key: cord-1014532-74yqqocc
authors: Najafi, Farid; Izadi, Neda; Hashemi-Nazari, Seyed-Saeed; Khosravi-Shadmani, Fatemeh; Nikbakht, Roya; Shakiba, Ebrahim
title: Serial interval and time-varying reproduction number estimation for COVID-19 in West of Iran
date: 2020-06-14
journal: New Microbes New Infect
DOI: 10.1016/j.nmni.2020.100715
sha: c6820ec506b86803993d9fd0640dba3b7e9e8856
doc_id: 1014532
cord_uid: 74yqqocc

There is no report on the serial interval (SI) of coronavirus disease 2019 (COVID-19) in Iran, the present report aims to estimate the SI and time-varying R of COVID-19 in western Iran. In this study, there were 1477 confirmed, probable and suspected cases of severe acute respiratory syndrome coronavirus 2 for Kermanshah from 22 February to 9 April. The close contacts of the confirmed cases were identified using telephone follow up of patients and their contacts. The SI distribution was used as an alternative. We fitted different models using the clinical onset dates of patients with their close contact (infector-infectee). Also, we applied a 'serial interval from sample' approach as a Bayesian methodology for estimating reproduction number. From 22 February to 29 March, 247 COVID-19 cases were confirmed by RT-PCR. Close contact between 21 patients (21 infector-infectee pairs), including 12 primary cases and 21 secondary cases, was confirmed. The mean and standard deviation of the SI were estimated as 5.71 and 3.89 days. The R varied from 0.79 to 1.88 for a 7-day time-lapse and ranged from 0.92 to 1.64 for a 14-day time-lapse on raw data. Also, the R varied from 0.83 to 1.84 for 7-day time-lapse and from 0.95 to 1.54 for a 14-day time-lapse using moving average data, respectively. It can be concluded that the low reproduction number for COVID-19 in Kermanshah province is an indication of the effectiveness of preventive and interventive programmes such as quarantine and isolation. Consequently, continuing these preventive measures is highly recommended.

Coronavirus is rapidly spreading around the world, and the number of confirmed and suspected cases is increasing worldwide. Therefore, estimating the epidemiological measures of is important in assessing the extent of epidemic transmission, predicting the future trends and designing control measures. Various studies have modeled the transmissibility of this virus [1, 2] . This research has focused on calculating the basic reproduction number (R 0 ) using the serial interval (SI) and intrinsic growth rate or using Markov Chain Monte Carlo (MCMC) methods [2, 3] .

The serial interval is defined as the time duration between the symptom onset in primary case (infector) to symptom onset in secondary case (infectee) and indicates the interval between the two infected patients [4] . R 0 and time-varying reproduction number (R t ) are also indices of the transmissibility that indicates the average number of new infections caused by an infected case in a naive population over the period of epidemic. In fact, the distribution of SI is a key input for determining the R 0 [5] . For R 0 >1, the number of patients is likely to increase and for R 0 <1, the transmission is likely to disappear. The basic reproduction number is a key concept in the epidemiology of infectious diseases and indicates the risk of an infectious agent to spread [6] .

This number can vary based on geographical areas and the number of close contact of people with each other. While there is no report on SI of COVID-19 in Iran, the present report is aimed to estimate the SI and time varying R of COVID-19 in Western part of Iran, where the epidemic had not reach to the sever situation and therefore was different from north part and central part of Iran.

