Modeling the impact of quarantine and intense medical intervention on the dynamics of COVID-19

This paper presents a nonlinear mathematics model that is formulated and analyzed to assess the impacts of quarantine and intense medical intervention on the dynamics of Coronavirus Disease 2019 (COVID-19). An extended SEIR model with quarantine and the hospitalization compartment is proposed to simulate the COVID-19 spread. The model considers seven stages of infection: susceptible, exposed, asymptomatic, symptomatic, quarantined asymptomatic, hospitalized symptomatically, and recovered. A deterministic system of bilinear incidence nonlinear differential equations is used to model it. It was found that the model has two equilibrium points: the disease-free equilibrium point and the endemic equilibrium point. The next-generation matrix approach is used to calculate the basic reproduction numbers. The global asymptotical stability of the proposed model's equilibria is examined using the Lyapunov function and the LaSalle invariance principle. When the basic reproduction number is less than unity, the disease-free equilibrium point is globally stable, and when the basic reproduction number is more than unity, the endemic equilibrium point with a special case is globally stable, which takes the form of a deterministic system of nonlinear differential equations with bilinear incidence. Sensitivity analysis and numerical simulation results, using a reasonable set of parameter values. Finally, we investigate how the prevalence of COVID-19 is affected by the rates of transmission, quarantine, and hospitalization.