The importance of quarantine: A bifurcation analysis and modeling of the transmission dynamics of Covid-19
Keywords:
Quarantine, Basic reproduction number, Stability, Backward bifurcation, COVID-19 model.Abstract
The research aims to construct a mathematical model for COVID-19 that includes features six compartments to evaluate the positive effects of quarantine measures. The model categorizes individuals into the
following classes: susceptible, exposed, quarantined, asymptomatic cases, symptomatic cases, and recovered
(SEQI1
I2R). Several assumptions regarding positivity and boundness are identified to ensure that the solution
originated within a certain class and that the basic reproduction number is analyzed. Of course, the existence
of an endemic equilibrium is argued, which provides an understanding of the long-term persistence of the
disease. More precisely, to enhance our understanding of the model’s dynamics, we have analyzed both the
local and global asymptotic stability of the disease-free equilibrium. Moreover, to assess the global stability
of the system, we employ a Lyapunov function which provides a comprehensive mathematical evaluation. At
the same time, our findings show evidence of a backward bifurcation which is recognized as a possible result
of the clinical transition from an asymptomatic state to symptom one.
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Ali, M., Shah, Syed Touqeer H., Imran, M. & Khan, A. (2020). The role of asymptomatic class, quarantine and isolation in the transmission of COVID-19. Journal of biological dynamics, 14(1), 389–408.
Adebiyi, Ayodeji. O. (2016). Mathematical modeling of the population dynamics of tuberculosis. A Master dissertation, University of the Western Cape, South Africa.
Anderson, R.M. & May, R.M. (1991). Infectious Diseases of Humans: Dynamics and Control. Oxford University Press.
Brauer, F. & Castillo-Chaves, C. (2012). Mathematical Models in Population Biology and Epidemiology. Springer New York, NY, Vol. 2, No. 40.
Castillo-Chavez, C. & Song, B. (2004). Dynamical models of tubercolosis and their applications. Mathematical Biosciences & Engineering, 1(2), 361–404.
Cherniha, R. & Davydovych, V. (2020). A mathematical model for the COVID-19 outbreak. Symmetry, 12(6), 990.
Ngonghala, Calistus N., Iboi, E., Eikenberry, S., Scotch, M., MacIntyre, Chandini R., Bonds, Matthew H. & Gumel, Abba B. (2020). Mathematical assessment of the impact of non-pharmaceutical interventions on curtailing the 2019 novel Coronavirus. Mathematical biosciences, 325, 108364.
Van den Driessche, P. (2017). Reproduction numbers of infection disease models. Infectious disease modelling, 2(3), 288–303.
Harapan, H. , Itoh, N., Yufika, A., Winardi, W., Keam, S., Te, H., Megawati, D., Hayati, Z. , Wanger, A. L. & Mudatsir, M. (2020). Coronavirus disease 2019 (COVID-19): A Literature review. Journal of infection and public health, 13(5), 667–673.
Hethcote, H., Zhien, M., & Shengbing, L. (2002). Effects of quarantine in six endemic models for infectious diseases. Mathematical biosciences, 180(1–2), 141–60.
Iannelli, Mimmo. (2005). The Mathematical Modelling of Epidemics. Lecture Notes on Mathematical Modelling in the Life Sciences: Theory and simulation Unitext-La Matematica per il 3 piu 2.
Idisi, Oke I., Yusuf, Tunde T., Owolabi, Kolade M. & Ojokoh, Bolanle A. (2023) . A bifurcation analysis and model of Covid-19 transmission dynamics with post-vaccination infection impact. Healthcare Analysis, 3, 100157.
Kermack, William O. & McKendrick, Anderson G. (1927). A contribution to the mathematical theory of epidemics. Proceedings of the royal society of london. Series A, Containing papers of a mathematical and physical character, 115(772), 700–721.
Luo, X., Feng, S., Yang, J., Peng, X. L., Cao, X., Zhang, J., Yao, M., Zhu, H., Li, M. Y., Wang, H. & al et. (2020). Analysis of potential risk of COVID-19 infections in China based on a pairwise epidemic model. Preprints, Computer Science & Mathematics, 2020020398.
Song, B. J. (2021). Basic reinfection number and backward bifurcation. Mathematical Biosciences & Engineering, 18(6), 8061–8083.
NDAM, J.N. (2021). Mathematical modelling of the dynamics of COVID-19 pandemic. Asia-Pacific Journal of Mathematics, 8(12), 1–17.
World Health Organisation. (2020). Coronavirus Disease 2019 (COVID-19) Situation Report-59, 19 March, 2020.
Youssef, I. K. & Hassan, M. H. (2022). A Comparative Study for Some Mathematical Models of Epidemic Diseases with Application to Strategic Management. Applied Sciences, 12(24), 12639.
Zhou, Xueyong & Shi, Xiangyun. (2022). Stability analysis and backward bifurcation on an SEIQR epidemic model with nonlinear innate immunity. Electronic Research Archive, 30(9), 3481–3508.
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Copyright (c) 1970 Fatma Mohamed, Mohamed H. Amsaad
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