key: cord-0823574-jlop0lui authors: Raines, K. S.; Doniach, S.; Bhanot, G. title: The transmission of SARS-CoV-2 is likely comodulated by temperature and by relative humidity date: 2020-05-26 journal: nan DOI: 10.1101/2020.05.23.20111278 sha: fcdcb9c81adc36f323ef4669a07fe65e63e7829c doc_id: 823574 cord_uid: jlop0lui Quantifying the role of temperature and humidity on the transmission of SARS-CoV-2 has been confounded by a lack of controlled experiments, the sudden rise in detection rates, and changing weather patterns. In this paper we focus our analysis on data from Colombia, which presents unique economic, demographic and geological characteristics that favor the study of temperature and humidity upon SARS-CoV-2 transmission: the weather varies dramatically across five natural regions (from the Caribbean coast and the Amazon rainforest to the Andean mountains), there are no pronounced seasons, there is a central port of entry, the use of public transportation dominates inter- and intracity travel, and indoor climate control is rare. While only controlled experiments can precisely quantify the role of temperature and humidity upon SARS-CoV-2 transmission, we observe significant attenuation of transmission in climates with sustained daily maximum temperatures above 30 degrees Celsius and simultaneous mean relative humidity below 78%. We hypothesize that temperature and relative humidity comodulate the infectivity of SARS-CoV-2 within respiratory droplets. The citizens live in the ambient conditions of temperature and humidity in his/her environment. This eliminates individual specific variation in temperature and humidity as a potential confounding factor. 5 . Swift and coordinated national response. The first Covid-19 case was con-20 firmed in Colombia on March 6, 2020 [28] . Nineteen days later, the government implemented a national quarantine, with tight cooperation at the local level and all testing orchestrated centrally through Bogotá, using uniform national guidelines [29] . This strong, centralized and swift action of the national government to the Covid-19 pandemic greatly simplifies the analysis because the data neatly separates 25 in time into pre-quarantine and post-quarantine periods. We call the rate at which SARS-CoV-2 was introduced into a city the drip rate. While the drip rate among the various regions of Colombia is unknown, the dominant port of entry (Bogotá) for international travel constrained the way the disease spread through the country. Furthermore, the heavy use of public transportation for inter- 30 and intracity travel ensured that the disease spread quickly throughout the country, even to regions with low tourism. Ostensibly, variations in the drip rate confound the analysis since cities with more tourism are likely to have received a higher influx of infected individuals. However, as we will show, the drip rate can be factored out of the analysis because 35 it does not affect the rate at which the disease spreads. In contrast to the detection rate, the drip rate does not affect the exponent of disease growth (see methods and D R A F T supplementary information for more discussion on the drip rate). Our data model considers both dynamic detection rates and variations in the drip rate between cities (see section 3.1) . From this model, we derive a measure of disease transmission that is independent of both the drip rate and the overall detection rate (equation 5). By combining Colombian city-data with our drip model, we have 5 largely mitigated the confounding factors (1-3) above and were able to identify a significant attenuation in transmission in hot cities with simultaneous moderate relative humidity. In this article, we do not consider the microscopic details of viral spread since there 10 are too many variables to consider (e.g. turbulent airflow on buses). However, we briefly review some features and findings of recent models as they pertain to our assumptions [30] First, we follow other researchers in using models of influenza to inform models of coronavirus, since seasonality is strongly correlated with infection rates in both The strong dependence of the probability of transmission on host-recipient distance underscores the need to separate the data into pre-quarantine and postquarantine segments since the degree of social distancing changed dramatically after quarantine was in place. Without this division, we would have to consider a time-dependent transmission rate, which unnecessarily complicates the analysis. Following Herfts [38] , we divide the transmission process into four basic steps: (1) a potential infectee interacts with the environment of an infectious host (2) 30 the infectious host transmits an intact virus to the infectee (3) the virus infects the potential infectee (4) the virus replicates sufficiently for the infectee to become infectious. In step (1), interaction, it is not necessary that the recipient and donor are in the "infective region" at the same time. With influenza-like diseases, virus- 35 4 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted May 26, 2020. . https://doi.org/10.1101/2020.05.23.20111278 doi: medRxiv preprint D R A F T droplets can remain