key: cord-0930619-vrate482
authors: Morris, Dylan H.; Yinda, Kwe Claude; Gamble, Amandine; Rossine, Fernando W.; Huang, Qishen; Bushmaker, Trenton; Fischer, Robert J.; Matson, M. Jeremiah; van Doremalen, Neeltje; Vikesland, Peter J.; Marr, Linsey C.; Munster, Vincent J.; Lloyd-Smith, James O.
title: The effect of temperature and humidity on the stability of SARS-CoV-2 and other enveloped viruses
date: 2020-11-13
journal: bioRxiv
DOI: 10.1101/2020.10.16.341883
sha: eb99a2da76d4115c16c591ed215fddb315ec6456
doc_id: 930619
cord_uid: vrate482

Understanding the impact of environmental conditions on virus viability and transmission potential is crucial to anticipating epidemic dynamics and designing mitigation strategies. Ambient temperature and humidity are known to have strong effects on the environmental stability of viruses, but a general quantitative understanding of how temperature and humidity affect virus stability has remained elusive. We characterize the stability of SARS-CoV-2 on an inert surface at a variety of temperature and humidity conditions, and introduce a mechanistic model that enables accurate prediction of virus stability in unobserved conditions. We find that SARS-CoV-2 survives better at low temperatures and extreme relative humidities; median estimated virus half-life was more than 24 hours at 10 °C and 40 % RH, but approximately an hour and a half at 27 °C and 65 % RH. Moreover, our model predicts observations from other human coronaviruses and other studies of SARS-CoV-2, suggesting the existence of shared mechanisms that determine environmental stability across a number of enveloped viruses. Our results highlight scenarios of particular transmission risk and point to broad strategies for pandemic mitigation, while opening new frontiers for the mechanistic study of viral transmission.

decay was relatively rapid at 65 % RH and tended to be slower either at lower (40 %) or higher 88 (85 %) humidities or when excess water was present during the evaporation phase (Fig. 1b) . Measurements at 40 %, 65 %, and 85 % RH reflect decay kinetics once the deposited solution has reached quasi-equilibrium with the ambient air. Estimated half-lives for the evaporation phase that occurs prior to quasi-equilibrium are plotted to the right, since conditions during this phase are mainly dilute, and thus analogous to high RH quasi-equilibrium conditions. (b) Schematic of hypothesized e ects of temperature and relative humidity on duration of virus viability. Virus half-lives are longer at lower temperatures, regardless of humidity, because inactivation reaction kinetics proceed more slowly. Relative humidity a ects virus half-life by determining quasi-equilibrium solute concentration in the droplet containing the virus. Above the e orescence relative humidity (ERH), solutes are concentrated by evaporation. The lower the ambient humidity, the more water evaporates, the more concentration occurs, and the faster inactivation reactions proceed. Below the ERH, solutes e oresce, forming crystals. Half-lives are thus not particularly sensitive to changes in sub-ERH relative humidity, and half-lives even slightly below the ERH may be substantially longer than half-lives slightly above it.

Many viruses, including SARS-CoV-2, exhibit exponential decay on surfaces and in aerosols 91 (8, 13, 18). We drew upon known principles of droplet chemistry and its potential e ects on 92 virus inactivation chemistry (Fig. 1c) to create a minimal mechanistic model incorporating the 93 e ects of both temperature and relative humidity on exponential decay rates. 94 We model temperature dependence with the Arrhenius equation, which describes a reaction rate

: as a function of an activation energy ⇢ 0 , an asymptotic high-temperature reaction rate , the 96 universal gas constant ', and the absolute temperature ): (Fig. 1c) . Below the ERH, the reaction no longer occurs in solution, and so inactivation may be 118 slower. The notable U-shape of virus inactivation as a function of relative humidity, observed in 119 our data (Fig. 1a) and elsewhere in the literature (24-27), including for coronaviruses (28, 29), 120 could be explained by this regime shift around the ERH (Fig. 1c) .

To quantify these e ects, we model virus inactivation at quasi-equilibrium on inert surfaces as reactants are less concentrated and decay is expected to be slower, as observed from our data 127 ( Fig. 1a,b ). If small initial droplet sizes are used-as in real-world depositions (predominantly < 128 10 µL (30-32)) and in some experiments-evaporative quasi-equilibration should be near instant, 129 and so inactivation should follow the kinetics at quasi-equilibrium. Larger droplets, such as 130 those used in our experiments, will take more time to equilibrate (depending on temperature and 131 humidity), allowing us to distinguish the quasi-equilibrium phase from the evaporation phase.

