The novel coronavirus disease pandemic, caused by the severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2) virus, has resulted in millions of cases, hundreds of thousands of deaths, and a negative economic impact worldwide. India, a country with over 1.3 billion people across metropolitan areas and rural villages and an underdeveloped medical infrastructure 1 , could be particularly hard hit with the unmitigated spread of COVID-19 2 . To address this challenge, India has implemented widespread lockdown measures, including social distancing and travel restrictions 3, 4 . On March 24, India first announced nationwide lockdown for three weeks, effectively home quarantining everyone in the country to curb the pandemic growth. The lockdown in India was subsequently extended three times, first to May 3, then to May 17, and currently to May 31 5 . Evidence from both India and abroad demonstrates that social distancing is essential to prevent the spread of COVID-19 and reduce mortality 1,6-10 , especially until a vaccine is developed. Nevertheless, several countries, including India, are now cautiously beginning to lift some restrictions in hopes of restarting the economy and preventing economic distress.
The government of India has categorized districts of India into three zones based on the COVID-19 risks. The hotspots of transmission, categorized as "red zones," are identified based on total active cases, doubling rate of confirmed cases, extent of testing, and district feedback.
Areas with declining or stable numbers of cases are classified as "orange zones" and areas with no reported cases for a significant number of days are classified as "green zones" 11, 12 . While nationwide lockdown continues until May 31, considerable relaxations for economic and public service activities are now being allowed in lower-risk districts marked as green and orange zones. During the first phase of reopening of the country-starting June 1-intra-state and inter-state travel will gradually be allowed without need of prior permission from the government. Similarly, places of worship, hotels, restaurants, malls and other hospitality services would resume operation from June 8 13 . As restrictions are eased within specific zones, attention should be directed to geographic hot spots that may disproportionately exacerbate the spread of COVID-19 14 .
Red light areas (RLAs), where thousands of sex workers typically live and work 15 , are one area of concern for rapid transmission of COVID-19. By design, these areas have high contact rates between sex workers and clients, and sex acts are not amenable to social distancing.
Sex workers are vulnerable to high rates of infectious diseases 16, 17 , experiencing particularly high rates of asymptomatic transmission of infections-a notable component of COVID-19 epidemiology. Moreover, visitors to RLAs include many truck drivers and migrant workers 18 , who not only live locally but travel long-distances and can potentially spread the virus more broadly, including to green and orange zones. The combined features of a high volume of visitors, high contact rates, potential higher infectivity of sex workers, and long-distance travel of clients across India may make the reopening of RLAs a risk to increasing COVID-19 transmission, health care utilization, and death. Therefore, the impact of COVID-19 within RLAs, on the cities in which they reside, and on the Indian populace requires critical evaluation.
An analysis in Japan has demonstrated a surge of COVID-19 cases transmitted in RLAs-cases that have overwhelmed local hospitals 19 . Considering the high risk of COVID-19 transmission, other countries, such as the Netherlands 20 , Germany 21 , and Australia 22 , have identified brothels as the last enterprises to reopen. In Australia, brothels and strip clubs are the only businesses to be designated as indefinitely closed.
Prior studies have evaluated the benefits of lockdown in India for slowing COVID-19 transmission 1,23,24 . However, no previous analysis has examined the effect that the reopening of RLAs would have on the spread of COVID-19 in India, or whether keeping them closed would lead to a reduction of cases, reduced health care utilization, and improved mortality rates. Such an analysis would be helpful to the national and local governments to make targeted decisions about when, where, and how to ease lockdown measures in the best interest of public health, the health care system, and the economy.
To understand the potential impact of extended closure of RLAs on COVID-19 in India, we developed a model that quantifies the effects of re-opening RLAs after the end of the lockdown.
We estimated the change in the time to reach peak COVID-19 cases: the change in cases, hospitalization rates, and mortality rates; and the spread of COVID-19 within RLAs at both the national level and among some of the largest cities in India that have been designated within the red zones 11 .
Data collected on RLAs ( Table 1 ) facilitated model parameterization. Closure of RLAs after lockdown significantly delayed the spread of COVID-19 in all cities and nationally, including reduced numbers of cases and deaths ( Fig. 2-3 ). The magnitude of these effects varied with greater infectiousness (increasing R 0 ; Appendix Tables 3-4 ) and increased with a greater resident population of RLAs relative to the general population of the city and with a greater contact rate between the general population of the city and residents of the RLA ( Fig. 3 ; Table 1 ).
