key: cord-0731960-jcxcu821
authors: Svenson, O.
title: People underestimate the change of airborne Corona virus exposure when changing distance to an infected person: On interpersonal distance, exposure time, face masks and perceived virus exposure.
date: 2022-03-15
journal: nan
DOI: 10.1101/2022.03.14.22272341
sha: df9cda74b3fb8abce402679ccb1afd50799d8cc6
doc_id: 731960
cord_uid: jcxcu821

Participants judged airborne Corona virus exposure following a change of inter-personal distance and time of a conversation with an infected person with and without a face mask. About 75% of the participants underestimated how much virus exposure changes when the distance to an infected person changed. The smallest average face to face distance from an infected person without a mask that a participant judged as sufficiently safe was about 12 feet (3.67 m). Correlations showed that the more a person underestimated the effects of change of distance on exposure the shorter was that persons own safety distance. On average the effects of different lengths of a conversation on exposure were correct, but those who judged the effects of time as smaller tended to select longer safety distances. Worry of own COVID-19 infection correlated with protective behaviors: keeping longer safety distances, avoiding public gatherings, postponement of meetings with friends. The results showed that the protective effects of both distancing and wearing a face mask were under-estimated by a majority of the participants. Implications of these results were discussed last.

168 169 D > 0, t > 0 (1) 170 171 We will call the function in Equation (1) the Virus Exposure Model, VEM. The exponent describes 172 change of exposure as as a function of change of distance . Applying n = 2.0 to a person who 173 approaches another infected person from 6 feet to 2 feet, it predicts an increase of exposure to 174 (6/2) 2 = 9 times. However, a person who applies a linear model, n = 1.0 will judge the exposure to 175 be 6/2 = 3 times the initial exposure after the approach. The study by Svenson is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted March 15, 2022. ; https://doi.org/10.1101/2022.03.14.22272341 doi: medRxiv preprint 224 distance to an infected person will co-vary with judgments of exposure following change of 225 distance and time. We predicted that a person who accepts only a longer distance from another 226 infected person to be safe will also judge a change in interpersonal distance to have a smaller effect 227 than a person who accepts a shorter safety distance. This is why the former needs to move further 228 away. We had no well grounded hypotheses about the effects on judged exposure of time of a 229 conversation and face mask investigated in study 2. However, the fact that a linear function is easy 230 to apply and elicit (Svenson, 2016) indicates that judgments of the effect of exposure time will not 231 be systematically biased. Research has shown that worry is one of the important drivers of is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The instruction continued with an example that introduced the problems about inter-personal 258 distance. The instruction to the condition with exposure from a longer distance compared with a 259 shorter distances included the following. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted March 15, 2022. ; https://doi.org/10.1101/2022.03.14.22272341 doi: medRxiv preprint 269 Problems varying the time of a conversation were introduced as follows in the from long to short 270 time condition. Ten of the participants had been infected with the Corona virus. We will include also these 296 participants in the group data analyses because the sample was too small for separate analyses. A 297 number of participants who were asked to judge percentages greater than 100 in a decreasing 298 distance condition (increasing exposure) gave judgments that were smaller than 100. In spite of a 299 detailed instruction, they may have misunderstood the task so that they judged the increment in 300 exposure instead of the total exposure after a change. When a judgment was smaller than 100 in an 301 increasing distance condition (decreasing exposure) the judgment was coded as missing. There 302 were only a few judgments above 100 in the increasing distance (decreasing exposure) conditions 303 and they were also coded as missing. The judgment distributions were all skewed with high . CC-BY 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted March 15, 2022. ; https://doi.org/10.1101/2022.03.14.22272341 doi: medRxiv preprint 304 skewness (less than -1.0 or greater than + 1.0) or moderate skewness (between +/-1.0 and +/-305 0.5). Therefore, we focused on medians in the data analyses and excluded means for some 306 conditions in Table 1 , because there were too many outliers distorting the means. Table 1 gives medians and quartiles for each of the distance problems. In comparison with the 311 VEM model with n = 2.0, the average participant overestimated exposure for increasing distance 312 and underestimated exposure for decreasing distance. This means that they were not sufficiently 313 sensitive to the effects on exposure of changing distance to an infected face to face speaker. