key: cord-0782687-yqk5euja
authors: Livadiotis, G.
title: Impact of environmental temperature on Covid-19 spread: Model and analysis of measurements recorded during the second pandemic in Cyprus
date: 2021-02-23
journal: nan
DOI: 10.1101/2021.02.19.21252106
sha: 22a36ee9a44a301c76ce66ead862f85abe87c170
doc_id: 782687
cord_uid: yqk5euja

The paper investigates the effect of the environmental temperature on the spread of COVID-19. We study the daily numbers of the cases infected and deaths caused by Covid-19 during the second wave of the pandemic within 2020, and how they were affected by the daily average-high temperature for the districts of the Republic of Cyprus. Among the findings of the paper, we show that (i) the average ratio of the PCR to rapid positive tests is ~2.57 {+/-} 0.25, as expected from the tests' responses, indicating that PCR overestimates positivity by ~2.5 times; (ii) the average age of deaths caused by Covid-19 increases with rate about a year of age per week; (iii) the probability of a person infected by Covid-19 to develop severe symptoms leading to death is strongly depended on the person's age, while the probability of having a death on the age of ~67 or younger is less than 1/1000; (iv) the number of infected cases and deaths declined dramatically when the environmental temperature reaches and/or climbs above the critical temperature of TC=30.1 {+/-} 2.4 C0; (v) the observed negative correlation between the exponential growth rate of the infected cases and the environmental temperature can be described within the framework of chemical kinetics, with at least two competing reactions, the connection of the coronavirus towards the receptor and the dissolution of the coronavirus; the estimated activation energy difference corresponding to the competing chemical reactions, 0.212 {+/-} 0.25 eV, matches the known experimental value; and (vi) the infected cases will decline to zero, when the environmental temperature climbs above the critical temperature within the summery days of 2021, which is expected for the Republic of Cyprus by the 16th of May, 2021.

A recently published paper by PLOS ONE [1] showed the first reported statistically significant relationship of negative correlation between the average environmental (or weather) temperature and exponential growth rates of cases infected by Covid-19. This relationship led to the derivation of the critical temperature T C , for which the exponential growth rate becomes zero and thus the COVID-19 spread declines once the environmental temperature T climbs higher than this critical value. The critical temperature was estimated to be T C~8 6.1 ± 4.3 F 0 or T C~3 0.1 ± 2.4 C 0 . The mentioned paper published first as a MedRxiv preprint in late April, 2020. Since then, several other studies across the globe also forecast the decline of the number of infected cases when the environmental temperature will climb above this critical value within the summer of 2021 for the Republic of Cyprus. Finally, Section 8 summarizes the conclusions.

We use publicly available datasets of (1) the environmental average-high temperature (e.g., see: [11] );

(2) time series of the daily number of the infected cases and the deaths caused by Covid-19 (e.g., see:

[10]) for the districts of the Republic of Cyprus.

During the second wave of the Covid-19 pandemic, confirmed cases or positive tests were counted with statistical sampling; therefore the majority of the confirmed cases were asymptomatic, because only a small fraction of the infected population presents symptoms, at least significant ones to be taken into account. In order to understand better this, we examine the official daily data sets as announced by the government of Cyprus [10] . As an example, we read the announcement of the 24 th of October, 2020, translated in Table 1 .

According to Table 1 , there were 2583 tests taken place in hospitals, health clinics, or in laboratories from private initiatives, that is, 2583 people felt like they have some sort of worrying symptoms, from which 92 cases were confirmed to be infected by . Also, there were 7 infected (mostly asymptomatic) cases out of 1308 tests sampled from diverse groups. Therefore, at that certain single day, and for the whole country, there were confirmed 92 symptomatic infected cases, i.e., people who felt symptoms and thus they were concerned enough to visit hospitals, clinics, or laboratories for testing, which came back positive for Covid-19. On the other hand, there were 7 asymptomatic infected cases out of 1308 samples, corresponding to ~6500 asymptotic cases for the whole population of Cyprus Republic (~1.2 millions as of February 2021 [12] ). Overall, there were 92 symptomatic cases (with symptoms intense enough to have people concerned about them and have tested), from which 11 cases were