suspended in the air for several hours in a suitable environment. An infectious host can also deposit the virus onto some surface that the potential infectee later touches. In step (2) , transmission, there is a timescale of virus viability that depends upon the environment. Influenza and SARS-CoV-2 are both enveloped by lipid-5 membranes derived from the budding host cell. The accumulation of damage to this membrane at higher temperatures may contribute to virus instability and decomposition. The probability of infection, step (3), depends upon the number of intact viruses that deposit on the potential infectee and the susceptibility of the infectee. Suscep-10 tibility to infection depends on many factors, including age, medical history, obesity and even internal humidity, as a dry respiratory tract is more prone to infection [39] . In step (4), replication, both demographic and environmental factors play a role and temperature correlates with viral titer (hotter temperatures producing less titer) [33] . 15 The rates, or probabilities, of these steps are not independent. Environmental factors influence the frequency and conditions under which people associate. Likewise, they regulate virus decomposition rates, modulate host susceptibility and the severity of infections within hosts. Finally, droplet settling times, droplet evaporation times, viral stability times, all depend on environmental factors such as 20 humidity, temperature, wind etc. To minimize the effects of these factors, it is essential to restrict the analysis to situations where the transmission occurs in environmental, social and economic steady-state conditions. The Colombian data meets these conditions because of (1) the lack of seasonality, resulting in nearly constant weather patterns in each region; (2) the widespread daily use of transportation in densely packed buses and subways; (3) the high population density in cities and (4) the suddenness and totality of the imposed quarantine. Since cities differ in many ways, identifying the key variables (e.g. weather) responsible for variations in infection rates among cities is complicated. However, 30 following research on influenza and coronavirus [37], we assume that averaging over populations sufficiently reduces the impact of all factors except population, public transportation usage, and weather. Apart from these, we will assume that the cities have roughly the same average demographic, economic and social conditions so that these variables do not confound our results. Consequently, we will assume 35 that although transmission rates in different regions may be different, the overall transmission rate within each city is constant. . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted May 26, 2020. [14] . In addition, SARS-CoV-2 has a long incubation period of up to ∼ 15 days [15] . During this time, the disease host is infectious but asymptomatic. 5 In Colombia, international travel was banned three days after the imposition of national quarantine [28], thus we approximate that the rate at which infectious travelers arrived in each city was roughly constant over the pre-quarantine period. We model the daily arrival of SARS-CoV-2 into each city as a Poisson process with mean I. That is, we assume that each day prior to the quarantine, I[t] infected 10 travelers arrive into a city where they begin infecting locals. We assume that on average, an infectious person infects r people each day, who in turn become infective (able to infect others) in one day. That is, on day t there are I[t] new infectious arrivals, as well as the N [t − 1] total infectious people from the day before, and the This difference equation can easily be solved. We find that the expected number of infections on day t is:N Equation (1) gives the expected number of infections in a given city on day t. In our analysis, we allow both I, the drip rate, and r, the transmission rate, to vary by city. While the disease is spreading, an infrastructure is being established to detect the disease which results in a dynamic disease detection rate. As a simple but useful case, consider a logistic increase in the detection rate. In supplementary information, we will consider more complicated models. We define the total probability of detecting an arbitrary infectious disease host on day t as: The detection rate increases from a small value (p(0) = p f /(1+e kh )) at rate k, to a final detection capacity of p f with half capacity reached on day h. The probability 6 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 26, 2020. . https://doi.org/10.1101/2020.05.23.20111278 doi: medRxiv preprint D R A F T of detecting c cases of SARS-CoV-2 on day t is distributed as a Binomial distribution B(N [t], p(t), c(t)). The average (expected) number of infections detected on day t is then:c When r is small (which covers all cases of interest), the time-derivative of the log of the expected number of confirmed cases (the expected case log-velocity) is: Note that the drip rate (I) and the overall detection rate (p f ) have fallen out. Equation (5) is the basic equation that we use to fit the data. However, we do not restrict our analysis to a logistic form for the increase in the detection rate (see supplementary materials). We downloaded the case history for Colombia from the Instituto Nacional de Salud (https://www.ins.gov.co/Noticias/Paginas/Coronavirus.aspx). Next, we downloaded the weather for all of the cities in Colombia from World Weather Online (https://www.worldweatheronline.com/). Then we downloaded population data for Colombia from City Population dot de (https://citypopulation.de/). 