Long-Term Predictions of COVID-19 in Some Countries by the SIRD Model

Abstract

As COVID-19 in some countries has increasingly become more severe, there have been significant efforts to develop models that forecast its evolution there. These models can help to control and prevent the outbreak of these infections. In this paper, we make long-term predictions based on the number of current confirmed cases, accumulative recovered cases, and dead cases of COVID-19 in some countries by the modeling approach. We use the SIRD (S: susceptible, I: infected, R: recovered, D: dead) epidemic model which is a nonautonomous dynamic system with incubation time delay to study the evolution of COVID-19 in some countries. From the analysis of the recent data, we find that the cure and death rates may not be constant and, in some countries, they are piecewise functions. They can be estimated from the delayed SIRD model by the finite difference method. According to the recent data and its subsequent cure and death rates, we can accurately estimate the parameters of the model and then predict the evolution of COVID-19 there. Through the predicted results, we can obtain the turning points, the plateau period, and the maximum number of COVID-19 cases. The predicted results suggest that the epidemic situation in some countries is very serious. It is advisable for the governments of these countries to take more stringent and scientific containment measures. Finally, we studied the impact of the infection rate β on COVID-19. We find that when the infection rate β decreases, the cumulative number of confirmed cases and the maximum number of currently infected cases will greatly decrease. The results further affirm that the containment techniques taken by these countries to curb the spread of COVID-19 should be strengthened further.