After confirming the epidemic of COVID-19 in Iran, data on patients with COVID-19 (confirmed, probable and suspected cases) by either real-time polymerase chain reaction (RT-PCR) test or chest CT-scan or clinical symptoms collected by two different sections: public health sectors and emergency unit of all selected hospitals. While public health sectors are responsible for massive phone screening programs supervised by deputy of Health in ministry of health and medical education in Iran, the emergency units of selected hospitals are referral centers for those who are in more serious condition. For the purpose of this study, we linked the data from both public health section (which are collected and stored for all districts by Disease Control Unit of the Health Deputies) and hospitals of each province. Public health data includes the characteristics of every individual who is tested regardless of the result. The data covers both the inpatient and outpatient cases. Such data include all information regarding province, district, age, sex, date of symptom onset, hospital admission, bedridden and discharge or death date, infection severity, symptom (cough, fever, shortness of breath, headache, runny nose, etc.), chronic diseases history, travel history, past history of other treatments, close contacts with other people and those who are confirmed cases of COVID-19. We defined a confirmed case as those with a positive RT-PCR result. A probable cases where those meeting the clinical criteria with close contact with a confirmed case of confirmed COVID-19 case in the 14 days before the onset of symptoms or those who had a positive lung CT scan diagnosed by a radiologists. Any person meeting the clinical criteria without any laboratory or radiologic diagnostic criteria were defined as possible cases. In Kermanshah province, from February 22, 2020, the information of confirmed, probable and suspected cases of Coronavirus is registered in daily.

In this study, the confirmed, probable and suspected cases of Coronavirus for Kermanshah from February 22 to April 9 were 1477 cases, of which the close contact for confirmed cases were identified using the phone calls follow-up of patients and their contacts. Then, we extracted the count of daily infection and the information about the symptom onset in primary cases (infector) and secondary cases (infectee) from the Integrated Health System and calculated the duration of symptom onset. In addition, we used the moving average smoothing with span 5 (2, 1, 2) for daily confirmed, probable and suspected cases.

In order to estimate the reproduction number, we need to determine the serial interval-a proxy of the generation time-which defined as the interval between clinical onsets in initial case and secondary case [5] . Since the COVID-19 generation time distribution is unknown, in this study, the serial interval distribution was used as an alternative. We fitted different models (lognormal, Weibull and Gamma) using the clinical onset dates of patients with their close contact (infectorinfectee) by "est.GT" function in R 0 package, and the best distribution was determined for the serial interval. Then, using the distribution of the serial interval, time-varying R 0 by Bayesian approach was used to estimate the R 0 for Kermanshah province.

Time-varying method is a likelihood based method for estimating effective reproduction number that uses pairs of cases to obtain the relative likelihood p ij -the probability that infection i at time t i has been infected by infection j at time t j . The relative likelihood p ij with ‫‬ ݆݅ =

formula used for calculating reproduction number on which w represents the generation time distribution. Therefore, the effective reproduction number can be obtained by averaging Rj

) over all infections that had the same symptom onset date with below formula:

In addition, confidence intervals for R t are calculated by 5000 simulation [7] .

We used "EpiEstim" package to estimate effective reproduction number of COV19-19 given the incident case counts data of Kermanshah by time-varying method. In the "EpiEstim" package, estimation of reproduction number by time-varying method can be done by various approaches for serial interval which are "non-parametric", "parametric", "uncertain serial interval", "serial interval from data" and "serial interval from sample". In the present study, we applied "serial interval from sample" approach as a Bayesian methodology for estimating reproduction number that use metropolis algorithm to get MCMC samples and Gelman-Rubin statistic to assess convergence of MCMC samples. Note that, credible interval is an alternative of confidence interval in the Bayesian setting, so we report credible interval of Rt because of using Bayesian approach. Data analysis was performed using the "R 0 " and "EpiEstim" packages in R 3.6.3

software.

Sensitivity analysis was perform for the robustness of the R 0 estimations by different serial interval distribution. For this purpose, different serial interval applied to show how reproduction number changed with various serial interval.

From February 22 to April 9, 1477 COVID-19 confirmed, probable and suspected cases by the PCR test and chest CT-scan were recorded in Kermanshah province. The epidemic curve for COVID-19 shows the two successive waves. The first wave increased from February 22 to

March 22 and then decreased, and the second wave increased from March 23 to April 9 (Fig 1) .

The doubling time i.e. the period required for the number of cases in the epidemic to double was 9.66 days (95% CI: 7.35-14.08) for the first wave and 13.82 days (95% CI: 8.94-30.38) for the second wave.

