Dynamics of Covid-19 model with public awareness, quarantine, and isolation

Risyqaa Syafitri, Trisilowati Trisilowati, Wuryansari Muharini Kusumawinahyu


This paper presents a new COVID-19 model that contains public awareness, quarantine, and isolation. The model includes eight compartments: susceptible aware (SA), susceptible unaware (SU), exposed (E), asymptomatic infected (A), symptomatic infected (I), recovered (R), quarantined (Q), and isolated (J). The introduction will be shown in the first section, followed by the model simulation. The equilibrium points, basic reproduction number, and stability of the equilibrium points are then determined. The model has two equilibrium points: disease-free equilibrium point and endemic equilibrium point. The next-generation matrix is used to calculate the basic reproduction number R0. The disease-free equilibrium point always exists and is locally stable if R0 < 1, whereas the endemic equilibrium point exists when R0 > 1 and is locally stable if satisfying the Routh-Hurwitz criterion. Stability properties of the equilibrium confirmed by numerical simulation also show that quarantine rate and isolation rate have an impact in the transmission of COVID-19


Epidemic Model; COVID-19; Public Awareness; Quarantine; Isolation; Stability Analysis

Full Text:



A. Mahajan, N. A. Sivadas, and R. Solanki, “An epidemic model SIPHERD and its application for prediction of the spread of COVID-19 infection in India,” Chaos, Solitons & Fractals, vol. 140, p. 110156, nov 2020. DOI: 10.1016/j.chaos.2020.110156

M. Masum, M. Masud, M. I. Adnan, H. Shahriar, and S. Kim, “Comparative study of a mathematical epidemic model, statistical modeling, and deep learning for COVID-19 forecasting and management,” Socio-Economic Planning Sciences, vol. 80, p. 101249, mar 2022. DOI: 10.1016/j.seps.2022.101249

M. Mwale, B. Kanjere, C. Kanchele, and S. Mukosa, “Simulation of the Third Wave of COVID 19 Infections in Zambia using the SIR Model,” PREPRINT (Version 1) available at Research Square, vol. February, p. 101249, 2022. DOI: 10.21203/rs.3.rs-1337105/v1

A. G. Harrison, T. Lin, and P. Wang, “Mechanisms of SARS-CoV-2 Transmission and Pathogenesis,” Trends in Immunology, vol. 41, no. 12, pp. 1100–1115, dec 2020. DOI: 10.1016/j.it.2020.10.004

R. R. Musafir, A. Suryanto, and I. Darti, “Dynamics of COVID-19 Epidemic Model with Asymptomatic Infection, Quarantine, Protection and Vaccination,” Communication in Biomathematical Sciences, vol. 4, no. 2, pp. 106–124, dec 2021. DOI: 10.5614/cbms.2021.4.2.3

R. R. Musafir and S. Anam, “Parameter estimation of Covid-19 compartment model in Indonesia using particle swarm optimization,” Jurnal Berkala Epidemiologi, vol. 10, no. 3, pp. 283–292, sep 2022. DOI: 10.20473/jbe.V10I32022.283-292

G. O. Fosu, J. M. Opong, and J. K. Appati, “Construction of Compartmental Models for COVID-19 with Quarantine, Lockdown and Vaccine Interventions,” SSRN Electronic Journal, 2020. DOI: 10.2139/ssrn.3574020

M. Chen, M. Li, Y. Hao, Z. Liu, L. Hu, and L. Wang, “The introduction of population migration to SEIAR for COVID-19 epidemic modeling with an efficient intervention strategy,” Information Fusion, vol. 64, pp. 252–258, dec 2020. DOI: 10.1016/j.inffus.2020.08.002

Z. Memon, S. Qureshi, and B. R. Memon, “Assessing the role of quarantine and isolation as control strategies for COVID-19 outbreak: A case study,” Chaos, Solitons & Fractals, vol. 144, p. 110655, mar 2021. DOI: 10.1016/j.chaos.2021.110655

R. Rogério Da Silva, A. Filipe, and D. Silva, “COVIF: Centro de Informação sobre a COVID-19 do IF Sertão-PE,” Jornada de Iniciação Científica e Extensão, vol. 16, no. 1, 2021.

L. Zuo and M. Liu, “Effect of Awareness Programs on the Epidemic Outbreaks with Time Delay,” Abstract and Applied Analysis, vol. 2014, pp. 1–8, 2014. DOI: 10.1155/2014/940841

Y. Yuan and N. Li, “Optimal control and cost-effectiveness analysis for a COVID-19 model with individual protection awareness,” Physica A: Statistical Mechanics and its Applications, vol. 603, p. 127804, oct 2022. DOI: 10.1016/j.physa.2022.127804

R. U. Hurint, M. Z. Ndii, and M. Lobo, “Analisis Sensitivitas Model Epidemi SEIR,” Natural Science: Journal of Science and Technology, vol. 6, no. 1, pp. 22–28, mar 2017. DOI: 10.22487/25411969.2017.v6.i1.8076

N. Chitnis, J. M. Hyman, and J. M. Cushing, “Determining Important Parameters in the Spread of Malaria Through the Sensitivity Analysis of a Mathematical Model,” Bulletin of Mathematical Biology, vol. 70, no. 5, pp. 1272–1296, jul 2008. DOI: 10.1007/s11538-008-9299-0

DOI: https://doi.org/10.34312/jjbm.v4i1.19832

Copyright (c) 2023 Risyqaa Syafitri, Trisilowati, Wuryansari Muharini Kusumawinahyu

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Jambura Journal of Biomathematics (JJBM) has been indexed by:


 Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Gorontalo
Jl. Prof. Dr. Ing. B. J. Habibie, Moutong, Tilongkabila, Kabupaten Bone Bolango 96554, Gorontalo, Indonesia
 Email: editorial.jjbm@ung.ac.id
 +6281356190818 (Call/SMS/WA)
 Jambura Journal of Biomathematics (JJBM) by Department of Mathematics Universitas Negeri Gorontalo is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.  Powered by Public Knowledge Project OJS.