probably severe enough to be tested in a hospital/clinic), and an estimation of ~6500 asymptomatic cases; therefore, the symptomatic cases are ~1.4%. If we assume that from the 81 cases confirmed from tests performed after private initiative, there were x asymptotic cases and 81−x symptomatic ones, then the estimation for the whole population is ~1.2·10 6 (7+x)/(1308+2187) asymptotic and 11+81−x symptomatic, corresponding to a percentage of symptomatic cases that maximizes for x→1 (at least one asymptotic case), i.e., ~ 3.2%. For one incubation period, τ ≈ 5.2±1.1 d [13] , we have about the same number of asymptomatic cases, but the symptomatic cases should be counted for each day of the period τ , i.e., ~ (11+81−x)·τ; thus, the maximum percentage of the symptomatic cases is ~14.3%, while if x=4 asymptomatic cases exists within the 81 confirmed cases, the percentage drops to ~10.5%.

Note that the key-point is to understand that the hospital/clinics and private initiate's related cases are not considered random statistical sampling and they are representative for the whole population (i.e., without having to estimate the numbers for ~1.2·10 6 ). Then, we estimate that for the Cyprus population, and at this date, the symptomatic cases constitute about one tenth the confirmed cases, or less. It has to be clarified though that the determined asymptomatic cases include also cases with minor symptoms which have been disregarded. The absolute zero symptoms cases may be about the same order as the symptomatic cases [14] . 

The record of the infected cases during the second wave of the Covid-19 was based on a daily statistical sampling of the population. The positive tests constituted the confirmed infected cases within the statistical sampling. The ratio of the positive to the total number of tests is called positivity percentage, and for estimating the infected cases for the whole population one has to multiply the positivity with ~1.2·10 6 .

The performed sampling was biased because of the following reasons:

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The copyright holder for this preprint this version posted February 23, 2021. ; https://doi.org/10.1101/2021.02.19.21252106 doi: medRxiv preprint -The random sampling was taking into account the number cases confirmed by tracing; however these cases were included within the personal circle of friends/relatives of previously confirmed cases.

-The random sampling was also counting the tests performed in hospitals/clinics and those performed by private initiative, which are representative of the whole population, instead of the selected random sample.

-The number of tests was not constant, characterized by large variations, ranging from less than a hundred to a few ten thousands.

In Figure 1 we plot the positivity percentage for tests performed in the five districts of the Greek Cyprus (Nicosia, Limassol, Larnaca, Paphos, Famagusta), normalized by the Country's average positivity percentage. We observe less variability as the number of the Country's average ratio of infected cases increases. 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) 

Starting on the 16 th of November, both PCR and rapid antigen tests were performed in the Republic of Cyprus. Positive rapid tests had to be confirmed with a PCR test until Christmas, 2020. However, it was soon realized that the rapid tests had been almost always confirmed by PCR tests (~98% success); therefore, beyond 12/25/2000, PCR tests were not required for confirming the infection.

The rate of detecting infections of antigen tests is between 84% and 98% (if a person is tested in the week after showing symptoms). The probability of detecting Covid-19 infection differs for rapid antigen and PCR tests. For both the tests, the probability starts to be nonzero as soon as the exposure period ends.

For the rapid test, the probability peaks in one week and becomes negligible in about two weeks (~17 days) from the exposure period; for the PCR, the probability peaks in two weeks and starts to tend to zero in about five weeks from the exposure period. The PCR's response is characterized by a nonzero probability for more than five weeks, that is, ~ 5 / 2 = 2.5 times compared to the rapid test [16] . The mean is estimated to be 2.57 ± 0.25, that is, the expected value, as explained above. In Figure 2 

(for further details, see: [17] ). The mode of the distribution coincides with the mean value derived in Figure 2 (a); in addition, a Normal distribution is fitted with mean and error given by 2.60 ± 0.26.

