key: cord-0873903-papz6uoa
authors: Pedersen, M. G.; Meneghini, M.
title: Data-driven estimation of change points reveal correlation between face mask use and accelerated curtailing of the COVID-19 epidemic in Italy
date: 2020-06-29
journal: nan
DOI: 10.1101/2020.06.29.20141523
sha: 3952ae9117b9dd18f28c821318cf3a6294876017
doc_id: 873903
cord_uid: papz6uoa

Italy was the first Western country to be seriously affected by COVID-19, and the first to implement drastic measures, which have successfully curtailed the epidemic. To understand which contain measures effected disease dynamics, we estimate change points in COVID-19 dynamics by fitting a compartmental model to official Italian data. Our results indicate that lockdowns managed to cause the epidemic to peak in late March 2020. Surprisingly, we found a change point during the decay from the peak, which does not correspond to obvious drastic legal interventions, but may be explained by widespread promotion and mandatory use of face masks. We confirm these interpretations at regional levels, and find that the gradual reopening of society since early May has caused no change in disease dynamics. We speculate that widespread use of face masks and other protective means has contributed substantially to keeping the number of new Italian COVID-19 cases under control in spite of society turning towards a new normality.

The COVID-19 disease due to the SARS-CoV-2 coronavirus is spreading rapidly across the 2 globe since its outbreak in China, and was declared a pandemic by the WHO on March 11, 2020. 3 After the first severe patient was brought to the hospital of Codogno, Italy on February 20, 4 2020, and subsequently tested positive for COVID-19, a rapidly increasing number of patients 5 have been identified, initially in Northern Italy and later in the rest of the country and Europe. 6 Italy is one of the most affected European country, with ∼240.000 confirmed cases and nearly 7 35.000 COVID-19 related deaths, and was the first to implement drastic contain measures. The 8 imposed restrictions, culminating with complete lockdowns, have turned out to be effective in 9 controlling the epidemic in Italy; the number of new daily cases peaked in late March 2020 at 10 ∼6000 and declined to ∼200 − 300 by early June. The limitations in activities were followed by 11 milder orders and direct invitations to behavioural change, such as distribution of face masks 12 accompanied by their mandatory use, first in the most hit regions and later nationwide. During 13 the month of May 2020, the country reopened many activities without compromising the decay 14 in the number of newly infected individuals. Analyzing the Italian data carefully may therefore 15 provide important insights into the epidemiology of COVID-19, and in particular to investigate 16 if, how and which limitations in activities and other actions affected the disease dynamics in 17 Italy.

Effective measures slow diffusion of the disease. By identifying such change points in COVID- 19 19 spreading [1] , it is therefore possible to associate interventions that were able to modify the 20 course of the epidemic without assuming any effect a priori. Further, such an approach may 21 reveal wether e.g. reopening of society lead to changes in disease dynamics, or could hint at 22 change points apparently unrelated to regulations that deserve further investigations. To find 23 such change points, it is advantageous to use relatively simple mathematical models of infectious 24 diseases, which compared to more complex models, can be fitted to data with a minimum 25 number of assumptions on model parameters [1] [2] [3] . However, even simple models should respect 26 that nature of the data. There is thus a compromise between using a parsimonious model but 27 sufficiently complex to be based on correct underlying assumptions.

In our setting, to fit the data on identified COVID-19 cases, a SIQR (susceptible -infectious 29 -quarantined -recovered) model [4] is appropriate. In this model, infected individuals may 30 be isolated, entering the "quarantined" subpopulation Q, so that these individuals no longer 31 transmit the disease. Since Italian positive cases have been put in isolation (in hospitals or 32 at home) immediately, the revealed data of active cases thus correspond to the number of 33 individuals in state Q.

By fitting a modified SIQR model to official Italian data, we find change points that correspond 35 well with general lockdowns. Our results indicate further that the mild restrictions imposed in 36 Italy during the first two weeks of the outbreak had negligible effects on the disease dynamics. 37 Surprisingly, we found an acceleration in the decay from the peak, which does not correspond 38 to obvious drastic legal interventions, but may be explained by widespread promotion and 39 mandatory use in face mask use. We confirm these interpretations at regional levels, and find 40 that the gradual reopening of society since early May appears not to have caused any change in 41 the disease dynamics. To be best of our knowledge, this is the first demonstration of a correlation 42 between widespread face mask use and a reduction in COVID-19 transmission dynamics.

