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

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.