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint We computed the percentages of participants who realized the degree to which exposure changes 351 with changes in distance following the VEM 2.0 function or faster. For the increasing distance 352 problems meaning a decrease in radiation, these percentages were for change from 4 to 5 feet, 353 40%, 2 to 6 feet, 22%, 4 to 6 feet, 27%, 2 to 5 feet 8%, 5 to 6 feet 33% and 2 to 4 feet 10% with 354 mean 23%. Hence, 77% of the judgments indicated that the participants did not realize how fast 355 virus exposure decreases with increasing distance to an infected person. 356 357 For the decreasing distance (increasing exposure) problems the participants who realized how fast 358 exposure increases compared to VEM 2.0 following an approach were from 5 to 4 feet, 28%, 6 to 2 359 feet, 16%, 6 to 4 feet, 21%, 5 to 2 feet, 11%, 6 to 5 feet, 31% and 4 to 2 feet, 19%.with mean 21%. 360 Hence, 79% of the judgments indicated insensitivity to the fast increase of exposure following an 361 approach towards an infected person. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted March 15, 2022. ; https://doi.org/10.1101/2022.03.14.22272341 doi: medRxiv preprint 390 We computed Cronbach's alfa for each of the four conditions. The six problems in the increasing 391 distance condition were reliable with alpha = 0.78 and in the decreasing time condition alpha 392 =0.82. The problems who invited percentage judgments above 100 were less consistent with 393 decreasing distance alpha = 0.06 and for increasing time alpha = 0.65. We computed the mean 394 judgments across items in each of the conditions omitting the decreasing distance items and called 395 the variable means D incr (increasing distance), T decr (decreasing time) and T incr (increasing time). 396 We then investigated co-variances between these variables and other items in the questionnaire. 397 There were no significant correlations between the three variables across participants, but a 398 marginally significant correlation between D incr and T incr (R =-0.20, p=0.06). The mean response to the question "shortest distance from an infected person that would make you 404 feel sufficiently safe" was 11.51 feet (SD=17.19), 3.51 meters. The Pearson correlations between 405 the shortest safe distance and D incr and T decr were R = -0.22 (p < 0.05) and R = 0.33 (p< 0.001) 406 respectively. Safe distance, and T incr were unrelated. Generally speaking, this means that if a 407 person wants a longer safety distance in a face to face conversation, she or he judges the effect of 408 withdrawal on decrease of exposure as greater (relatively smaller percent judgments after change) 409 than a person who needs only a shorter safety distance. Correspondingly, when a person wants a 410 longer safety distance she or he judges the effect of shortening a conversation on exposure to be 411 smaller (relatively greater percent judgments after change) than a person who states a shorter 412 safety distance. 413 414 We asked: "assume a new Coronavirus epidemic occurred and no vaccine was available. 415 Compared to the average person like yourself, how likely do think that it is that you would become 416 sick? (Much less risk = 1, same risk as average person = 50, much greater risk =100)". The median 417 response was 50 meaning that overall there was no optimism bias (Svenson, 1981) . We wanted to 418 know if those judging themselves less likely to catch the disease were more optimistic than those 419 who judged themselves as more likely to catch the disease were pessimistic. The mean response 420 gives a hint about this question and it was 42.79 (SD = 24.66), which is significantly lower than is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted March 15, 2022. ; https://doi.org/10.1101/2022.03.14.22272341 doi: medRxiv preprint 424 factors with judgments around 50 (the midpoint of the VAS scale 1 -100) with mean = 46.67 (SD 425 = 28.33) and mean = 53.27 (SD=31.27) for the poor luck and poor behavior questions respectively. 426 However, the difference is not statistically significant and these judgments had no correlations 427 with optimism or pessimism. 428 As predicted, the question "How worried have you been over your own personal risk of becoming 429 sick with COVID-19 during the pandemic?" correlated with "shortest acceptable distance", R = 0. 433 However, there were no significant correlations with this worry variable and D incr or T decr . In 434 summary, worry over catching COVID-19 was not directly related to judgments of the factual 435 effects of changing distance and time of a conversation but to judgments of an acceptable distance 436 to an infected person. We also asked about "general worry over things that may go wrong in life" 437 but this unspecific worry did not correlate with protective behaviors. