The forecasting of COVID-19 with mortality using SIRD epidemic model for the United States, Russia, China, and the Syrian Arab Republic

Marwan Al-Raeei

doi:10.1063/5.0014275

Abstract

In this paper, we apply an algorithm for simulating the susceptible-infected-recovered-dead pandemic model for demonstrating the forecasting and the spreading of the new coronavirus disease. For this purpose, we apply an implicit analytical solution for parts of the model, in addition to applying the finite difference methods for other parts of the model. Based on the collected data of the number of infected cases, recovered cases, and deceased cases of the new coronavirus pandemic as of 30 May 2020, we find the values of the coefficient of infection, the coefficient of recovery, and the coefficient of mortality of the new coronavirus pandemic for four different countries, namely, China, the United States, Russia, and the Syrian Arab Republic. Besides, we find the ratio of the average rate of recovery to the average rate of death of the new coronavirus pandemic for the same four countries. For the following months, we predict the number of the infected cases, the recovered cases, and the deceased cases of the pandemic for the United States, Russia, and the Syrian Arab Republic using the methods normally used for the epidemic model. We find that the number of infected cases of the new coronavirus disease may increase to about two million cases in the United States, about eight hundred thousand cases in Russia, and about three hundred cases in the Syrian Arab Republic. We believe that the algorithm we use for simulating the spreading and the forecasting of the new coronavirus disease can be applied for finding other related coefficients of the pandemic such as the basic reproduction numbers with a certain population.

Highlights

We have made a fitting of the reported observed results of the new coronavirus pandemic; for China, the first case of the pandemic appeared at the end of 2019; for the United States, which has the highest number of the cases, the first case was observed in January 2020; for Russia, which has the second highest number of cases of the pandemic, the first case was observed at the end of January 2020; for the Syrian Arab Republic, where the number of cases is relatively low, the first case was observed in March 2020
The number of deceased cases in China and the Syrian Arab Republic is small; if we compare the number of recovered cases in the two countries with that in Russia, we see that the ratio is higher for Russia, and this aspect explains why the ratio of the number of recovered cases to mortality cases is relatively high for Russia and gives the physical insight of this ratio
We calculated the predicted number of the infected cases of the new coronavirus pandemic, the recovered cases, and the deceased cases in mid-June 2020, mid-July 2020, midAugust 2020, and the beginning of September 2020 in the Syrian Arab Republic based on the same values of the coefficients of the SIRD model which we found for this country

Summary

Introduction

The susceptible-infected-recovered-dead (SIRD) model is one of the mathematical models used in epidemiology to describe the relation between the susceptible cases s(t), the infected cases i(t), the recovered cases r(t), and the deceased cases δ(t) in a certain population with a specific epidemic; of the multiple epidemic models being used, some have ordinary differential equations, and others have fractional differential derivatives.. The SIRD model takes mortality into consideration, and this model is described by four differential equations; the first equation describes the rate of the susceptible cases with respect to time, and this equation is given by ds(t) = − α1 i(t)s(t). The second equation describes the rate of the infected cases with respect to time, which is given by di(t) dt = − α1 i(t)s(t) N − α2i(t) − α3i(t).

Methods

Results

Conclusion