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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.
Co-Authors Alfiniyah, Cicik Fatmawati, Fatmawati Trisilowati Trisilowati, Trisilowati Ummu Habibah, Ummu