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted March 15, 2022. ; https://doi.org/10.1101/2022.03.14.22272341 doi: medRxiv preprint 456 457 Procedure and Material 458 As in study 1, a Qulatrics questionnaire was distributed to the participants and a participant used 459 on average 11 min to complete the task. We analyzed three questions about virus exposure 460 comparing the protective effects of distance and face mask and two questions asking about the 461 shortest distance from an infected person that the participant would accept as sufficiently safe. The 462 three distance questions were presented in a random order that was unique for each participant and 463 the other questions in appendix 1 were presented after them in a predetermined order. The 464 introductory general instruction was as follows. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The face masks and distance problems were followed by a set of questions concerning the 499 participants that were the same as in study 1 except the problems measuring cognitive ability. They 500 were omitted because they did not co-vary with any of the other variables in study 1. In addition to 501 the questions in study 1, we asked about the shortest inter-personal distance from an infected 502 person that a participant could accept as sufficiently safe for a face to face 5 min conversation, 503 with and without a mask on the infected person. Typically, a high quality FFP2 mask stops 95% of the virus exposure if the mask is correctly fitted 508 to the face (Howard et al., 2021) We decided to specify 90% efficiency in our problems to allow 509 some mask misfit when we calculated predictions of correct solutions of the problems. A total of 510 29 participants had been diagnosed with Covid-19 but because they were such a small group they 511 were not treated separately in the following analyses. 512 513 We will use meters as a measure of distance in Table 3 and in the following calculations. First, we 514 denote the distance without a face mask D i meters for the distance pair i. The distance with a 515 mask that equals the protective effect of distance D i is D imask . Then the mask reduction of 516 exposure from 100% at D i to 10% at D imask; To repeat, without a mask the radiation is 100% at 517 D imask and the mask reduces exposure to 10%. We have to move away to Di without a mask to 518 match that exposure. Then, according to Equation (1), with exposure decreasing with the square of 519 the distance and (D imask /D i ) 2 = (10/100); D imask 2 = 0.10 D i 2 ; D imask = 0.316 D i . Table 3 shows the 520 predicted values for the first two problems. The linear estimates in the two first rows follow from 521 (D imask /D i ) = (10/100). The prediction of exposure when changing from 2 to 6 feet follows from 522 n=2 in equation (1), (2/6) 2 and for the linear prediction with the exponent 1.0. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint For illustrative purposes, we tested the differences of the means from the predicted VEM 2.0 530 values for the three first rows in Table 3 in two tailed t tests. The test for the 6 feet distance . CC-BY 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted March 15, 2022. ; https://doi.org/10.1101/2022.03.14.22272341 doi: medRxiv preprint 563 51%, of the exposure and the subjective efficiency is 49%, which again indicates underestimation 564 of the actual efficiency. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted March 15, 2022. ; https://doi.org/10.1101/2022.03.14.22272341 doi: medRxiv preprint 565 566 The closest safe distances in Table 3 offers another way of estimating the subjective efficiency of a 567 mask. Comparison of mean shortest distance without mask, 3.54 m and shortest distance with 568 mask, 2.16 m indicates that the mask reduces the distance with 1.38 m which corresponds to the 569 reduction of exposure. A subjective linear VEM decrease of exposure gives a remaining exposure 570 2.16/ 3.54 = 61% and the estimated efficiency of the mask is 39%. 571 572 The responses to the first two problems comparing situations with and without a mask correlated 573 significantly R = 0.56, p < 0.001 and we decided to use the mean of the judgments in a search for 574 covariance between the mask problems and other judgments. 575 However, there was only one marginally significant correlation between the means of the two 576 mask problems and another variable, withdrawal from 2 feet to 6 feet, R = 0.16, p= 0.065. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted March 15, 2022. ; https://doi.org/10.1101/2022.03.14.22272341 doi: medRxiv preprint 630 intuitively and subjectively may downplay the importance of keeping a sufficient distance and 631 wearing a face mask. Then, their protective behavior depends on efficient facts and risk . CC-BY 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted March 15, 2022. ; https://doi.org/10.1101/2022.03.14.22272341 doi: medRxiv preprint Never = 0, Always = 100 __________ 796 . CC-BY 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted March 15, 2022. ; https://doi.org/10.1101/2022.03.14.22272341 doi: medRxiv preprint

