key: cord-0715655-fj3a2y1o
authors: Li, H.; Xiao, H.; Zhu, R.; Sun, C.; Liu, C.
title: Warmer weather and global trends in the coronavirus COVID-19
date: 2020-05-05
journal: nan
DOI: 10.1101/2020.04.28.20084004
sha: 888c4a8022d2ce985b917103d649420f72bdb349
doc_id: 715655
cord_uid: fj3a2y1o

Predicting COVID-19 epidemic development in the upcoming warm season has attracted much attention in the hope of providing helps to fight the epidemic. It requires weather (environmental) factors to be included in prediction models, but there are few models to achieve it successfully. In this study, we proposed a new concept of environmental infection rate (RE), based on floating time of respiratory droplets in the air and inactivation rate of virus to solve the problem. More than half of the particles in the droplets can float in the atmosphere for 1-2 hours. The prediction results showed that high RE values (>3.5) are scattered around 30N in winter (Dec.-Feb.). As the weather warms, its distribution area expands and extends to higher latitudes of northern hemisphere, reaching its maximum in April, and then shrinking northward. These indicated that the spread of COVID-19 in most parts of the northern hemisphere is expected to decline after Apr., but the risks in high latitudes will remain high in May. In the south of southern hemisphere, the RE values tend to subside from Apr. to July. The high modeled RE values up to July, however, suggested that warmer weather will not stop COVID-19 from spreading. Public health intervention is needed to overcome the outbreak.

The COVID-19 pandemic, caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has sickened >2.2 million people and killed >0.15 million people in 202 countries worldwide as of 18 April 2020, and may greatly weaken the global economy 5 . Numerous studies on past outbreaks such as influenza [6] [7] [8] showed that spread of respiratory infectious diseases seems to be easier at low temperatures and low humidity. So more and more people and governments hope that warmer weather will slow down or stop the spread of COVID-19. But there is still no evidence to support it 9 .

Unlike diseases that rely on insect vectors for transmission, for example malaria 10 , predicting human-to-human respiratory diseases such as COVID-19 is somewhat difficult. A key parameter for model prediction is the basic reproduction rate (R 0 ), which is usually estimated with various types of complex mathematical models. The R 0 value is affected by biological (cell structure 11 and concentrations of virus, immunity of susceptible population, etc), socio-behavioral 12, 13 and environmental factors 14 . Because environmental factors are different in regions and time, it may be unsuitable for the applicability of R 0 outside the region where it was calculated 15 . Actually, many studies have found close correlation of epidemic development with environmental factors such as wind, temperature (T) and relative humidity (RH) [6] [7] [8] , which affects viable virus concentrations and exposure time of virus to susceptible population. Here, a new reproduction rate that depends on environmental factors (T and RH), environmental reproduction rate (R E ), was introduced. Using R E , it is possible for us to predict the epidemic development with time (season) and places (countries) of a specific respiratory disease.

In the R E estimation, we assumed that there was no individual difference (age and gender) in the COVID-19 transmission 16 because biological structure of SARS-CoV-2 is suitable for infecting all people 11 and SARS-CoV-2 is a new virus, almost all people have no immunity to the disease 1 . The R E value of COVID-19 can be estimated with effective floating time of respiratory droplets in the air (t C0 ) (Fig. 1) , the infection period (d i ) and a correlation coefficient (β) in the absence of control measures. The t C0 is a factor that only correlated with meteorological parameters (T and RH) and

half lifetime (t 1/2 ) of active viruses in aerosols. hours before onset (n i-2 and n i-3 ) are contagious to family members (blue arrows) and susceptible people (n i ) in public places (red arrows). The incubation period and infection period (d i ) were set at 4 days 23 and 3 days, respectively. b. Conditions for spreading viruses in public places. See

Method Section for more details.

