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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