We use a SIQR model [4] to describe COVID-19 dynamics in Italy. Since we will be fitting 45 the cumulative number of official cases, we unite the Q and R compartments in a "cases" 46 compartment C = Q + R. The model equations are

where β is the rate of infection, η models the average rate with which infectious individuals 48 become tested and quarantined, and eventually appear in the official statistics, and α is the 49 rate with which unidentified infectious individuals recover or die from the disease. We do not 50 explicitly model the number of recovered or deceased non-identified COVID-19 patients, but 51 only the rate α with which these patient become non-infectious. Further, N is the total number 52 of individuals in the population, assumed constant since we are studying the early phase of 53 the epidemic. Note that S + I + C = N . To obtain such a conservation law, an additional 54 compartment R I that model recovered but non-identified patients could be added with dynamics 55 dR I /dt = αI. 56 2 . 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 June 29, 2020. .

Since there is evidence that COVID-19 can be transmitted in the absence of symptoms [5, 6] , 57 we do not include an explicit exposed-but-noninfectious (E) state, i.e., we do not consider a 58 SEIQR model [7] . Further, from the Diamond Princess cruiseship and from the Italian village 59 Vo' Euganeo, it has been found that ∼50% of COVID-19-positive individuals do not develop 60 symptoms [8, 9] . We assume that such positive but asymptomatic individuals can transmit the 61 disease, i.e., the I state includes both individuals that will not develop symptoms, cases that 62 did not develop symptoms yet, and symptomatic patient that still have not been tested positive 63 and isolated.

In spite of the fact that almost 300,000 individuals have been found COVID-19 positive, and 65 possibly a few millions of unidentified cases have occurred, the total number of persons that have 66 had the infection constitute a relatively small fraction of the Italian population of ∼60 million. 67 Thus, it is a reasonable approximation that most of the population is still susceptible, S ≈ N , 68 and hence, as well known, the number of infected individuals follows at any time exponential 69 growth or decay, unless parameters change.

To identify change points, we allow β to be a piecewise constant function of time, thus 71 modelling how contain measures may affect the rate of COVID-19 transmission. We estimate 72 both the time points (change points, T 1 , T 2 , T 3 ) where β changes and the values of β = β i in the 73 intervals (T i−1 , T i ] with T 0 = 0 (Feb. 21, 2020) and T 4 = 122 (June 22, 2020; last data point). 74 The assumption of piecewise constant β is equivalent to I(t) being a piecewise exponential 75 function (under the assumption S ≈ N ).

As mentioned, the cumulative number of identified COVID-19 cases corresponds to C. With 77 the above assumptions, we obtain from (2) with S = N and by integrating (3),

where ρ i = β i − (α + η), i = 1, 2, 3, and C 0 is the initial value of identified cases. We fit this 79 expression to the Italian COVID-19 data from February 22, 2020 through June 18, 2020 ( Fig. 1) , 80 using the nls function in R [10] . 81 We note that the values of η and α are irrelevant for the fitting procedure and the main 82 findings in this manuscript regarding the identification of change points, but they permit us 83 to estimate e.g. the (time varying) basic reproduction number

To estimate α and η we use previous findings. The probability that a 85 COVID-19 positive individual is tested and quarantined is δ = η/(η + α). It has been estimated 86 that the average incubation time is ∼5 days [11, 12] and the duration of the milder cases of 87 disease it 5-10 days [5] . Identified cases are mostly symptomatic patients, which we assume 88 are tested and isolated a few days after the incubation time is over and first symptoms appear, 89 i.e., after ∼10 days. We also assume an average time of duration from infection to recovery 90 or death of non-isolated cases of 10 days, i.e., on average infectious individuals are removed 91 from compartment I with rate 0.1/day, either because they recover (milder cases) or become 92 3 . 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 June 29, 2020. tested and enter compartment C. Hence, α + η = 0.1. Since ∼50-75% of the population is 93 asymptomatic [8, 9] , but some milder cases may also go unnoticed and not end in isolation, we 94 assume that δ = 1/3 of infectious individuals are eventually tested. We thus set α = 0.067/day 95 and η = 0.033/day.

