Reproduction number R of the SARS-CoV-2 Virus in Romania
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Chart created in colaboration with statistician Valentin Parvu , who processed the data.
In order to avoid biased estimation, the latest reproduction number R reported is from 4 days ago. The effective reproduction number R with 95% credible interval corresponding to 8 Iunie 2022 was R = 0.96 (0.86, 1.06)
What is the "Reproduction Number R"?
The reproduction number R represents the average number of patients infected from a single case. When R is above 1 the epidemic is growing in intensity, while when R is under 1 the epidemic is decreasing; when R is 1 or close to 1, the daily new cases are approximately the same every day, with no clear trend. Incubation period, duration from symptom onset to case reporting, and the time it takes to transmit the virus to subsequent cases are needed in order to estimate R.
Why is there a 4-day delay in reporting?
After being infected with SARS-CoV-2, it takes an average of 4-5 days until symptoms appear: the majority of cases will develop symptoms within 2-7 days from infection. There are also delays in case reporting after developing symptoms, due to specimen collection and testing.
The reproduction number R which reflects transmission today can only be estimated approximately 4 days from today. By that time a sufficient proportion (over 10%) of all transmissions occurring today are expected to actually be reported officially as cases. Other methods which report R on the current day are based either on predicting new cases in the future, or are based on the day of symptom onset (not available for Romania) and not actually on the day of infection. We consider best to report transmissibility as the day when infections actually occurred.
Technically, the following procedure was used for estimating the effective reproduction number R:
- Infection dates for all reported cases were imputed. A Gamma distribution with mean 5.3 days (1 - 13 days) was used for incubation period, and an Exponential distribution with mean 6.1 days was used for average reporting delays. Overall, cases are reported on average approximately 11 days after infection (Table S1 in Kucharski et al).
- The number of new infections which have not yet been reported were estimated using the negative binomial distribution. Taking into consideration incubation period and reporting delays distributions, the number of infections which occurred at least 4 days ago and were already reported can be estimated. The number of infections which occurred today or in the last 3 days cannot be estimated precisely, so the last reported R corresponds to 4 days ago.
- The effective reproduction number (R) was calculated using the method described in Cori et al for weekly windows. The serial interval distribution (time duration until a patient transmits the virus to next patients) was assumed to be Gamma with a mean of 4.7 days (as in Nishiura et al).
- Steps 1-3 were repeated for 1000 random Monte-Carlo simulations. Mean R, along with 50%, 90%, and 95% credible intervals were then calculated from the 1000 simulations.
References:
- Kucharski, A. J., Russell, T. W., Diamond, C., Liu, Y., Edmunds, J., Funk, S., ... & Davies, N. (2020). "Early dynamics of transmission and control of COVID-19: a mathematical modelling study." The Lancet infectious diseases.
- Cori, A., Ferguson, N. M., Fraser, C., & Cauchemez, S. (2013). "A new framework and software to estimate time-varying reproduction numbers during epidemics." American journal of epidemiology, 178(9), 1505-1512.
- Nishiura, H., Linton, N. M., & Akhmetzhanov, A. R. (2020). "Serial interval of novel coronavirus (COVID-19) infections." International journal of infectious diseases.