. 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. We observe that the average ratio of the PCR positive tests to the rapid positive tests, as performed in Cyprus in 2020, is given by 2.57 ± 0.25; this coincides with the expected ratio of the PCR's response to the rapid test response.

Early research suggested that it takes 2 weeks for the body to get over a mild illness. On the other hand, data indicate that persons with mild to moderate COVID-19 remain infectious no longer than 10 days after symptom onset [18] . Therefore, a "positive" PCR result reflects only the detection of viral RNA and does not necessarily indicate presence of viable virus [19] . PCR's response is characterized by a nonzero probability for more than 5 weeks; hence, it provides an overestimation of the positive tests, and thus, of the infected cases, about ~5/2 = 2.5 times compared to the rapid test [16] .

It is generally expected that a response with only two weeks of nonzero probability is satisfactory and reliable for detecting the infection. The PCR's response is characterized by a nonzero probability for more than 5 weeks; hence, it provides an overestimation of the positive tests, and thus, of the infected cases (about 2.5 times compared to the rapid test) [18].

The basic model for describing the evolution of the infected cases is based on the combination of two factors [20] : (i) the per-capita growth of its population, represented by a function proportional 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.

The copyright holder for this preprint this version posted February 23, 2021. ; https://doi.org/10.1101/2021.02.19.21252106 doi: medRxiv preprint population, e.g., ( ) λ E x x = ⋅ , and (ii) the negative feedback that models the factors that flattens the curve, e.g., We are interested in studying the physical mechanisms behind the value of exponential growth rate λ .

For this, we hereafter ignore the value of b, setting it at zero and considering only the exponential growth modeling, i.e.,

that is,

or, for slowly changing rate,

The exponential rate is given by [1, 21] :

where τ is the incubation period [13] , and the reproduction number R 0 is defined as the average number of people that a single infected person will spread the disease [22] , that is, a measure of how contagious a disease is, and depends on the physical characteristics of coronavirus [23] ; Characteristic values for COVID-19 is R 0~2 -4 [13] .

The main factors that can affect the exponential rate λ are: (a) culture in social activities, and (b) environmental temperature and/or other thermodynamic parameters [1] [2] [3] [4] [5] [6] [7] [8] [9] . Intense cultural and social activities have frequently close contacts, leading reasonably to a positive correlation with R 0 . Measures against the virus spread prevent the exponential growth leading soon or later to a decay, but do not modify the exponential rate which is a characteristic of the population and its thermodynamics with environment and weather.

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The detailed statistical analysis of data sets (taken from Italy and USA), performed in [1] , showed that the rate can be modeled by (i) a parameter p 1 affected by the culture of the population, and (ii) a parameter p 2 primarily affected by the environmental temperature; namely, 1 2

rewritten as

where the critical temperature, for which the exponential rate becomes zero ceasing the exponential growth, is given by [1] :

Next we model the exponential growth of the infected cases per number of performed tests (positivity percentage), separately for the PCR and rapid tests. There is a slow variation of the average daily environmental temperature; this can be empirically modelled by

where time t is in days, with the day t=0 corresponding to the 8/25/2020. Then, we substitute Eq.(6) in the following to derive the affected cases to model the number of the infected cases, N t ,

which has to be divided by the total population ~1.2·10 6 . Figure 3 plots the ratios of the observed infected cases per number of PCR (red) tests or total (PCR and rapid) tests (blue), recorded from 8/25/2020 to 12/31/2020. The time series interval corresponding to the exponential growth is modelled by Eq. (7) (black).

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The vast majority of the recorded deaths caused by Covid-19 were with underlying health conditions. Interestingly, the moving average increases with time. Figure 4 plots the mean and its error of the age of deaths for moving windows of (a) 5 days and (b) 10 days. The detected trend is:

The last ~10 days of 2020 the average age appears to be approaching the mode of the whole age distribution (plotted in Figure 4 (c)), that is ~85±7.

. 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) is the Normal distribution with (μ=85,σ=7) for the best fit in Figure 4 (c) (black). When weighted by the age distribution of the population in Cyprus (red), the resulting weighted age distribution becomes to be expressed by the Normal distribution with (μ=89.3,σ=7.2) (blue).