The initial nationwide lockdown is projected to substantially delay the peak of the epidemic for each city considered and India ( Fig. 2, Appendix Table 3 ). Extended closure of RLA after the lockdown is lifted can further delay the epidemic peak further by at least 8 days and up to 23 days with an R 0 of 1.75-2.25 in India ( Appendix Table 3 ) . There was variation between peak delays among cities. The smallest delay in the peak of cases with an extended closure of the RLA in Mumbai was a 9-day delay using R 0 = 2.25 (a 114-day delay to a 123-day delay; Appendix Table 3 ). The largest delay in the peak of cases with an extended closure of the RLA in Kolkata was 117 days-close to the delay that was produced by lockdown alone-using R 0 = 1.75 (a 126-day delay to a 243-day delay; Appendix Table 3 ).
We found that an extended closure of RLAs after the initial lockdown period would avert 32% to 60.2% of cumulative cases and 43% to 67.6% of cumulative deaths across India when compared at the date of the peak of epidemic under re-opening of RLAs ( Fig. 3 , Appendix Table 4 ). Among cities, these reductions of COVID-19 cases and deaths were at least 49.7% and 59.2% respectively for R 0 = 2 ( Fig. 3 ). In Kolkata, Pune, and Nagpur, reductions in cumulative cases and deaths at the date of this peak were more than 90% for all R 0 considered ( Appendix Table 4 ).
Extended closure of RLAs after the initial lockdown reduced cases, hospitalizations, and mortality within RLAs in accordance with potential R 0 values for COVID-19. With re-opening of the RLAs, 32.5% (207,408) to 44.9% (285,908) of all RLA residents were projected to be infected by COVID-19 by the peak of the epidemic in India ( Appendix Table 5 ). By the same date under a scenario of extended closure of the RLA, the proportion of RLA residents infected would be between 12.9% to 30.5%. For R 0 = 2, the maximum reduction in cumulative cases at the peak of epidemic occurs within the RLA of Kolkata (from 8,436 cases to 42 cases; Appendix Table 5 ) and the minimum reduction occurs within RLA of Mumbai (from 2195 cases to 1104 cases; Appendix Table 5 ). 
India has approximately 1.9 million hospital beds, 95 thousand ICU beds, and 48 thousand ventilators. Most of the beds and ventilators in India are concentrated in seven states-Uttar Pradesh (14.8%), Karnataka (13.8%), Maharashtra (12.2%), Tamil Nadu (8.1%), West Bengal (5.9%), Telangana (5.2%), and Kerala (5.2%) 25 . As a result of extended closure of RLAs after the initial lockdown, current hospital capacity would be reached on October 26 rather than October 15 2020 (Fig. 5) . Moreover, at the projected November 19 peak of cases, India would need 10 times more hospital capacity than current capacity, while under extended closure of RLAs, required hospital capacity would be 5.8 times higher ( Fig. 5 ) .
Indian central and state governments are adding additional beds on a daily basis to ramp-up the healthcare capacity. Under the scenario in which closure of RLAs is not extended, the high number of imminent cases and consequent demand for hospitalization/ICU admission and ventilator use rates will likely surpass India's peak medical resource capacity, especially in the vulnerable zones-leading to a higher mortality rate (Fig. 5 ).
Our study demonstrates a beneficial impact of extended closure of RLAs in India compared with their re-opening on COVID-19 cases, hospitalization and mortality. Extended closure would delay the peak number of cases by 8-23 days and result in a 32.0-60.2% reduction in the cumulative number of COVID-19 cases nationally, when compared at the date of the epidemic peak under a scenario of re-opening the RLAs. There would also be a 43-67.6% reduction in the cumulative number of COVID-19-related deaths nationally. These benefits of extended closure of RLAs, including a delayed peak in cases, a reduced increase in cases, and a reduction in deaths were demonstrated in Mumbai, New Delhi, Pune, Nagpur, and Kolkata, as well as across India. Mumbai and Kolkata (at the two extremes of R 0 considered) produced the most disparate results across cities-a difference that can be attributed to the size of the resident populations of the RLAs relative to the general population of the city and to the contact rates between the general population of the city and residents of the RLA.
The lockdown, contact tracing, and other post-lockdown government interventions 26, 27 can continue to suppress transmission and flatten the curve, but it is unlikely for the pandemic to be resolved until there is a vaccine for the population 28 . Vaccine development and widespread distribution throughout India may take at least 18 more months 29 . In the absence of efficacious treatments or vaccines for COVID-19, there are limited public health interventions that can substantially reduce COVID-19 cases and deaths when re-opening a country as large and diverse as India 30, 31 . Extended closure of RLAs in India may be one of these interventions-and it is feasible. Given the disproportionate impact of RLAs on COVID-19 transmission and the increase of mortality associated with its spread, extension of closure is essential to the protection of sex workers; their clients; the people who interact closely with sex workers and those close to RLAs, including local businesses, police personnel, NGO workers, and the local community; and the population of India at large. In addition to the lower immediate cases, hospitalizations, and deaths, extended closure confers additional time for the nation to plan and execute measures to protect public health and the economy, and to exchange public health and medical advances with the rest of the world. Similar to decisions to close cinema halls, gyms, and large public gatherings, RLAs should be critically evaluated for their ongoing potential to accelerate COVID-19 transmission and spread.
