Dynamic Analysis of COVID-19 Model  with Quarantine and Isolation

Muhammad Abdurrahman Rois; Trisilowati Trisilowati; Ummu Habibah

doi:10.31764/jtam.v5i2.5167

Dynamic Analysis of COVID-19 Model with Quarantine and Isolation

Muhammad Abdurrahman Rois, Trisilowati Trisilowati, Ummu Habibah

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.

Keywords

COVID-19 Model; Basic Reproduction Number; Local Stability; Numerical Simulations.

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DOI: https://doi.org/10.31764/jtam.v5i2.5167