. 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) Figure 5 . This is given by

The age cumulative probability distribution, multiplied by the number of total deaths N d , determines at what age we expect to have N d =1. In Figure 6 (b) plots N d · P C (Age) for N d = 10 γ with γ =2, 3, 4, and 5.

Therefore, the age for which the number of deaths becomes less than one is, respectively, 72.6, 67.1, 62.5, and 58.6 ( Figure 6(c) ). According to the same cumulative probability distribution, there is a probability 1:1000 of a person younger than ~67 y.o. to have died from Covid-19 in the examined time interval. The conclusion that can be interpreted from Figure 6 is the following: the probability of a person infected by Covid-19 to develop severe symptoms leading to death is strongly depended on the age of 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) 

Here we investigate the impact of the environmental temperature on the number of daily new cases infected and the number of deaths caused by Covid-19. In [1] it was shown that rate of the exponential growth of the cases infected by Covid-19 decreases when temperature increases, while it is reduced to zero when the temperature reaches, or escalates above, the critical temperature of T C~8 6.1 ± 4.3 F 0 or We observe that by mid-October and thereafter, the temperature dropped below its critical value T C .

A transition region appears between mid and end of October. The (normalized) number of infected cases, recorded with PCR tests after mid-October, increased and escalated up to one order-of-magnitude higher than the respective number of cases recorded before mid-October. (Note: the infected cases recorded with rapid test is excluded from the analysis with respect to the environmental temperature. The number of the daily infected cases recorded with rapid tests is about 2.5 times lower than that of PCR; as shown and discussed in Subsection 2.4, this is caused by an overestimation that likely characterizes PCR's response, that is, of about 2.5 times compared to the rapid test response.)

In addition, we observe that the number of deaths increased rapidly after mid-October. The rate of log(N d ), where N d is the number of the daily new number of deaths, is significantly smaller for t < 10/19/2020, when T > T C , than for t > 10/19/2020, when T < T C . In order to show this, we perform a statistical analysis to fit the two-parameter linear statistical model 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.

The copyright holder for this preprint this version posted February 23, 2021. as we can see, the rate of the logarithm of the number of deaths increased by ~6.7 times after the mid-October, that is, when the temperature dropped below the ~ 30 C 0 .

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The copyright holder for this preprint this version posted February 23, 2021. there are two subsequent phases plotted, the pre-exponential (pre-exp) and exponential (exp) growth phases, which had occurred before the number of the cases started to decline; (b) Daily average-high environmental temperature (also averaged over the districts of Nicosia and Limassol), and (c) the number . 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 February 23, 2021. Next we examine the number of the infected cases directly against the environmental temperature. In particular, in Figure 8 , the confirmed infected cases N + (positive tests), normalized to the number of the PCR tests N T , i.e., the percentage of positivity, is plotted as a function of the environmental temperature T. We observe that the normalized infected cases drops down by 3-5 times as the temperature values increase from ~15 C 0 towards the critical temperature T C ; however, when the temperature reaches and exceeds its critical value, the infected cases decreased with much steeper rate (i.e., ~30 times larger rateabsolute value). In the linear scale in Figure 8(a) , the infected cases appear to drop down to zero, while their steep decreasing rate is clearer in the log scale shown in Figure 8 (b); the infected cases per tests decreases by about two orders of magnitude just within the ribbon of temperatures 30 ± 2 C 0 .

We now perform the fitting of . 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 February 23, 2021. logarithmic (b) panels. In (a) the infected cases appear clearly to decrease with increasing temperature and vanish as soon as the temperature reaches ~ 31 C 0 , that is, the limit of critical temperature T C = 30 ± 2 C 0 (purple ribbon). In (b) we observe two different functional behavior on each side of the ribbon; the number of infected cases decreases with much steeper slope for T>T C than for T<T C ; the corresponding expressions are given in Eqs.(11a,b) , and plotted with -1σ (red dash lines) to show the temperature (~29.5 C 0 ) at which the two data regions intersect.