2021) asked their participants to indicate the inter-personal distance that they 208 preferred without the Corona virus and during the pandemic and the distances were 1.18 m and 209 1.83 m. However, the latter distance decreased over time during the pandemic to 1.41 m in some 210 kind of adaptive process. Hall (1966) suggested different interpersonal distances: close distances 211 for partner/ family (up to 0.45 meters), distance to friends (0.45-1.20 meters) and distance to 212 strangers (1.20 -3.65 meters). With reference to these distances and recommended inter-personal 213 distance during the pandemic

Based on earlier results, we predicted that the effects on 219 virus exposure from changing inter-personal distance will be underestimated for both approaching 220 and moving away conditions. Based on the fact that a linear functions is the most easily available 221 tested in a hierarchy of subjective functions we predicted that a majority of the time judgments will 222 be described by a linear function, the first function to be elicited in an unknown situation 223 (Svenson, 2016). Furthermore, we predicted that a person's shortest acceptable face to face 531 problem

We also investigated the distribution of judgments to find out about the proportions of participants of participants who judged the distance to be smaller than 0.58 m In all, 35 participants 540 (23%) gave distances that were equal or smaller than the predicted exposure. Hence, 77% 541 underestimated the protective effect of a mask and selected a greater distance than required. For 542 the 11 feet (3.35 m) problem with a cut point 1.06 m 45 (30%) of the participants gave distances 543 that were equal to or smaller than the VEM 2.0 prediction, again indicating an underestimation of 544 the protective effect of a mask

We know from study 1 and the earlier 553 study of Corona virus exposure (Svenson et al., 2020) that a linear VEM function predicts how 554 judgments will describe the increase in exposure after coming closer to a person

This can be compared with the stated efficiency 90% . Hence, the participants 560 underestimated the effect of a face mask. The corresponding analysis of problem (2) gives for an 561 approach from 3

Following the computation above, this problem indicates that the mask allows (204 -100)/204 with distance (Bjorn & Nielsen

Therefore, when we reported that participants underestimated the change of exposure following a 601 change of distance

The normal inter individual distance in a face to face conversation, 1.91 m was increased to 3.54 m 606 to make an average person feel safe when the other person was infected with a virus

On average, those who were more 611 sensitive to the effect of distance change selected longer safety distances. A participant who 612 choose a relatively greater safety distance for her or himself judged the efficiency of official 613 behavioral advice as relatively higher. When a participant wanted a longer safety distance, she or 614 he judged the effect of shortening a conversation on exposure to be smaller than a person who 615 indicted a shorter safety distance

The effect that included a linear relationship between distance and exposure and within this model 625 (and objectively) the effect of wearing a face mask was underestimated. In general, people are not 626 used to make the judgments that we have asked for, but our results indicate relationships in 627 peoples' mental models about airborne virus exposure that are relevant for behavior. We believe 628 that this result is relevant for peoples' actual protective behaviors when there is an ongoing 629 epidemic disease or pandemic. For example, people including health workers (Atnafie et al., 2021) 632 communications without an intuitive psychological foundation. Policy makers and politicians 633 influenced by their intuitive understanding of the virus protective power of distancing and face 634 masks, may hesitate to regulate their citizens' behavior and not require distancing and face masks

