The importance of quarantine: A bifurcation analysis and modeling of the transmission dynamics of Covid 19

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 thefollowing classes: susceptible, exposed, quarantined, asymptomatic cases, symptomatic cases, and recovered(SEQI1I2R). Several assumptions regarding positivity and boundness are identified to ensure that the solutionoriginated within a certain class and that the basic reproduction number is analyzed. Of course, the existenceof an endemic equilibrium is argued, which provides an understanding of the long-term persistence of thedisease. More precisely, to enhance our understanding of the model’s dynamics, we have analyzed both thelocal and global asymptotic stability of the disease-free equilibrium. Moreover, to assess the global stabilityof the system, we employ a Lyapunov function which provides a comprehensive mathematical evaluation. Atthe same time, our findings show evidence of a backward bifurcation which is recognized as a possible resultof the clinical transition from an asymptomatic state to symptom one.