Next, we perform a statistical analysis to examine whether the determined temperature dependence of the infected cases and deaths is subject to statistically significant concentrations or rarefactions; namely, whether possible heterogeneities within the distribution of sample points plays significant role in the fitted relationships in Eqs.(10a,b) and (11a,b) . For this, we derive the temperature infected relationship by . 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 February 23, 2021. ; https://doi.org/10.1101/2021.02.19.21252106 doi: medRxiv preprint fitting the homogenized set of sample points, instead of the raw sample points; then, we examine whether the fitting parameters differ from those derived from fitting the raw sample points.

We homogenize the sample points by grouping them in temperature binning of Δ T=2C 0 (e.g., see similar analyses in [28, 29] ). Then, we estimate the weighted mean and error of the rates included in each bin. Figure 9 (a) shows the homogenized dataset and its fitting.

We observed that homogenized datasets result in a smooth relationships between the values of binned temperature and the (logarithm of) positivity percentages. The linear relationship for T<T C has large slope dlog(N + /N T )/dT characterized by high statistical confidence for the raw or homogenized datasets (p-values much higher than the significant limit of 0.05). Therefore, the arrangement of sample points do not affect significantly the fitting results. We confirm this result by applying the method of generating data points, as in Figure 2 (b), and then, refit the "enriched" dataset. In particular, for each of the given N 0 = 12 data points of

(for further details, see: [17] ). The results are shown in Figure 9 (b,c), confirming the statistical significance of the difference of slopes dlog(N + /N T )/dT, taken for T>T C than for T<T C .

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The copyright holder for this preprint this version posted February 23, 2021. ; for the "enriched" dataset (see text), in order to ensure that the statistical significance of the difference of slopes dlog(N + /N T )/dT, taken for T>T C than for T<T C .

As it has already been discussed in [1] , the observed dependence on temperature on the number of the infected cases and death caused by Covid-19 can be interpreted within the framework of chemical kinetics.

Coronavirus uses their major surface spike protein to bind on the ACE2 receptor -another protein that acts like a doorway into a human cell [30] . As long as the exponential growth takes place, the environmental temperature has an effective role on the chemical reaction between virus and spike protein.

The whole process is a slow chemical reaction, where the mechanism behind can lead to rates negatively . 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 February 23, 2021. ; https://doi.org/10.1101/2021.02.19.21252106 doi: medRxiv preprint correlated with temperature, i.e., increasing rate with decreasing temperature. This is consistent to reaction rate proportional to the Arrhenius exponential with negative activation energy

We recall that the exponential growth phase, which starts at some time t=t 0 following the preexponential phase characterized by a mild logarithmic and often vague growth, is given by

or, for a constant exponential rate,

A physical interpretation of the inverse proportionality of the exponential growth rate with the environmental temperature could be given through the kinetics of the chemical reaction between the coronavirus (C) and the receptor (A),

where the coefficient of the reaction speed is

that involves the pre-exponential Arrhenius frequency factor f Α and the (negative) activation energy 

and the expansion rate becomes

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In a more realistic model, the coronavirus is not always reaching the receptor, because it is being destroyed in the air (product denoted by C-O), or dissolved through a reaction that competes the one that describes the connection with the receptor. The combination of both the parallel reactions can lead to the inversely-proportional dependence of λ on temperature. Indeed, we have 

which can be approximated, as in the previous model in Eq. (17) , by assuming sufficiently slow reactions,

leading to the same results as in Eq. (19) . On the contrary, in the approximation of fast reaction, Eq. (23) gives 0 O ( )

Next, we apply the following approximations: (i) ignore any virus-related source, i.e., 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 February 23, 2021. ;  .

(32) Figure 10 plots the model shown in Eq.(32), for fixed n=3d -1 (upper panels) and fixed frequency factor f A =0.01s -1 (lower panels). 