The concentration of viable viruses in droplets at the time t depends on the inactivation rate (α), which can be described by 17

where k is the rate coefficient of inactivation. When α is 0.5, t is the half lifetime of the virus (t 1/2 , min). The half lifetime of SARS-CoV-2 is 1.1 hours 18 , and then k can be calculated to be 0.0105. So t e -0.0105 = α The volume of the droplet air mass changes with air temperature, which will affect the concentrations of viruses in the air. Using the Ideal Gas Law, the concentration of virus in droplets . CC-BY-NC-ND 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 5, 2020. 

where g is the proportion of susceptible population; n i is the number of new COVID-19 cases confirmed at day i; N is the sum of free COVID-19 transmitters confirmed at days i-4, i-3 and i-2 ( Fig. 1a, 1b) ; β (h -1 ) is the correlation coefficient between g×t C0 and R d . In the absence of control measures (g = 1), environmental reproduction rate (R E ) can be calculated by

When RH is less than 50%, the equilibrium particle size (d eq ) of droplets will not change with RH ( Fig. 2) . Therefore, in the mathematical model established, we regarded RH less than 50% as 50%. . CC-BY-NC-ND 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 5, 2020. 

The RH controls the floating time of respiratory droplets in the air. A longer floating time of virus-bearing droplets in the air will increase the risk of exposure to the virus. Droplets do not evaporate completely in the air because they contain substances such as salts and proteins 19 . The number of droplet particles at 2-12 microns (μm) ejected during speaking, coughing, sneezing accounts for more than 90%, and the initial particle size (d 0 ) of the peak number is 7-10μm 20 (Fig.   2a ). Droplet particles of large size (>100μm) settled rapidly due to gravity. The droplet particles of small size reached an equilibrium particle size (d eq ) rapidly (in a few seconds 14, 19 ) and floated in the air for some time (t) depending on RH (Fig. 2b) . When RH is <95%, the main natural weather conditions, the settling of >90% droplet particles may take more than 5 hours (Fig. 3) . For 10-50μm (d 0 ) droplets, the exposure risk under low RH (60%) is more than 20 times larger than that at RH 100% (Fig. 4 ). The 7-10μm (d 0 ) droplets, floated in the air for up to 1-2 hours under RH 60%, are the most important vector of virus transmission (Fig. 5a ). Here we used the floating time of 10μm droplets in the R E estimation. When RH is in the range of 50-100%, the floating time (t, min) of droplets with initial particle size (d 0 ) of 10μm in the air is a function of RH (Fig. 5a 19 . The t 1/2 of SARS-CoV-2 in aerosols is 1.1 hours 20 , similar to the floating time of 7-10μm particles in the air under RH 60% (Fig. 2a) , indicating that ~ half of viruses died during settling from the air in dry weather.

The number of new cases and meteorological parameters during the outbreak in Wuhan (WH), China, have been analyzed, allowing us to fit the t C0 to daily infection rate in public places (R d ). In the presence of control measures, β ×g×t C0 = R d , where g is the proportion of susceptible population.

The implementation of control measures for public health intervention in WH includes locking down the city (January 23), home quarantine (January 23) and gating communities (February 14).

Before January 23, COVID-19 patients were found mainly elderly (>60 years old) and middle-aged (30-60 years old), each accounting for ~50% 21 (Fig. 5b) , and mainly associated with . CC-BY-NC-ND 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 5, 2020. . https://doi.org/10.1101/2020.04.28.20084004 doi: medRxiv preprint food shopping 22 . So we believed that half of susceptible population (young and half the middle-aged) in the city was not involved (g = 0.5). The age structure of cases changed after January 23. For example, according to the epidemiological survey data in Guangdong and Sichuan provinces (China) 16 , among all the 1,836 cases, 1,308 cases were associated with 344 times of aggregation (1 person infected 3 people), and about 3/4 of the cases confirmed were mainly in the family. The age structure of the cases is very consistent with the age structure and family member structure of China and the two provinces (Fig. 5c) . Therefore, 3/4 of the susceptible population were isolated at home during this period, i.e. g = 0.25. After gating communities on February 14, the number of people who appeared in public places decreased sharply to 1/8 (one person from one family went out on the second day), and thus g was 0.125 (Fig. 5d) . Additionally, in the R E estimation we increased the g value on some days due to special events, e.g. buying food on weekends (custom) before locking down the city, outdoor activities on sunny day of January 28 after a long period of rain and a claim on returning to work on February 14 (canceled on February 13) (Fig. 5d) .

