Cicik; Fatmawati, Fatmawati; Rois, Muhammad Abdurrahman; Jamil, Khadija
Jambura Journal of Biomathematics (JJBM) Volume 6, Issue 4: December 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v6i4.34027

Abstract

In this paper, we developed a fractal fractional model for Covid-19 dynamics in Indonesia with comorbidity and various immunization stages doses is presented and examined. The system is analysed disease-free according to reproductive number. We conducted both qualitative and quantitative research on the COVID-19 model using the Atangana-Baleanu fractal-fractional operator. We demonstrated the existence and uniqueness of the model with the Atangana-Baleanue fractal-fractional operator as continuous and compact integral components, by means of Krasnoselskii fixed point theorem. We ensure that our proposed model has a unique fixed-point solution by including the properties of both the Schauder and Krasnoselskii theorems into the contraction mapping. We conduct a thorough examination of the suggested model’s stability using the Ulam-Hyers stability concept. We discuss how the Proportional Integral Derivative (PID) impact in a fractional COVID-19 model improves stability. Since these control methods have a great potential to improve overall treatment outcomes, minimise side effects, and correctly regulate these treatments to achieve this goal, their use will stabilise the dynamics behaviour while accurately regulating the administration, leading to better vaccination outcomes with fewer adverse effects inferred from this. A numerical approach based on Lagrange interpolation is presented. The dynamics of disease transmission throughout a range of fractional-order ϖ and fractal dimensions ϑ are then visually represented by the numerical results that have been obtained. The findings demonstrate the deep impact of fractional dynamics and fractal dimensions on the processes of vaccination, recovery, and propagation, exposing intricate, time-dependent epidemic characteristics.
Co-Authors Alfiniyah, Cicik Farman, Muhammad Fatmawati, Fatmawati Jamil, Khadija Trisilowati Trisilowati, Trisilowati Ummu Habibah, Ummu