Influence of pulmonary ventilation rate and 645 breathing cycle period on the risk of cross-infection

Assessment of exposure 647 risks to COVID-19 among frontline health care workers in Amhara Region, Ethiopia: A cross-648 sectional survey

Host-to-host 650 airborne transmission as a multiphase flow problem for science based social distance 651 guidelines

Dispersal of exhaled air and personal exposure in 654 displacement ventilated rooms

Turbulent gas clouds and respiratory pathogen emissions: potential 656 implications for reducing transmission of COVID-19

Exposure of health care workers and 658 occupants to coughed airborne pathogens in a double-bed hospital patient room with 659 overhead mixing ventilation

Relationships between initial COVID-19 risk 661 perceptions and protective health behaviors: a national survey

Not even the air of empty spaces is coronavirus free (Two meters is not a safe 665

Experiences and Social Distancing: Insights From the Theory of 668 Planned Behavior

The Hidden Dimension

An evidence review of face masks against COVID-19 Proceedings of the 673 National Academy of

A Bayesian approach to reveal the 675 key role of mask wearing in modulating projected interpersonal distance during the first 676 COVID-19 outbreak

Short-range airborne transmission of expiratory droplets 678 between two people

COVID-19: Reduction of airborne transmission needs paradigm shift in 680 ventilation

Even one metre seems generous. A reanalysis of data in: Chu et al. 682 (2020) Physical distancing, face masks, and eye protection to prevent person-to-person 683 transmission of SARS-CoV-2 and COVID-19

Airborne transmission of SARS-CoV-2: The world should 685 face the reality

Airborne cross-687 infection risk between two people standing in surroundings with a vertical temperature 688 gradient

Distribution of exhaled con-690 taminants and personal exposure in a room using three different air distribution 691 strategies

The risk of airborne cross 693 infection in a room with vertical low-velocity ventilation

Adherence to COVID-19 protective behaviors: A m

Are we all less risky and more skillful than our fellow drivers? Acta 699

Towards a framework for human judgements of quantitative information: the 701 numerical judgment process, NJP model

Without a mask: 704 Judgments of Corona virus exposure as a function of inter-personal distance. Judgment 705 and Decision Making

Worry, perceived threat and media 707 communication as predictors of self-protective behaviors during the COVID-19 outbreak in 708

Influence of human breathing modes on 710 airborne cross infection risk

Accurate representations of the microphysical processes occurring during the transport of 713 exhaled aerosols and droplets

Modelling the load of SARS-CoV-2 virus in human 715 expelled particles during coughing and speaking

Physical distancing 718 and the perception of interpersonal distance in the COVID-19 crisis

You have answered questions about inter-personal distance and virus exposure

If you were infected with a new Corona virus, to what extent do you think that this could be 735 caused by just you being unlucky or your own poor protective behavior? 736 My poor luck

Poor protective behavior _____________(not at all = 0, only poor behavior = 100

What is the shortest distance between you and a Corona virus infected person that would make 740 you feel sufficiently safe to start a conversation of 3 minutes?

If you always follow the advice of keeping distance to other people. To what degree do you 752 think that this behavior can protect you from being infected by a Corona virus assuming no 753 mask ?

Other or no answer___ you had the COVID -19 infection and were sick, for how many days were 766 you sick? ______ 767 I have had no Covid infection

Yes ________ I received the second dose ______(month)

No or only one dose______ (mark applicable alternative

Assuming a new Corona virus epidemic without a vaccine, how likely do think that it is that 780 you would be sick compared to the average person like yourself? 781 My risk would be (scale 1 -100) _________ 782 (Much less risk = 1, same risk as average person = 50

If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to 802 make 100 widgets? 803 Number of minutes:________ 804 805 44