ABSTRACT
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.
ABSTRACT
Due to the outbreak of the COVID-19 epidemic in 2020, people are very worried about the situation of the epidemic. Being able to model the number of cases over time is crucial. This model is used to predict numbers of people who may get diseases in the future. We construct a model with some unknown parameters and decide those parameters by making the mean square error of the predicted value with actual data. The epidemic model is generalized SEIR model and it helps us to match with reality. The data we use are from database built by Hopkins University. The result shows that disease will finally disappear. We can see that the virus increase at a very fast speed at first but begin to decrease from the curve. It is because that more people to take actions for protecting themselves. This result shows the virus can be defeated if we put effort to stop spreading them.