What Can We Estimate From Fatality and Infectious Case Data Using the Susceptible-Infected-Removed (SIR) Model? A Case Study of Covid-19 Pandemic

Abstract

The rapidly spreading Covid-19 that affected almost all countries, was first reported at the end of 2019. As a consequence of its highly infectious nature, countries all over the world have imposed extremely strict measures to control its spread. Since the earliest stages of this major pandemic, academics have done a huge amount of research in order to understand the disease, develop medication, vaccines and tests, and model its spread. Among these studies, a great deal of effort has been invested in the estimation of epidemic parameters in the early stage, for the countries affected by Covid-19, hence to predict the course of the epidemic but the variability of the controls over the course of the epidemic complicated the modeling processes. In this article, the determination of the basic reproduction number, the mean duration of the infectious period, the estimation of the timing of the peak of the epidemic wave is discussed using early phase data. Daily case reports and daily fatalities for China,

Analytical Parameter Estimation of the SIR Epidemic Model. Applications to the COVID-19 Pandemic

“…This can be eventually extended to predicting the effects of different containment measures or the lack thereof [ 8 ]. Presented analysis corroborates the finding of other authors about the utility of the SIR model in analysing the COVID-19 pandemics [ 4 , 6 , 7 , 8 ]. Presented results indicate that there is a universality in the time evolution of COVID-19 and the same epidemic model, notably SIR, can be applied to countries having large differences in populations sizes and densities.…”

“…Therefore, outcome variables, such as mortality, can be foretasted more easily using a simpler model, e.g., using the SIR model. Recently, several authors demonstrated that the first wave of COVID-19 followed SIR dynamic, which by itself, is an interesting finding [ 4 , 5 , 6 , 7 , 8 , 9 ].…”

On the Time Shift Phenomena in Epidemic Models

“…7 for some parameter values. To this end, the pair (R 0 , 1/c) is chosen (2.5, 5), (5, 5), (10, 5), (2.5, 10), (5, 10), (10, 10), (2.5, 20), (5,20), and (10,20), respectively, and the numerical evaluations for various infectious stages N are shown in Figure 10. It can be observed from this figure that the delay is almost half of the infectious period.…”

“…Moreover, the works [17,18] provide some useful results on the final size of the epidemic for SIR models. With the same motivation of these works but rather a different contribution to literature, we use a multistage model [14] in this article to explain the time shift observed in several surveys such as Spanish flu (1918)(1919) [19], SARS (2002SARS ( -2004, the 2009 H1N1 in Istanbul, and recently, COVID-19 [20] (see Figures 1-3).…”

COVID-19 outbreak in Wuhan demonstrates the limitations of publicly available case numbers for epidemiological modeling

“…As the parameter estimates depend on the model characteristics, such simplifications can result in biased estimates and predictions. The case report data provide only limited information about the process, in particular the distribution of inter-event times are difficult of reconstruct, which is also discussed in multiple other studies ( Zhao et al, 2020b , Roosa et al, 2020 , Chowell, 2017 , Ahmetolan et al, 2020 , Anastassopoulou et al, 2020 , Mukandavire et al, 2020 , Liu et al, 2020b ). …”