Article DOI: Severe Acute Respiratory Syndrome Coronavirus .

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Article DOI: https://doi.org/10.3201/eid2608.200536Severe Acute Respiratory SyndromeCoronavirus Transmission Potential, Iran,2020AppendixEstimate of reproduction number from daily reported cases (Method 1)Using the daily curve of reported cases in Iran, we estimate the reproduction number ofCOVID-19 (Appendix Table 2, Figure 1). For this purpose, we first characterize the dailyreported incidence using the generalized growth model (GGM) (1). This model characterizes thegrowth profile via two parameters: the growth rate parameter (𝑟𝑟) and the scaling of the growthrate parameter (𝑝𝑝). The model captures diverse epidemic profiles ranging from constantincidence (𝑝𝑝 0), sub-exponential or polynomial growth (0 𝑝𝑝 1), and exponential growth(𝑝𝑝 1) (1). The serial interval is assumed to follow a gamma distribution with a mean of 4.41days and a standard deviation of 3.17 days based on recent reports ([2]; C. You et al., unpub.data, .20021253v2).Next, to estimate the most recent estimate of Rt, we simulate the progression of incidentreported cases from the calibrated GGM, and apply the discretized probability distribution (𝜌𝜌𝑖𝑖 )of the serial interval using the renewal equation (3–5) given by𝑅𝑅𝑡𝑡𝑖𝑖 𝑖𝑖𝐼𝐼𝑖𝑖𝑗𝑗 0(𝐼𝐼𝑖𝑖 𝑗𝑗 )𝜌𝜌𝑖𝑖.In the renewal equation we denote the total incidence at calendar time 𝑡𝑡𝑖𝑖 by 𝐼𝐼𝑖𝑖 . Here, thedenominator represents the total number of cases that contribute to the incidence cases at time 𝑡𝑡𝑖𝑖 .Next, we estimate 𝑅𝑅𝑡𝑡 from 300 simulated curves assuming a Poisson error structure to derive theuncertainty bounds around our estimate of the reproduction number (6) (Appendix Table 4).Page 1 of 15

Estimate of reproduction number from epidemic doubling times (Method 2)We ran simulation to generate 10,000 sets of estimates of epidemic doubling times for agiven time series of cumulative number of reported cases (Appendix Table 3), and to computethe arithmetic mean of each set. Then, the harmonic mean of these estimates was calculatedacross 10,000 sets of simulations and was reported as our estimated epidemic doubling time,with 95% confidence interval (Appendix Table 5).Next, we drew 10,000 random values for the serial interval from a gamma distributionwith a mean of 4.41 days and a standard deviation of 3.17 days (2); C. You et al., unpub. 02.08.20021253v2). We generate 10,000 valuesfor the reproduction number by calculating the reproduction number for each pair of values(arithmetic mean of epidemic doubling time and serial interval respectively) following theequation as in Vynnycky and White (7), Table 4.1, Equation 4.14:Reproduction number 1 growth rate serial intervalWe reported the mean and 95% confidence intervals (CI) of the 10,000 estimated valuesof the reproduction number (Appendix Table 5).Results for Regions of IranIran is geographically arranged into five regions, each of which contains a number ofprovinces (see Appendix Table 1). In addition to estimating the reproduction number of COVID19 across Iran, we further analyzed the data for each of the five regions of Iran.Appendix Tables 4 and 5, and Figures 2–8, present our estimates for Regions 1 to 5 usingMethods 1 and 2. The estimates obtained from Method 1 had a smaller variance. The estimatesobtained from Method 2 had a larger variance, given the large variance of the serial intervalestimate that we used. Given that the 95% CIs of our reproduction number estimates obtained viaMethod 2 were large, they overlapped with those obtained via Method 1.From February 19 through March 1, it appeared that whether it was for Iran as a whole,or for its five regions, the point estimate of the estimated basic reproduction number for eachregion was 2.0 or higher before the effect of social distancing interventions kicked in. FromMarch 6 through 19, the effective reproduction number for each region had dropped to a rangePage 2 of 15