15 In order to apply equation 5 to the data, we first approximated the expected count number from the daily count number by computing a weighted average over neighboring days. That is, we smoothed the raw case number data for each city with a seven day triangle function. Next, we calculated the numerical derivative of logc[t]. Then we fit this log-velocity to the drip model by equation (5) as discussed in the supplementary information. This fit results in an error volume e(r, k, h) that measures the error between the model under (r, k, h) and the transformed data. Since the computation of the log velocity is non-linear and our fit error function is nonlinear, we cannot compute standard statistics on the quality of the fit. This is the 25 price we pay for removing the drip rate and the overall detection rate from our model. Instead, we quantify the variation in the quality of the fits by the percent 7 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 26, 2020. In order to divide the data into pre-quarantine and post-quarantine times, we analyzed the detection rate in Bogotá (see figure 2 ). By subtracting the infection logvelocity from the count log-velocity in equation (5) we obtained a free-form estimate 5 of the detection rate in Bogotá. Since our model assumes a constant transmission rate, the decline in transmission of SARS-CoV-2 induced by the quarantine shows up as a decline in the detection rate, which we observe on April 3, 2020 (figure 2). From this date, we compute a threshold of April 7, 2020 for the remainder of cities throughout the country (Bogotá entered into quarantine 4 days prior[28]). Research estimates that Covid-19 can incubate for up to ∼ 15 days, with a mean incubation period from 5 − 7 days [15] . Additionally a three day delay between clinical presentation and diagnostic confirmation of Covid-19 was typical around this time. 4 Results and discussion 15 Inferring the rate of disease spread from daily case numbers can be deceptive, since variations in the disease detection rate and the drip rate result in detection of significantly larger or smaller fractions of the disease population. To account for this and other factors, we developed the drip model which removes the overall 20 detection rate. Since the data span about 30 days, exponential growth will only be manifest for cities with transmission rates significantly greater than 1/30 ∼ 0.033. We consider 0.05 to be the minimum threshold on the transmission rate for observing exponential growth in a city. We associate transmission rates above this threshold with airborne transmission and transmission rates below this threshold with tourism 25 and direct transmission [40] . The data only show clear exponential growth in large cities with humidity over 80% and mean maximum daily temperatures below 30 degrees Celsius (Bogotá, Cali, and Medellín). The humidity in these cities is roughly the same (82 %), and they have similar total populations and urban population densities (table 1). The 30 transmission rate declines among these cities with increasing temperature. Since these cities had the largest number of confirmed cases of Covid-19, these fits have the highest confidence. We note that none of the smaller cities at any temperature and humidity regis-8 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 26, 2020. . https://doi.org/10.1101/2020.05.23.20111278 doi: medRxiv preprint D R A F T tered significant transmission rates in the pre-quarantine data. For example, Soacha and Bucaramanga compare to Bogotá and Medellín respectively. Soacha shares climate with Bogotá but has one tenth the total population (Soacha and Bogotá are neighboring cities and are connected by urban rail). Soacha has a higher urban population density than Bogotá. Bucaramanga has nearly one-fifth the population 5 of Medellín (at similar temperature and humidity) and half the population density. Bogotá is more than 10 times larger than Soacha and Medellín more than twice as large as Bucaramanga. Moreover, Bogotá and Medellín are regional transportation hubs. Thus we conclude that the lack of transmission in Soacha and Bucaramanga is attributable to transportation factors as governed by total population and regional 10 importance. As we were preparing this manuscript, we observed an outbreak in Cartagena de Indias, a hot city in the Caribbean coast that had exhibited low case numbers for over two months. This outbreak began about 50 days into the quarantine and showed a higher transmission rate than at any previous time in Cartagena and thus 15 suggests that the outbreak could not be solely attributable to quarantine violations. Since international travel had been banned and intercity travel highly restricted for nearly 50 days prior