We conducted a prospective observational study of the COVID-19 outbreak in Jodhpur, India. We used two data sources for the study. Firstly, serial intervals were estimated based on contact history of laboratory confirmed SARS-CoV-2 infected individuals. Secondly, the publicly available daily case count data were used together with the serial intervals to estimate R₀ and project the size of the epidemic over the next 30 days. Individuals meeting the definition of a suspected case of COVID-19 were tested with the real time reverse transcriptase–polymerase chain reaction (rRT-PCR) at our institute in Jodhpur, India, as per national guidelines [15]. People who tested positive for SARS-CoV-2 were further assessed for their contact history with known COVID-19 cases in their household. The serial intervals were estimated based on the length of time between the onset of symptoms of the identified infectors and infectees. For asymptomatic individuals, the date of collection of the first positive sample was taken as a proxy of symptom onset.

The basic reproduction number (R₀) is defined as the average number of susceptible individuals infected by a single primary case [16]. For R₀ estimation, serial interval values along with daily case count data were taken from the official daily report released by the Jodhpur District administration. These data are also available on the internet [17].

Informed consent was obtained prior to eliciting contact history for serial interval estimation. The study was approved by the Institutional Ethics Committee (Ref: AIIMS/IEC/2020-21/3047).

The mean (SD) of the serial intervals was calculated. Further, the serial interval data were fitted to weibull, log-normal, log-logistic, and generalized gamma distributions using the Flexsurv package in R software version 4.0.0 [18]. The estimates of the median serial interval were taken from the best-fitting model based on the minimum Akaike information criterion (AIC) value. The standard maximum likelihood approach was used to obtain the best model fit to the actual data.

The daily COVID-19 case data in Jodhpur District were converted to incidence objects using the Incidence package in R software [19]. The EarlyR and EpiEstim packages in R were used to estimate the overall and instantaneous values of R₀, respectively, using the parameter estimates of the serial interval [20,21]. We used two main standard methods of estimation of the instantaneous R₀ values to visualize their response to changes in case trends and to assess their utility for understanding real-time transmission dynamics at a local level. These methods use different mathematical modeling principles and assumptions.

Instantaneous R₀ values were first calculated using the method of estimating daily incidence based on a Poisson process determined by daily infectiousness, as proposed by Jombart et al [19] and Nouvellet et al [22]. Here, λ_t, the force of infection observed on day t, is expressed by the following equation:

The numbers of daily and cumulative COVID-19 cases for the next 30 days were forecasted based on the overall R₀ value and the R₀ value for the past 30 days as input parameters using the projections package in R [19]. The observed serial interval distribution was specified as the scale and shape parameters of the gamma distribution. Daily COVID-19 cases were predicted based on a Poisson process determined by daily infectiousness [22]. The specified serial interval distribution was taken as a prior while using the Bayesian methodology for Markov chain Monte Carlo sampling using the Metropolis algorithm. The 95% CIs of the projected daily and cumulative incidences were calculated using the bootstrap resampling method with 1000 samples.

Further, we considered two scenarios: one with a reasonable reduction of 25% SARS-CoV-2 transmission and one with an aggressive reduction of 50% transmission. A reasonable reduction would be related to compliance with strengthening of existing measures, such as contact tracing, testing, and prompt isolation of infected individuals along with physical distancing measures. Aggressive transmission reduction measures included universal mask-wearing and measures to reduce outdoor transmission through prevention of gatherings: closures of places of worship, marketplaces, restaurants, schools, and gymnasiums, along with introduction of nighttime curfews [24].

From the reporting of the first case of COVID-19 in Jodhpur District on March 9, 2020, to July 6, 2020, 3178 cases were reported in the district in a span of 120 days (see Figure 1). Serial interval data for 103 infector-infectee pairs were obtained through contact tracing of known infected cases (Multimedia Appendix 1).

The mean serial interval was 6.23 days (SD 3.49). The generalized gamma distribution was found to best fit the serial interval and showed the minimum AIC value (see Table 1).

The median and 95th percentile values of the serial interval were 5.23 days (95% CI 4.72-5.79) and 13.20 days (95% CI 10.90-18.18), respectively, estimated from the fitted generalized gamma distribution (see Figure 2).