from 1.48 of Region 3 to 1.77 of Region 5. However, the 95% CI of each region’s estimate doesnot overlap with 1. Therefore, the transmission of SARS-CoV-2 (that causes COVID-19)remains active in all 5 regions of Iran (as effective reproduction number 1) before the PersianNew Year Day of March 20, 2020.This study in the context of recent pre-print literature on the 2020 COVID-19epidemic in IranOn April 2, 2020, we searched for “COVID-19” and “Iran” on medRXiv pre-print serversand identified 6 manuscripts that fit mathematical or statistical models to COVID-19 case countdata obtained via official Iranian reports. See Appendix Table 6 for a summary. Three of thesepapers provide reproduction number estimates (A. Ahmadi et al., unpub. 03.17.20037671v3; N. Ghaffarzadegan et al.,unpub. data, 20040956v1; Sahafizadeh etal., unpub. data, .20038422v2). Ourestimates of the basic reproduction number are comparable to theirs. These three papers alsoidentified a lower effective reproduction number for the Iranian epidemic once social distancinginterventions kicked in. However, only one paper suggested that the effective reproductionnumber has dropped below unity by March 20, 2020 (N. Ghaffarzadegan et al., unpub. 3.22.20040956v1). The other two estimated aneffective reproduction number 1 (A. Ahmadi et al., unpub. 03.17.20037671v3; Sahafizadeh et al., unpub.data, .20038422v2), that is consistent withour results.References1. Viboud C, Simonsen L, Chowell G. A generalized-growth model to characterize the early ascendingphase of infectious disease outbreaks. Epidemics. 2016;15:27–37. PMID: 272668472. Nishiura H, Linton NM, Akhmetzhanov AR. Serial interval of novel coronavirus (COVID-19)infections. Int J Infect Dis. 2020;93:284–6. PubMed https://doi.org/10.1016/j.ijid.2020.02.060Page 3 of 15

3. Nishiura H, Chowell G. Early transmission dynamics of Ebola virus disease (EVD), West Africa,March to August 2014. Euro Surveill. 2014;19:20894. PubMed 44. Nishiura H, Chowell G. The effective reproduction number as a prelude to statistical estimation oftime-dependent epidemic trends. In: Chowell G, Hyman JM, Bettencourt LMA, Castillo-ChavezC, editors. Mathematical and Statistical Estimation Approaches in Epidemiology. 2009. p. 103–21.5. Paine S, Mercer GN, Kelly PM, Bandaranayake D, Baker MG, Huang QS, et al. Transmissibility of2009 pandemic influenza A(H1N1) in New Zealand: effective reproduction number and influenceof age, ethnicity and importations. Euro Surveill. 2010;15:19591. PubMed6. Chowell G. Fitting dynamic models to epidemic outbreaks with quantified uncertainty: a primer forparameter uncertainty, identifiability, and forecasts. Infect Dis Model. 2017;2:379–98. PubMedhttps://doi.org/10.1016/j.idm.2017.08.0017. Vynnycky E, White RG. An introduction to infectious disease modelling. Oxford: Oxford UniversityPress; 2010.Appendix Table 1. Regions and provinces of Iran.RegionProvinces1Qom Province (QOM), Tehran Province (TEH), MazandaranProvince (MAZ), Alborz Province (ALB), Semnan Province (SEM),Golestan Province (GOL), Qazvin Province (QAZ).2Esfahan (ESF), Fars (FRS), Hormozgan (HOR), Kohgiluyeh andBoyer-Ahmad (KOH), Chaharmahal and Bakhtiari (CHA), andBushehr (BUS).3Gilan Province (GIL), Ardabil Province (ARD), East AzerbajianProvince (AZS), West Azerbajian Province (AZG), Kurdistan (orKordestan) Province (KUR).4Markazi (MAR), Hamedan (HAM), Khazistan (KHZ), Kermanshah(KRS), Lorestan (LOR), and Ilam (ILM).5Razavi Khorasan (KHR), Sistan and Baluchestan (SIS), Yazd (YAZ),South Khorasan (KHS), Kerman (KER), and North Khorasan (KHN).Page 4 of 15

Appendix Table 2. Daily number of new reported COVID-19 cases in Iran and its five regions*Date (yyyy-mmdd)IranRegion 1Region 2Region -1811925052551992020-03-191046359160210Region 818312118612697134120140Region 70110216127157113177*COVID-19, coronavirus disease.†The daily new cases for each of the 5 regions on March 2 and 3, 2020, were interpolated using cubic spline. ‡The reported number of the nationaltotal on March 5 does not match the sum of the 5 regions.Page 5 of 15