We obtained an excellent fit to the Italian data of cumulative COVID-19 cases assuming three 98 change-points (Fig. 1A) . Our results indicate that the early Italian containment measures 99 introduced in late February (school closings, hygiene indications, etc.) had negligible, if any, 100 effect on the disease dynamics. The first change points T 1 was estimated to fall on March 10, 101 2020, corresponding very well to the lockdown of the Northern regions on March 8, 2020, which 102 was followed by complete lockdown of Italy within a few days. These interventions lowered the 103 growth rate ρ by approximately one third. However, only later around March 20, 2020, did the 104 growth rate become negative, and the number of infected individuals started to decline. This 105 corresponds reasonably with the more stringent control measures and closure of all non-essential 106 work places introduces around this date. Indeed March 20, 2020, was the last work day before 107 4 . 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 June 29, 2020. . the wider lockdown of all non-essential companies. Another reasonable interpretation is that 108 the two change points reflect a gradual change in dynamics caused by a distributed, delayed 109 effect of the major lockdown of March 8, as discussed further in the Discussion. A third change 110 point was found at April 20, 2020 where the decay was further accelerated. 111 From the plot of the cumulative number of cases it may be hard to see the abrupt changes in 112 dynamics. In particular, the assumption of piecewise constant ρ (and β) -and hence exponential 113 growth or decay of the number of infectious individuals in each subinterval defined by the change 114 points -is difficult to verify graphically from this figure. Therefore, we plotted the daily number 115 of new cases on logarithmic scale (Fig. 1B) with the derivative of the fit from Fig. 1A . Indeed, 116 straight lines, corresponding to exponential growth or decay in I(t) = (dC/dt)/η, are easily 117 identified, justifying the assumption of piecewise constant parameters.

The latter change point identified at April 20, 2020, is apparently not related to any specific 119 containment measures. We speculated that the introduction of mandatory face mask use also 120 outdoors in Lombardy (from April 4, 2020) and Veneto (from April 13, 2020) might be the cause 121 of the acceleration of the decline occurring from this date. In addition, other hard-hit regions 122 such as Tuscany, Emilia-Romagna, Piedmont and Liguria had distributed free face masks during 123 April, encouraged their use, and some municipalities had made them mandatory in public spaces. 124 This promotion of face masks anticipated mandatory use from April 20, 2020 in Tuscany and 125 from May 4, 2020 nationwide. We thus proceeded to fit the data from these six regions with the 126 largest number of official COVID-19 cases. For Lombardy and Veneto, we were able to identify 127 three change points as for the agglomerated Italian data, whereas for the other four regions 128 only two change points were identified, likely due to the relatively low number of cases in these 129 regions during the first week of March. 130 We found that all regions had a change point in late March (Lombardy and Veneto had 131 two, similar to what we found for the national data) and another in late April. The change 132 in dynamics at this latter change point was very mild in Lombardy, but in other regions it 133 was very strong and clearly seen in the raw data (Fig. 2) . Lombardy introduced mandatory 134 face mask use on April 4, 2020, very close to the epidemic peak where the regional health care 135 system was close to a collapse. The data may therefore be unreliable near the peak, masking 136 the effect of face mask use, or the effect of face masks may be hidden behind the other regional 137 strict containment measures, lockdown and high level of alert in the region. For Veneto, the 138 introduction of the lockdowns in March, which correspond well to the first two identified change 139 points, stabilized the number of daily new cases at ∼400 with a small decline until the change 140 point found at April 20. The number of new cases then shown a marked exponential decline. 141 The identified change point corresponds well to the mandatory use of face masks from April 13 142 in Veneto.

For Tuscany and Piedmont, we found a similar pattern with a near-constant plateau during 144 late March -early April followed by exponential decline. The corresponding latter change 145 points were, respectively, April 14 and April 19. For Tuscany, the date corresponds well with 146 regional order of April 6, 2020, regarding the distribution of face masks in Tuscany from April 147 7, anticipating mandatory use in single municipalities once the distribution had completed, and 148 from April 20 in the entire Region. Piedmont did not require face masks until May 4, 2020, 149 but the regional government announced April 15 that masks would become mandatory and 150 started their distribution soon after. Similar patterns and explanations hold for Emilia-Romagna 151 (change point April 28) and Liguria (April 26).