From February 22 to March 29, 247 COVID-19 cases were confirmed by RT-PCR test. Close contact between 21 patients (21 infector-infectee pairs), including 12 primary cases and 21 secondary cases were confirmed. The Weibull distribution provides the best fit for the serial interval of the COVID-19 outbreak in Kermanshah. The mean (µ) and standard deviation (SD) of the SI were estimated 5.71 and 3.89 days, respectively (Fig 2) .

From February 22 to April 9, 1477 COVID-19 confirmed, probable and suspected cases by the RT-PCR, chest CT-scan and clinical diagnosis by physician were recorded in Kermanshah province.

According to Figure (Fig 3-left column) .

Raw (Fig 3-right column) .

We performed sensitivity analysis to determine the effect of changes in serial interval on the reproduction number in two different time-lapse, 7-days and 14-days. For 7-day time-laps, the estimated values of reproduction number for COVID-19 were robust as serial interval parameters change (Fig 4-top row) . In addition, the impact of different serial interval on R-values for second time-lapse (14-days) were also robust (Fig 4-bottom row) .

Serial interval, incubation interval, and basic reproduction number are important parameters to

show the shape and form of the epidemic curve. The results of this study showed that the mean and median of SI for COVID-19 were 5.71, 4.75 days, respectively. As far as we know, this is the first report on serial interval from Iran, one of top 10 countries with highest number of reported cases of COVID-19. A study showed that the mean of serial interval in 468 confirmed

Chinese cases (with 59 infector-infectee pairs) was 3.96 days [8] . Other studies estimated the mean of SI to be 4.6 [9] and 4.2 [10] in Japan and china, respectively. Also, a systematic review study by Minah Park et al. indicated the serial interval for COVID-19 to be 4-8 days [11] .

Generally, different studies suggest that the serial interval is shorter than the incubation period for COVID-19. This may be indication of pre-symptomatic transmission; and therefore, further attention should be centered on preventive efforts. In fact, the present study showed that the serial interval for COVID-19 in western part of Iran was longer compared the other reports from elsewhere. This may be due to preventive interventions, training, and better mitigation policies in Iran, which has limited the transfer of person to person. Of course, SI can change over time, space and situation [6] .

In fact, the serial interval for COVID-19 was shorter than that of SARS-CoV and longer than that of the influenza which was consistent with results of the other studies conducted in this area [12, 13] . Different studies have shown that the serial interval for SARS-CoV and MERS-CoV are 8.4 and 8-13 days, respectively [14, 15] . Such characteristics contribute to more rapid transmission of Covid19 than the other coronaviruses; therefore, contact tracing must compete against the rapid replacement of case generations [11] .

In addition, the reproductive number for COVID-19 was lower than what was found in the other studies. Given that the serial interval is important factor in calculating the reproduction number and considering the fact that our study showed longer serial interval, the rate of spreading in this disease is slower and, therefore, the reproductive number will be lower as well [10] .

WHO has estimated the ranged of COVID-19 R 0 to be 1.4 to 2.5; however, some studies have calculated this number to be higher and, consequently, the pace of spread to be faster. For instance, a review study found the average R 0 to be 3.2 [6] ; whereas, another study reported this number to be 2.28 [16] . It seems the estimation of reproductive number is highly dependent on the used methods. Plus, one of the reasons behind this difference might be different time-periods in which the estimation have been taking place. Needless to say, R 0 in early stages of epidemic is higher than in the following stages. One of the strengths of this study is that time-frames are included in the estimation of R 0 s.

All in all, it can be concluded that the low reproduction number for COVID-19 in Kermanshah province is an indication of the effectiveness of preventive and interventive programs such as quarantine and isolation. Consequently, continuing these preventive measures are highly recommended. 

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COVID-19 in Kermanshah-Iran (Using the MCMC method and for time-laps 7 days (top row) and 14 days (bottom row) on raw data)

Time(Day) Reproduction Number Time Dependent Reproduction Number-7 Days-Sensitivity Analysis