We partition inactivation at quasi-equilibrium into two humidity regimes, e oresced and solu-133 tion, according to whether the ambient RH is below the ERH (e oresced) or above (solution).

In either case, we approximate virus inactivation as a first-order reaction with rate : e or : sol , 

We estimated ⇢ 0 , e , and sol from our data, constraining all to be positive. We treated 

We used the mechanistic model to predict SARS-CoV-2 half-life for unobserved temperature and 173 humidity conditions from 0 to 40 C, and from 0 to 100 % RH. We chose these ranges to reflect 174 environments encountered by human beings in daily life. We did not extrapolate to temperatures 175 below 0 C since inactivation kinetics may be di erent when fluid containing the virus freezes.

The exact freezing points of suspension medium and human fluids at sea level will depend on 177 solute concentration, but will typically be below the 0 C freezing point of pure water.

Median predicted SARS-CoV-2 half-life varies by more than three orders of magnitude, from 179 less than half an hour at 40 C just above the modeled approximate ERH, to more than a 180 month at 0 C and 100 % RH ( Fig. 3a and c) . We find good qualitative agreement between 181 model predictions and model-free estimates from our data, including long half-lives prior to 182 quasi-equilibrium. The U-shaped e ect of humidity on virus half-life is readily explained by 183 the regime-shift at the ERH (Fig. 3a) . In particular, half-lives become extremely long at cold 184 temperatures and in very dilute solutions, which are expected at high RH (Fig. 3a,b) . Of note, 185 the worst agreement between predictions and model-free estimates is found at 10 C and 85 % 186 RH (Fig. 3b) . This is partially explained by the fact that the quasi-equilibrium concentration 187 reached under those conditions was higher than our model prediction of concentration from RH 188 (SM Fig. S9) . Accordingly, the half-life prediction for 10 C and 85 % RH based on measured 189 concentration (Fig. 3b) is superior to the prediction based on modeled concentration (Fig. 3a) .

As a stronger test of our model's validity, we used our estimated ⇢ 0 and values to make out- Tables S5-S2 ).

Where both temperature and RH were available, we compared these model-free estimates to were measured to be substantially shorter than our prediction, correspond to samples exposed 267 Several analyses have projected that SARS-CoV-2 transmission will be faster in temperate win- reactions-and therefore unfavorable to viruses. 305 We used SARS-CoV-2 strain HCoV-19 nCoV-WA1-2020 (MN985325.1) (58) for this study. to around 0.010 mg. We measured initial droplet mass (< (0)) and final droplet mass (< (1)) 334 under closed-chamber conditions to increase accuracy.

Statistical analyses and mathematical modeling 336 We quantified the stability of SARS- We estimated parameters of our mechanistic models by predicting titers based on those models 343 and then applying the same Poisson single-hit observation process to estimate parameters from 344 the data. See the SM (section 5.5) for a complete description, including model priors. 345 We estimated evaporation rates and corresponding drying times by modeling mass loss for each temperature-RH conditions. We generated estimates of half-life and uncertainties (SM Table S2 ) 355 and compared those estimates to the half-lives predicted by the mechanistic model parametrized 356 from our SARS-CoV-2 data. As data on evaporation kinetics were not available, we estimated 357 a unique half-life for each experimental condition, covering both the evaporation and quasi-358 equilibrium phases. As virus decay during the evaporation phase is expected to be minimal, and 359 the evaporation phase to be short, the estimated half-life can be used as a proxy for the quasiequilibrium half-life. The complete data selection, extraction and analysis process is detailed in 361 the SM (section 6). 362 We also included data from SARS-CoV-1 and MERS-CoV collected by our group during 363 previous studies (18). Those data were collected at 22 C and 40 % RH on polypropylene using (Table S5) . 

Applied and environ-411 mental microbiology

Proceedings of the National Academy of Sciences

Emerging Infectious Diseases In press

The Stan Core Library, Version 2

ggplot2: Elegant Graphics for Data Analysis

ggdist: Visualizations of Distributions and Uncertainty

tidybayes: Tidy Data and Geoms for Bayesian Models