Appendix Table 3. Daily cumulative number of daily reported COVID-19 cases in Iran*Date (yyyy-mmdd)IranRegion 1Region 2Region 68Region 1268145415801677181119312071Region 317147415871764*NR, not reported by the Iranian Government.Appendix Table 4. Method 1 (February 19 through March 1, 2020): Estimated epidemic growth rate (95% Confidence intervals, CI),scaling parameter (95% CI) and basic reproduction number obtained via a generalized growth model.LocationEpidemic growth rate (r, 95% CI)Scaling parameter, pBasic reproduction number (95% CI)Iran0.65 (0.56, 0.75)0.96 (0.93, 1)4.4 (3.9, 4.9)Region 10.55 (0.51, 0.65)0.99 (0.94, 1)4.3 (3.8, 4.6)Region 21.20 (0.58, 2.20)0.76 (0.52, 1)3.4 (2.3, 5.0)Region 33.00 (1.50, 5.00)0.52 (0.37, 0.69)2.1 (1.7, 2.7)Region 40.75 (0.67, 0.96)0.97 (0.87, 1)5.8 (4.4, 6.4)Region 50.83 (0.68, 1.30)0.94 (0.72, 1)6.0 (3.8, 7.3)Page 6 of 15

Appendix Table 5. Method 2 (February 19 through March 1, and March 6 through 19, 2020): Estimated epidemic doubling time (95% Confidence intervals, CI), epidemic growth rate(95% CI) and the basic (or effective) reproduction number (95% CI) obtained via Method 2. Epidemic growth rate (r) ln(2)/doubling time. Reproduction number was calculated basedon equation: R0 1 growth rate serial interval, assuming serial interval following a gamma distribution with a mean of 4.41 days and a standard deviation of 3.17 days.Basic ReproductionEffective Reproduction numberEstimated epidemic doubling times (95% CI)*Epidemic growth rate (r, 95% CI)number (95% CI) §(95% CI) §LocationFeb 19 – Mar 1Mar 6 – 19Feb 19 – Mar 1Mar 6 – 19Feb 19 – Mar 1Mar 6 – 19Iran1.20 (1.05, 1.45)5.46 (5.29, 5.65)0.58 (0.48, 0.66)0.13 (0.12, 0.13)3.50 (1.28, 8.14)1.55 (1.06, 2.57)Region 11.32 (1.16, 1.61)6.04 (5.80, 6.29)0.53 (0.43, 0.60)0.11 (0.11, 0.12)3.28 (1.26, 7.59)1.50 (1.06, 2.42)Region 21.12 (0.87, 1.59)5.71 (5.32, 6.04)0.62 (0.44, 0.80)0.12 (0.11, 0.13)3.69 (1.29, 8.84)1.53 (1.06, 2.50)Region 31.38 (1.12, 1.78)6.23 (5.86, 6.51)0.50 (0.39, 0.62)0.11 (0.11, 0.12)3.17 (1.24, 7.24)1.48 (1.06, 2.37)Region 41.67 (1.43, 2.30)5.19 (4.58, 5.79)0.41 (0.30, 0.49)0.13 (0.12, 0.15)2.79 (1.20, 6.15)1.58 (1.07, 2.65)Region 51.13 (0.92, 1.61)3.92 (3.54, 4.32)0.62 (0.43, 0.75)0.18 (0.16, 0.20)3.66 (1.30, 8.79)1.77 (1.09, 3.19)*Harmonic mean of the arithmetic means of 10,000 sets of simulated epidemic doubling times.§Calculated based on the 10,000 arithmetic means of 10000 sets of simulated epidemic doubling times and 10,000 random numbers drawn from a gamma distribution with a mean serial interval of 4.41 days(SD: 3.17 days).Page 7 of 15

Appendix Table 6. Manuscript pre-prints on the COVID-19 epidemic in Iran fit to Iranian official reports available on medRXiv as of April 2, 2020*PapersA. Ahmadi et al., unpub. 03.17.20037671v3medRXivIranian officialpre-printCOVID-19version as of reports†: timeApr 2, 2020rangePre-printFebruary 19version 2through March19, 2020Other datasourcesNot appliedMethodsLogistic differentialequation, Gompertzdifferential equation, VonBertalanffy’s differentialgrowth equation, CubicPolynomial PolynomialsFebruary 19 Unofficial reports; Compartmental (SEIR)through March and international model fit to reported data19, 2020media newsreportsFebruary 22Not appliedCompartmental (SIR)through Marchmodel fit to data18, 2020N. Ghaffarzadegan et al., unpub. 03.22.20040956v1Pre-printversion 1E. Sahafizadeh et al., unpub. 03.20.20038422v2Pre-printversion 2A. Zahiri et al., unpub 03.29.20046532v1Pre-printversion 1February 19through March24, 2020China’s officialCOVID-19reportsB. Zareie et al., unpub 03.19.20038950v1Pre-printversion 1January 22‡to March 8,2020China’s officialCOVID-19reportsC. Zhan et al., unpub 03.08.20032847v1Pre-printversion 1February 19through March6, 2020China’s officialCOVID-19reportsCompartmental (SIR)model fit to data; also fitIranian dat