It is straightforward to forecast the decline of the number of infected cases when the environmental temperature will climb above this critical value within 2021 for the Republic of Cyprus. The number of the daily new infected cases are expected to decline to zero after the 16 th of May, 2021, as shown in Figure 11 .

. 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) Encouraging as this result is, it is necessary to recall the conclusive statement from [1] . The resulting high statistical confidence of the negative correlation of the environmental temperature on the exponential growth rate of the cases infected by COVID-19 is certainly encouraging for loosening super-strict socialdistancing measures, at least, during the summery high temperatures. However, we are, by no-means, recommending a return-to-work daily basis to be ensued by this analysis. Nonetheless, we do think that this work may be part of the decision, as well as an inspiration for repeating the same analysis in other heavily infected regions.

The paper improved our understanding of the effect and the functional dependence of the environmental temperature on the spread of COVID-19 and the rate of its exponential growth. We studied the daily number of the cases infected by Covid-19 during the second wave of the pandemic within 2020, as well as the daily number of the following deaths, and how they were affected by the daily average-high temperature for the districts of the Republic of Cyprus.

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The copyright holder for this preprint this version posted February 23, 2021. ; https://doi.org/10.1101/2021.02. 19.21252106 doi: medRxiv preprint In particular, for the period from 8/25 to 12/31, that is, the second wave of the Covid-19 pandemic in 2020, we (i) examined the daily numbers of the infected cases with respect to the number and types of the tests performed, (ii) modelled the evolution of the number of the infected cases during the exponential growth phase, (iii) performed a statistical analysis for comparing the time series of the infected cases and the average-high environmental temperature, (iv) developed a model within the framework of chemical kinetics that describes the observed behavior and characteristics of the number of the infected cases and its exponential growth rate with respect to the environmental temperature, (v) performed a statistical analysis of the number of deaths caused by Covid-19 and their age distribution, and finally, (vi) understand the importance of the critical temperature that eliminates the exponential growth rate of the infected cases.

Among the main findings of the paper, are the following:

-Analyzed the results of the PCR and rapid antigen tests and showed that the average ratio of the PCR positive tests to the rapid positive tests is ~ 2.57 ± 0.25; this coincides with the expected ratio of the PCR's to the rapid test responses; the PCR's response is characterized by a nonzero probability for more than 5 weeks and overestimates the positive tests (about 2.5 times, compared to the rapid test), and thus, the infected cases.

-Presented the common biases of the statistical sampling performed in the recording of the infected cases during the second wave of the Covid-19.

-Analyzed the time series of the age of deaths and showed that the average age shifts to older ages with rate Δ Age/Δt ~ 0.156 ± 0.050 [age year / day], i.e., about a year of age per week.

-Analyzed the total age distribution and showed that the probability of a person infected by Covid-19 to develop severe symptoms leading to death is strongly depended on the age of the person; in particular, the probability of having a death on the age of ~67 or younger is less than 1/1000, for the second wave of the pandemic in Cyprus.

-Analyzed the data with respect to the environmental temperature and showed that the number of infected cases declined dramatically for temperatures reaching, and/or climbing above, the critical temperature of T C = 30 ± 2 C 0 ; since the number of the deaths is positively correlated to the number of the infected cases, similarly drop of the number of deaths is observed for high temperatures, above T C .

-Developed a model that describes the observed negative correlation between the exponential growth rate of the infected cases and the environmental temperature, which is based on the chemical kinetics of two parallel and competing reactions, describing the connection of the coronavirus towards the receptor, and the reaction of the dissolution of the coronavirus; the model results to the exact observed expression of the exponential rate with temperature.

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persons per day and for (at least) τ days. Hence, the ratio of the total concentration of the infected receptors out of the initial concentration of coronavirus, R 0 , givesHence, the exponential rate is given bythus, comparing to the exponential rate in Eq.(12b), we findNote: Given that a single infected person spreads the disease to n ≈ 3 other persons per day for τ ≈ 5.2 days, with a deviation ±1 person, the propagated error isis consistent with the error in the measurements of T C .Next, we derive the activation energies, characterizing the connection of the coronavirus with the receptor, ,