Our chosen values for α and η yield an initial infection rate β 1 = 0.294/day and consequently 153 5 . 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.

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May Jun the basic reproduction number is estimated to be R 0 = β/(α + η) = 2.94, in line with previous 154 estimates of R 0 falling between 2 and 4 [11, [13] [14] [15] [16] . Further, we obtain an estimate of the number 155 of infectious individual at the moment of the outbreak of I 0 = 65.0/0.033 ≈ 2000, although with 156 a large uncertainty because of the large standard error on the estimate of ηI 0 , and because the 157 calculated I 0 obviously depends on the value of η. Based on the dynamics before the outbreak 158 (δ = 0), we can estimate that the first infectious case appeared in Italy log(I 0 )/(β 1 − 0.1) ≈ 40 159 days before the outbreak, i.e., around January 12, 2020.

Our data fitting procedure identified three change points where the dynamics of the COVID-19 162 epidemic changed. The first two correspond with the major lockdowns imposed in Italy during 163 March 2020. We therefore conclude that these were effective in halting the spreading of the 164 disease, which lead to the peak in new cases seen in late March. More surprisingly and in 165 6 . 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 June 29, 2020. . contrast to our expectations, we found a change point around April 20, which at first glance did 166 not correspond to any specific interventions. The major new containment measure introduced 167 in April were the orders of mandatory face mask use in Lombardy, Veneto and Tuscany, and 168 the distribution of free face masks in many regions. Analyzing regional data, we were able 169 to distinguish change points for each region that correspond well to the introduction of face 170 mask distributions or orders in the individual regions. Face masks have been suggested to be 171 important mainly for reducing COVID-19 transmission from asymptomatic individuals [17] that 172 may be responsible for the major number of newly infected cases due to the large fraction of 173 hidden-to-quarantined SARS-CoV-2 positive individuals (∼10-fold difference) [17] [18] [19] . 174 We considered alternative explanations for the acceleration of the decline of new cases seen 175 in late April. The number of COVID-19 tests did not decline in correspondence to the identified 176 change point, and the fraction of positive tests showed an acceleration in the decline similar 177 to the number of new cases. Mobility data (https://www.google.com/covid19/mobility/) 178 showed, if anything, increased activity in late compared to early April, excluding that reduced 179 activity underlie the change. The weather was mild and dry in April in Italy (https://www. 180 3bmeteo.com), with little variation in temperature during the month. Virtually no rain fell 181 during the entire month until April 27. Thus, no abrupt change in weather was seen around 182 mid-April, which might have been the cause of the change in dynamics. In summary, no obvious 183 alternative explanations for the acceleration of the end of the epidemic were found. 184 Our model assumes that the rate of infection changes instantaneously, which is not completely 185 realistic, but simplifies the model. We verified (not shown) that assuming that the change in 186 growth rate occurred in a linear fashion over 2, 5 or 10 days [1] did not change the conclusions. 187 The more graduate change in dynamics smoothened the curve, which made it harder to distinguish 188 the two first change points. The data was well fitted with a first change point shortly after the 189 lockdown on March 8 and a second one around April 15. 190 We estimated that there were ∼2000 of infectious but undetected individuals in Italy at the 191 time of the outbreak around February 21, 2020. Only when a patient with severe symptoms 192 was hospitalized and tested for COVID-19, and the first infected person died from COVID-19 193 on the following day, wide testing and isolation efforts started. By backward interpolation, we 194 estimated that the first infectious individual ("patient zero") appear in Italy around January 12, 195 2020. This estimate suggests that COVID-19 was present in Italy even earlier than a presumed 196 patient zero, suggested to be a German citizen linked to a cluster in Munich [6] visiting Italy 197 around January 25, 2020 [20] .

In conclusion, identifying change points confirmed that strict lockdown measures were infective 199 in slowing the spread of the epidemic, leading to its peak in late March. Face mask use appeared 200 as a plausible explanation for the further acceleration of the decline in the number of new cases 201 in April. The reopening of society in May did not lead to change in the decay rate (Fig. 1) , also 202 when analyzing the individual regions (Fig. 2) , which may be due to the mandatory use of face 203 masks nationwide from May 4. Our results thus lend further support to the importance of face 204 mask use for controlling COVID-19 during the reopening of societies [17, 21, 22] . 205 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)

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