A seiqrd epidemic model to study the dynamics of covid-19 disease

In this paper, we propose a COVID-19 epidemic model with quarantine class. The model contains 6 sub-populations, namely the susceptible (S), exposed (E), infected (I), quarantined (Q), recovered (R), and death (D) sub-populations. For the proposed model, we show the existence, uniqueness, non-negativity, and boundedness of solution. We obtain two equilibrium points, namely the disease-free equilibrium (DFE) point and the endemic equilibrium (EE) point. Applying the next generation matrix, we get the basic reproduction number (R-0). It is found that R-0 is inversely proportional to the quarantine rate as well as to the recovery rate of infected sub-population. The DFE point always exists and if R-0 < 1 then the DFE point is asymptotically stable, both locally and globally. On the other hand, if R-0 > 1 then there exists an EE point, which is globally asymptotically stable. Here, there occurs a forward bifurcation driven by R-0. The dynamical properties of the proposed model have been verified our numerical simulations.