The large proportion of asymptomatic patients is the major cause leading to the COVID-19 pandemic which is still a significant threat to the whole world. A six-dimensional ODE system (SEIAQR epidemical model) is established to study the dynamics of COVID-19 spreading considering infection by exposed, infected, and asymptomatic cases. The basic reproduction number derived from the model is more comprehensive including the contribution from the exposed, infected, and asymptomatic patients. For this more complex six-dimensional ODE system, we investigate the global and local stability of disease-free equilibrium, as well as the endemic equilibrium, whereas most studies overlooked asymptomatic infection or some other virus transmission features. In the sensitivity analysis, the parameters related to the asymptomatic play a significant role not only in the basic reproduction number R0. It is also found that the asymptomatic infection greatly affected the endemic equilibrium. Either in completely eradicating the disease or achieving a more realistic goal to reduce the COVID-19 cases in an endemic equilibrium, the importance of controlling the asymptomatic infection should be emphasized. The three-dimensional phase diagrams demonstrate the convergence point of the COVID-19 spreading under different initial conditions. In particular, massive infections will occur as shown in the phase diagram quantitatively in the case R0>1. Moreover, two four-dimensional contour maps of Rt are given varying with different parameters, which can offer better intuitive instructions on the control of the pandemic by adjusting policy-related parameters.
This study establishes a compartment model for the categorized COVID-19 risk area. In this model, the compartments represent administrative regions at different transmission risk levels instead of individuals in traditional epidemic models. The county-level regions are partitioned into High-risk (H), Medium-risk (M), and Low-risk (L) areas dynamically according to the current number of confirmed cases. These risk areas are communicable by the movement of individuals. An LMH model is established with ordinary differential equations (ODEs). The basic reproduction number R0 is derived for the transmission of risk areas to determine whether the pandemic is controlled. The stability of this LHM model is investigated by a Lyapunov function and Poincare–Bendixson theorem. We prove that the disease-free equilibrium (R0 < 1) is globally asymptotically stable and the disease will die out. The endemic equilibrium (R0 > 1) is locally and globally asymptotically stable, and the disease will become endemic. The numerical simulation and data analysis support the previous theoretical proofs. For the first time, the compartment model is applied to investigate the dynamics of the transmission of the COVID-19 risk area. This work should be of great value in the development of precision region-specific containment strategies.
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