The overall R₀ value in the 30 days after the first case was reported was 1.62 (95% CI 1.07-2.17), which subsequently decreased to 1.15 (95% CI 1.09-1.21). The overall R₀ value for the entire outbreak duration was 1.07 (95% CI 1.04-1.11), whereas it was 1.20 (95% CI 1.14-1.27) in the last 30 days.

The time-dependent instantaneous R₀ values calculated using the method by Jombart et al [19] and Nouvellet et al [22] yielded maximum values of 6.53 (95% CI 2.12-13.38) and 3.43 (95% CI 1.71-5.74) using sliding time windows of 7 days and 14 days, respectively (see Table 2 and Figure 3). Similarly, using the method described by Wallinga and Teunis [23], the maximum values of the instantaneous R₀ were 2.96 (95% CI 2.52-3.36) and 2.92 (95% CI 2.65-3.22) for the 7- and 14-day time windows, respectively (see Table 2 and Figure 3). The peak R₀ values corresponded with the daily rising trend in COVID-19 cases that was reported (see Figure 3).

The latest instantaneous R₀ values estimated on July 6, 2020, using the method by Jombart et al [19] and Nouvellet et al [22], were 1.21 (95% CI 1.09-1.34) and 1.12 (95% CI 1.03-1.21) for 7- and 14-day sliding time windows, respectively (see Table 2 and Figure 3). Similarly, the latest instantaneous R₀ values estimated on July 6, 2020, using the method by Wallinga and Teunis [23] were 0.32 (95% CI 0.27-0.36) and 0.61 (95% CI 0.58-0.63), for the 7- and 14-day sliding time windows, respectively (see Table 2 and Figure 3).

The number of daily cases projected for the next month based on an overall R₀ value of 1.20 (corresponding to the most recent 30 days of transmission) ranged from 55 (95% CI 38-71) on July 7, 2020 (day 1), to 143 (95% CI 110-175) on August 5, 2020, (ie, on day 30; see Figure 4). Similarly, the number of daily cases projected for the next month while taking the most recent 14-day rolling instantaneous R₀ value of 1.12 ranged from 52 (95% CI 38-66) on day 1 to 91 (95% CI 66-116) on day 30 (see Figure 4). The cumulative projections of the number of COVID-19 cases over the next 30 days using the R₀ values of 1.20 and 1.12 were 2817 (95% CI 2374-3259) and 2131 (95% CI 1799-1462), respectively.

The scenarios of 25% and 50% transmission reduction of the most recent time-dependent R₀ estimate (ie, reduction of R₀ from 1.12 to 0.84 and 0.56, respectively) resulted in monthly projections of 880 cases (95% CI 699-1061) and 341 cases (95% CI 265-418); these projections correspond to 58.7% and 84.0% reductions in the epidemic size in Jodhpur, respectively.

Our observation of the mean serial interval fell within a range of 4 to 8 days, as estimated by a meta-analysis of 7 studies conducted during the early phase of the COVID-19 pandemic [25]. Another meta-analysis including studies only from China estimated a range of serial intervals from 4.10 to 7.5 days [26]. Our experience suggests that the median and 95% CI estimates of the serial interval should be reported alongside the mean and SD, as the latter approach is more susceptible to influence by extreme values. It has also been suggested that longer serial interval intervals may be due to preventive interventions introduced during the course of the epidemic, which tend to reduce transmission [27,28]. Therefore, it is preferable to estimate the recent serial interval at a local level to better understand the transmission of SARS-CoV-2.

The distribution of R₀ values was consistent with observations from other countries, indicating a similar transmission pattern [4,28]. The peak of the R₀ value was reached in the first week of April 2020. The subsequent reduction toward the end of April can be attributed to aggressive testing, contact tracing, and isolation measures implemented in the urban area of Jodhpur during that month. Our R₀ estimate for the first month (1.61) was slightly higher than the national estimate of 1.47 and lower than the estimate from the state of Tamil Nadu (1.88) in India during the same period of March to April 2020 [9,13]. District level R₀ estimates are more likely to show pronounced fluctuations than state or national estimates, as the latter are aggregated across a wide range of epidemiological settings. Because district-level R₀ estimates were not available from India, we compared our findings with those from the cities of Qom and Shahroud in Iran [29,30]. Similar to these cities, Jodhpur showed a trend of high values of R₀ in the first 14-30 days, with a subsequent decrease toward 1 [29,30]. The initially high R₀ values can be attributed to the suddenness of the outbreak if the surveillance system is robust. The high values may also be due to a sudden start of case reporting following an initial period of underreporting, leading to an artefactual peak in R₀ [30].