The outcomes of our model are supported by the experiences of other countries with COVID-19 and RLAs. In Japan, for example, medical facilities were overwhelmed by a surge of cases linked to an RLA 19, 32, 33 . The sharp increase in cases manifested among sex workers and their clients, and was largely contained within that sector only because of targeted and robust public health interventions. Japanese medical institutes have placed sex workers in the highest risk category for contracting the virus-the only profession in that classification not related to the medical field 34 . In Germany and Australia, brothels remain indefinitely closed, with some politicians calling for their permanent closure in Germany 35 . Due to concern regarding COVID-19 transmission, sole-operator sex workers and strip clubs have also been banned in Australia 21, 22 . The diversity of businesses that function to enable commercial sex work or other activities involving close physical proximity as part of the nature of service share many of the same risk factors as the sex workers. These other businesses include strip clubs, ladies' bars, hotels that also commerce in sexual services, private sex-work establishments, spas, and massage parlors.
There are many social, economic, and health challenges, alongside the spread of COVID-19, that sex workers and their families will face under extended closure. Residents of RLAs typically live in confined, communal living spaces. Without sex work, they have very limited access to food and other vital living supplies. Furthermore, many sex workers lack government-approved documentation and thus are unable to benefit from the government's financial relief packages 36, 37 Table 2 ). Individuals Table 2 ). The probability of infection given a contact between a client from the general population and a resident of an RLA was assumed to be one, if the resident was a sex-worker, and , if the resident was a non-sex worker. As non-sex workers account for five times more interactions with clients than sex-workers, we calculated the probability of infection given a contact between a client from the general population and any resident of the red-light area as the weighted average of these two probabilities,
The interactions between the general population and the RLA occurring via clients were defined by the connectivity matrix where is the contact rate between the two communities. This contact rate was calculated as the per-capita daily clients from the general population who visit the red-light area.
We used social contact matrices estimated for India overall and within specific locations such as households 41 to construct contact patterns between age-groups based on whether individuals are quarantined in their home or not. The contact patterns between age-groups were captured by two matrices: ( Table 1) to the average number of interactions in the contact matrix .
We specified that individuals with asymptomatic and mild infections are only 50% infectious compared to severe infections ( Appendix Table 2 ).
To generate epidemic projections, we first estimated the initial prevalence of COVID-19 at Table 2 ) using the least-squares method. Using our calibrated model, we generated results under scenarios of no initial lockdown, initial lockdown followed by return to status quo, and initial lockdown followed by extended closure of the RLA.
To implement the 68-day national lockdown in our model, we specified that everyone remained at home, and their contact patterns were informed by the household matrix for the duration of lockdown. Moreover, we set the interaction rate between the general population and the RLA at zero during this period.
After the initial lockdown period, contact patterns were informed by the overall contact matrix , and it was assumed that as a result of improved contact-tracing capacity achieved during lockdown, 50% of symptomatic cases were isolated after the lockdown period 10 . For the scenario of extended closure of the RLA after lockdown, we maintained the contact rate ;
with no extended closure, it returned to its original value.
The basic reproduction number, R 0 , is the expected number of cases directly generated by an infected person in a completely susceptible population early in an epidemic, without public health intervention. For example, if early in an outbreak, a single individual typically develops the infection and passes it to 2 people, the R 0 is 2. If R 0 > 1, there will be an exponential spread of the infection. If R 0 < 1, the rate of infection spread will be lower and eventually stop.
Epidemics grow faster with higher R 0 . In this study, we show a range of results based on R 0 values of 1.75 to 2.25 calculated in recent research on the COVID-19 pandemic 10, 44, 45 .
To obtain current estimates of city-level population data, we applied population growth rate For national-level data, the number of sex workers, brothels, and client visits was determined from secondary sources 51, 52 . Exhaustive face validation with subject experts was conducted for the dynamic data sets pertaining to the movement of sex / non-sex workers, clients, and their interaction within the brothels due to the high volatility of movement patterns of primary respondents at any given time-space in RLAs. Where more general secondary sources exhibited discrepancies with the specific RLA surveys, the more specific estimates from the five RLA surveys were used to compose final data at the national level.
References for all the data used in the analysis are provided in the article and supplementary material. All data generated from this study is shared publicly at the Github repository https://github.com/abhiganit/RedlLightAreas-COVID19
The mathematical model used to generate results for this study were developed and implemented in MATLAB. All code used for this study are publicly available at the Github repository https://github.com/abhiganit/RedlLightAreas-COVID19 Table 3 : Delay (in days) in the peak of outbreak for each location and . 