to the outbreak, we conclude that the outbreak must reflect a change in environment. While the weather in Colombia is nearly constant, there are small temperature 20 and humidity shifts associated with rainy and dry seasons. This outbreak, and several other smaller outbreaks, exhibits a remarkable correlation with sustained humidity above about 78%. Based upon the fact that (1) this outbreak occurred during quarantine and (2) international travel was banned and local travel highly restricted for 50 days prior to the outbreak and (3) temperature was nearly constant 25 prior to the outbreak and (4) there was no observable spike in testing around the outbreak, we conclude that this outbreak was driven by relative humidity (see figure 6 ). Finally, we note that lack of rainfall appears to offer additional protection from Covid-19 outbreaks. Rainfall has been identified as a correlate of influenza outbreaks 30 in the tropics [41] [42] , likely due to increased crowding from sudden tropical storms [42] . Additional weather variables such as hours per day of sunlight, UV, etc., also show some correlation with our data. A post-quarantine analysis, and likely an analysis with international data, will be needed to establish all of the weather factors on Covid-19 outbreaks. 35 9 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 26, 2020. . https://doi.org/10.1101/2020.05.23.20111278 doi: medRxiv preprint Our analysis focuses upon the pre-quarantine dynamics of Covid-19 in Colombia. During this time, the humidity and temperature was nearly constant by region and we assume social and economic steady state conditions. We observed a clear separation of the data according to three variables: total population, temperature, 5 and relative humidity. Cities with populations significantly under 1 million did not exhibit any significant outbreak of Covid-19. Large cities with warm weather (maximum daily temperature above 30 degrees Celsius) and simultaneous moderate humidity (below 78%) did not experience outbreaks and showed transmission rates consistent with tourism and direct contact. Large cities with high humidity (above 10 80%) experienced significant outbreaks, with transmission rates that declined with increasing temperature. Cartagena de Indias, a hot Caribbean city that showed very low transmission rates for March and April, experienced an outbreak in early May consistent with high transmission rates. This outbreak followed a sustained rise in daily mean 15 humidity above 80%, a threshold that has been previously identified as favorable to enveloped viruses. Comodulation of viral infectivity by temperature and by humidity has been experimentally demonstrated in a variety of enveloped viruses [43] such as SARS-CoV [44] , influenza [ influenza of an order of magnitude between 5 and 30 degrees Celsius in guinea pigs [33] . However, viral titer cannot explain the outbreak in Cartagena which appears to be driven entirely by relative humidity; it is improbable that small variations 30 in ambient humidity could affect viral titer given that the air within the human respiratory system is saturated and unlikely to vary with small changes in ambient RH [52] . The timescale of temperature-only destabilization in solution appears to be on the order of minutes [45] [50] [49] , although direct measurements at shorter 35 timescales in conditions that mimic respiratory droplets are lacking [51] . Droplet 10 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 26, 2020. . https://doi.org/10.1101/2020.05.23.20111278 doi: medRxiv preprint D R A F T settling timescales vary between minutes and hours depending upon droplet size [51] . Given the dense packing on public transportation of cities with attenuated transmission, we reason that the mechanism behind this attenuation must act on the timescale of seconds [53] [33] and thus rule out droplet settling and temperatureonly viral destabilization. 5 Airborne respiratory droplets evaporate down to half size in about one second [51] [46] . This evaporation is thought to influence viral stability through salt and protein concentrations, pH gradients, and surface sheering [46] . Humidity and temperature both influence droplet evaporation, with temperature influencing the rate and relative humidity determining the final droplet size [33] . While the timescale 10 of droplet shrinkage has been studied, the timescale of viral inactivation within the shrunken and toxic respiratory droplets is, to our knowledge, unknown [51] . In conclusion, we analyzed the pre-quarantine dynamics of the spread of SARS-CoV-2 in Colombia and found an attenuation in transmission for temperatures above 30 degrees Celsius when the mean humidity was simultaneously below 75%. We ob- 35 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 26, 2020. . served an outbreak in Cartagena that closely followed sustained humidity above 78%. Given the over-crowded public transportation systems and high urban population densities of cities with highly attenuated transmission, we hypothesize that the attenuation is caused by rapid viral inactivation within the droplet matrix as mediated by evaporation through temperature and relative humidity, with direct 12 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 26, 2020. . https://doi.org/10.1101/2020.05.23.20111278 doi: medRxiv preprint . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 26, 2020. 14 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 26, 2020. . https://doi.org/10.1101/2020.05.23.20111278 doi: medRxiv preprint D R A F T . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 26, 2020. . https://doi.org/10.1101/2020.05.23.20111278 doi: medRxiv preprint D R A F T . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 26, 2020. . https://doi.org/10.1101/2020.05.23.20111278 doi: medRxiv preprint D R A F T . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 26, 2020. . https://doi.org/10.1101/2020.05.23.20111278 doi: medRxiv preprint D R A F T . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 26, 2020. . https://doi.org/10.1101/2020.05.23.20111278 doi: medRxiv preprint D R A F T . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted May 26, 2020. . https://doi.org/10.1101/2020.05.23.20111278 doi: medRxiv preprint D R A F T [29] C. Ministerio de Salud, "Lineamientos para el uso de pruebas di-agnÓsticas de laboratorio durante la pandemia del sars-cov-2 (covid-19) 30 en colombia." https://www.minsalud.gov.co/Ministerio/Institucional/ Procesos%20y%20procedimientos/GIPS21.pdf. Accessed: 2020-05-12. . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted May 26, 2020. . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted May 26, 2020. . https://doi.org/10.1101/2020.05.23.20111278 doi: medRxiv preprint Epidemiology, genetic recombination, and pathogenesis of coronaviruses The molecular biology of coronaviruses Asymptomatic coronavirus infection: Mers-cov and sars-cov-2 (covid-19) Neurologic features 10 in severe sars-cov-2 infection Clinical characteristics of 50466 patients with 2019-ncov infection Pathological findings of covid-19 associated with acute 15 respiratory distress syndrome Clinical characteristics of coronavirus disease 2019 in china Asymptomatic and presymptomatic sars-cov-2 infections in residents of a long-term care skilled nursing facility-king county, washington Does sars-cov-2 has a longer incubation period than sars and mers? Presymptomatic transmission of sars-cov-2-singapore Substantial undocumented infection facilitates the rapid dissemination of novel 10 coronavirus (sars-cov-2) The difference in the incubation period of 2019 novel coronavirus (sars-cov-2) infection between travelers to hubei and nontravelers: the need for a longer quarantine period The sars-cov-2 outbreak: what we know Coronavirus disease 2019 (covid-19): situation report Covid-19: how doctors and healthcare systems are tackling coronavirus worldwide The global community needs to swiftly ramp up the response to contain covid-19 Evaluation of nine commercial sars-cov-2 immunoassays Management of ill travellers at points of entryinternational airports, seaports and ground crossings-in the Viral kinetics and exhaled droplet size affect indoor transmission dynamics of influenza infection Review of aerosol transmission of influenza a virus A probabilistic transmission dynamic model to assess indoor airborne infection risks A comprehensive breath plume model for disease transmission via expiratory aerosols Humidity-dependent decay of viruses, but not bacteria, in aerosols and droplets follows disinfection kinetics Transmission routes of respiratory viruses among humans Mechanisms by which ambient humidity may affect viruses in aerosols Seasonality of respiratory viral infections Drivers of airborne human-tohuman pathogen transmission Early local immune defences in the respiratory tract Transmission of influenza virus in temperate zones is predominantly by aerosol, in the tropics by contact: a hypothesis Modeling and predicting seasonal influenza transmission in warm regions using climatological parameters The role of temperature and humidity on seasonal influenza in tropical areas: Guatemala, el salvador and panama The effect of environmental parameters on the survival of airborne infectious agents The effects of temperature and relative humidity on the viability of the sars coronavirus Virus survival as a seasonal factor in 15 influenza and poliomyelitis Relationship between humidity and influenza a viability in droplets and implications for influenza's seasonality Progressive 20 ordering with decreasing temperature of the phospholipids of influenza virus Avian influenza virus in water: infectivity is dependent on ph, salinity and temperature Stability of sars-cov-2 in different environmental conditions Survival of the enveloped virus phi6 in droplets as a function of rela Mechanistic insights into the effect of humidity on airborne influenza virus survival, transmission and incidence Heat and water exchange in the respiratory 5 tract Dispersion of coughed droplets in a fully-occupied highspeed rail cabin Tolerability of nasal delivery of humidified and warmed air at 10 different temperatures: a randomised double-blind pilot study Efficacy of steam inhalation with inhalant capsules in patients with common cold in a rural set up Antiviral effect of hyperthermic treatment in rhinovirus infection