Earlier detection of infection followed by isolation is known to reduce the R₀ value by limiting both the duration of effective contact and the number of susceptible people an infected individual can come in contact with [16]. Our findings further support that parameters such as the serial interval, incubation period, and R₀ value are likely to vary throughout the course of the epidemic and will depend on local factors influencing transmission, such as demographics, environmental conditions, modeling methodology, and stringency of control measures [16,30].

The projected estimate of daily cases and the final outbreak size were found to depend on the value of R₀ entered in the model [31-33]. The method used to estimate the R₀ value and the time window over which R₀ was calculated both influenced the final projection by a wide margin. The 14-day time window yielded less variable instantaneous R₀ estimates compared to the 7-day time window. We found that the method by Wallinga and Teunis was more sensitive to recent fluctuations in daily case count than the method by Jombart et al in the same time window. Further, per the renewal equation stated earlier, the values of R₀ are most influenced by the trend in daily cases reported within the range of the serial interval (ie, within 5 to 6 days). This model also assumes homogenous mixing, which becomes less applicable with larger populations in which cases emerge from widely separated clusters. Also, the impact of the method of R₀ estimation and the time window was more pronounced when there was a fluctuating trend in cases or when the R₀ value was close to 1. In research settings, R₀ values should be tested through sensitivity analyses by considering variations in time windows and durations and using different methods so that reliable projections can be provided for larger populations [31]. For routine use within program settings at the district level, the method by Jombart et al may be preferable for monitoring the effectiveness of control methods and providing prior R₀ values for projections compared to the method by Wallinga and Teunis and the overall R₀ estimation using the EarlyR package in R.

Our study was based on contact history of infected individuals instead of on daily follow-up of contacts of infected individuals for disease onset. Therefore, we minimized underreporting of longer serial intervals, which may be due to right-truncation in the follow-up method for assessing the serial interval [30]. Further, the use of the time-varying method for daily R₀ estimation and the maximum likelihood method for overall R₀ estimation has the benefit of lower bias compared to the exponential growth and sequential Bayesian methods [34]. It also enables assessment of the effectiveness of control measures on a real-time basis, in contrast to other methods that only provide an aggregate R₀ value [30].

One limitation of our study is that population level estimates relying on daily official reports can underestimate the value of R₀ compared to those of closed populations because many infected individuals are likely to be missed, especially if the testing capacity is limited or the proportion of asymptomatic people is high [31]. Further, modeling assumptions such as assuming a finite probability of interaction of infector-infectee pairs reported within a serial interval range may not be applicable for large population cohorts [23]. To overcome these limitations, use of both spatial and temporally structured data has been proposed [35]. The use of contact tracing applications that provide anonymized geolocated data and serial interval estimates could provide more timely and robust epidemiological understanding of emerging diseases such as COVID-19 [36,37].

Public health measures such as testing, contact tracing, and home isolation were found to reduce the instantaneous R₀ value and could thereby reduce the final outbreak size. Instantaneous R₀ estimated using the method proposed by Jombart et al is recommended for guiding COVID-19 response strategy at district level in preference to the method proposed by Wallinga and Teunis and to aggregate R₀ calculation. The final epidemic size was found to be influenced by the R₀ value, which in turn depended on the stringency of control measures. Even a marginal reduction in R₀ as a result of strengthening control measures was found to considerably reduce the projected COVID-19 burden at the district level. Projections based on publicly released daily COVID-19 case data are feasible and could be useful in guiding a data-driven COVID-19 response strategy at a local level. This could be used for both surge capacity planning of the number of hospital beds and ventilators required and for public health responses such as the number of staff required for contact tracing and for provisioning of institutional quarantine or isolation facilities. Therefore, considering the increasing caseload and dynamic situation of COVID-19, a decentralized evidence-driven approach is currently needed.