The t C0 (hour) obtained by running the model (See Method Section) is in good agreement (r = 0.92, p < 0.001) with R d (Fig. 5e, 5f ), meaning that t C0 corresponds to R d of 2.37 every 1 hour.

According to this, modeled daily infection rate (R E-d ) during the entire epidemic in WH averaged 0.93(95% CI: 0.50-1.30). Since the R d value was calculated with an assumption that d i is 3 days, the R E value then was 2.8, which is equivalent to the reported R 0 value 3,4 . The 3 days of infection period (d i ) of COVID-19 are considered based on the reports that COVID-19 patients are infectious two days before 16 and one day after onset of illness (Fig. 1a) . The d i value is lower than that reported in ref. 3 (5.2 days). But increasing d i means a decrease in the R d calculated (Fig. 1b; See Method Section), so the R E value does not change much with d i . After home quarantine on January 23, the R E-d averaged 0.25(95% CI: 0.11-0.59) and thus the modeled public infection rate (R E-p , =R E-d ×d i ) was 0.75, corresponding to a declined COVID-19 spread by 73%. After gating communities on February 14, the mean R E-p value dropped to only 0.33, and the disease diminished considerably by 88% (Fig. 5e) , indicating that these control measures are very effective to prevent the spread of the epidemic. In the estimation, we did not consider family cases because they were basically isolated at home, and the infection stopped later. The outbreak of COVID-19 was mainly in China, South Korea, Iran and Italy around 30°N before March 2020, and spread to almost all parts of the world after March 10 (Fig. 6a) . In Europe, for example, the epicenter was Italy before March. After the 10th day of March, it raged in Western Europe and began to spread in Northern Europe. Global distribution of R E value modeled with 10-day averages of T and RH showed a similar trend. In the modeled R E -distribution maps (Fig. 6b) , regions with the R E values higher than 3.5 are scattered in Europe in early March, while linked together after March 10. This assured us that meteorological conditions in March played an important role in promoting the rapid spread of COVID-19.

. CC-BY-NC-ND 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 5, 2020. The modeled R E value of COVID-19 worldwide ranged between 2.15 and 4.25 (Fig. 7) . The low R E value appears at ocean, and the value on land in temperate zone is generally higher than 2.8 even in July, indicating that warmer weather may not halt the spread of COVID-19 at the stage when humans have no immunity to SARS-CoV-2. In northern hemisphere, distribution areas with high modeled R E values (>3.5) are the largest in April and then shrinks to the north. It suggested that in the region of 30°-60°N where the outbreak was very severe in April, warmer weather was conducive to slowing the spread of COVID-19 while the risk in Northern Europe, Russia and Canada is still high in May. In southern hemisphere, regions with high global R E values (>3.3) also expand northward as air temperature rises. The fall of R E value is the most obvious in East and . CC-BY-NC-ND 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 5, 2020. In the above R E estimation, except for biological factors (t 1/2 and d i ), we only used meteorological factors. Although there are large meteorological differences between regions and dates, even within one day (causing R E differences in a day; Figure 8 ), today's meteorological satellites allow easy access to high-resolution weather data. For spread of a specific disease, therefore, R E is a useful index for global epidemic prediction.

. CC-BY-NC-ND 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 5, 2020. . https://doi.org/10.1101/2020.04.28.20084004 doi: medRxiv preprint The estimation of R E value is under atmospheric static and steady conditions without considering the influence of wind and airflow turbulence. Wind (>3m/s) is effective at blowing away aerosols, so it is unlikely to be infected in windy open areas (Fig. 9 ). Indoor airflow (i.e. caused by air conditioning and walking) can reduce the floating time of droplets and disperse viruses in the air, but also significantly increase exposure chance to viruses. Unless the MID of COVID-19 is small enough, airflow disturbance may not significantly increase the infection rate. So the modeled R E values may be a upper limit. We noticed that the similar half lifetime of SARS-CoV-1 (caused Severe Acute Respiratory Syndrome, SARS) to SARS-CoV-2 in aerosols 20 , so the spread of the two epidemics should be consistent. But SARS disappeared in the summer of 2003, which was probably due to the . CC-BY-NC-ND 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 5, 2020. . https://doi.org/10.1101/2020.04.28.20084004 doi: medRxiv preprint

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