key: cord-0960570-uqrlza4k authors: Jardim, L.; Diniz-Filho, J. A.; Rangel, T. F.; Toscano, C. M. title: The effective reproductive number (Rt) of COVID-19 and its relationship with social distancing date: 2020-07-29 journal: nan DOI: 10.1101/2020.07.28.20163493 sha: 2a31c2a11095737847d6a2c23ea0d53aa13060bb doc_id: 960570 cord_uid: uqrlza4k The expansion of the new coronavirus disease (COVID-19) triggered a renewed public interest in epidemiological models and on how parameters can be estimated from observed data. Here we investigated the relationship between average number of transmissions though time, the reproductive number Rt, and social distancing index as reported by mobile phone data service inloco, for Goias State, Brazil, between March and June 2020. We calculated Rt values using EpiEstim package in R-plataform for confirmed cases incidence curves. We found a correlation equal to -0.72 between Rt values for confirmed cases and isolation index at a time lag of 8 days. As the Rt values were paired with center of the moving window of 7 days, the delay matches the mean incubation period of the virus. Our findings reinforce that isolation index can be an effective surrogate for modeling and epidemiological analyses and, more importantly, can be an useful metrics for anticipating the need for early interventions, a critical issue in public health. The global expansion of the new coronavirus disease (COVID-19) triggered a great and renewed public interest in epidemiological models to understand temporal and geographical patterns of expansion of the pandemics and to use such models to guide decision making processes regarding public health measures to mitigate its spread 1, 2 . As so, it is of utmost importance to better understand clinic, immunologic and epidemiologic characteristics of the new coronavirus (SARS-CoV-2) that causes COVID-19 and how these can be translated into statistical parameters that can be estimated from observed data and used in predictive models. In the core of such discussions is the basic reproduction number (R0), which reflects the average number of new infections generated from an initial infection in a susceptible population 3 . This parameter synthetizes, under a more realistic view, incubation and transmission periods of the infectious agent 4, 5 , but actually it is not constant though time. During an epidemic, changes in the effective or realized infection transmission through time (here denoted as Rt) also reflect the demographics of the host-pathogen interaction, which in turn is regulated by several . CC-BY-NC 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 July 29, 2020. . https://doi.org/10.1101/2020.07.28.20163493 doi: medRxiv preprint 3 extrinsic environmental effects (mainly population density and social contact) 6, 7 . Thus, in the particular case of COVID-19 pandemic, for which no specific therapeutic or preventive strategy is yet available, the downward shifts in Rt is the expected outcome of non-pharmaceutical interventions, including social distancing measures to reduce the number of transmissions 1 . This result in a flattening of the epidemic curve, allowing healthcare systems to prepare and manage the expected cases of disease, while waiting for a vaccine to be developed and made available. Although it is relatively simple to estimate the infection Rt based on incidence data and estimates of serial interval 8 , it is much more difficult to explain its continuous temporal variation given the implementation of interventions, in particular social distancing measures 6 . Given the characteristics of COVID-19, among them a large proportion of asymptomatic cases, the ability to be transmitted by asymptomatic individuals, and its rapid spread, it is impossible to accurately identify the number of infected individuals early on in the epidemic. As such, it is important to have surrogates for continuous tracking of the Rt dynamics. The broad-scale real time monitoring of mobility derived from mobile phones has been reported to significantly correlate with decrease in the number of COVID-19 cases and increased social distance in the population 6 . Particularly in extremes of the epidemic, social distancing estimated by mobility indicators have been one surrogate of the Rt dynamics 7, 9, 10 . However, in addition to these extremes, it is interesting to assess whether a more continuous relationship between mobility and Rt over time, as this would allow closer and timely monitoring of disease transmission which may in turn guide public health responses tailored at the local level 6 . Here we investigate the relation between Rt, estimated from incidence curves of confirmed casos and deaths, and social distancing measured by mobility indicators from mobile phone data in Goiás State, in Central Brazil. The first COVID-19 cases were identified in Goiás in mid-March, mostly clearly imported from São Paulo and foreigner countries. Shortly after the identification of these few imported cases notified to the local surveillance system, the State Government implemented strict social distancing measures, including cancellation of events, school and workplace closures, closure of commercial establishments, and services except for essential services 11 (see also https://medidascovidbr-iptsp.shinyapps.io/painel/). After that social distancing was relaxed and isolation . CC-BY-NC 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 July 29, 2020. . https://doi.org/10.1101/2020.07.28.20163493 doi: medRxiv preprint indicators gradually decreased, thus providing an opportunity to evaluate the continuous relationship between Rt and social distancing. Goiás state has approximately 7 million inhabitants living in its 246 municipalities 12 . We considered epidemiologic and mobility data from all municipalities in the state. We here present the mobility indicator as its inverse denominated isolation indicator (resulting from 1-mobility and presented as %), as reported by mobile phone data service inloco (https://mapabrasileirodacovid.inloco.com.br/pt/). Isolation indicador was obtained for each municipality in Goiás state. Epidemiologic data for COVID-19 including confirmed cases and deaths were obtained from the Goias State Health Department (SES-GO, available at http://covid19.saude.go.gov.br/). The study period ranged from March 16 to June 6, 2020. We estimated the Rt values based on the incidence curve of confirmed COVID-19 symptomatic cases reported in the study period representing a total of 14,751 cases. We also obtained data from deaths (summing 500 confirmed deaths by July 01, by date of death) and used the package EpiEstim of the R plataform 13, 14 to analyze incidence by dates of symptom. Despite the significant delay for case confirmation in the system, of approximately 7-10 days in Goiás state, as we considered cases by date of symptom onset, we have enough replicatons to test the main effects of change in the isolation indicator. We estimated the posterior distribution of Rt modeling the COVID-19 disease incidences through time as a Poisson distribution with mean ∑ − ,, where ws is the probability of secondary infection time 14 . A gamma distribution (a = 1, b = 5) prior distribution is assumed for Rt with discretized gamma distribution with generation time µ = 5.2 and σ = 0.6 for ws, approximating the one used by other authors 7, 8, 15 . The values of Rt were calculated using a moving average considering 7-day window. Although more sophisticated methods are available to account for such delays and eventually sub notifications 16 , here we simply truncated the end of the distribution of cases as our goal is not to have a real-time estimate of Rt, but rather to correlate the shifts in the time series with the isolation indicator and to evaluate the impact more rigid or flexible social distancing measures in place in the State throughout the study period, as well as the observed decreasing levels of isolation from middle April on. . CC-BY-NC 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 July 29, 2020. . https://doi.org/10.1101/2020.07.28.20163493 doi: medRxiv preprint The population-weighted mean isolation indicators for the entire state were correlated with the Rt values, initially using standard Pearson correlations. We paired the Rt values to isolation assuming that each Rt reflects the middle of each time window. However, considering date of symptom onset and the fact that infection transmission take place in average 5 days earlier 4, 5 , we also calculated these correlations considering different time lags to evaluate its behavior. Because of the strong autocorrelation in both series, especially in the Rt values (as they are calculated using overlapping moving windows), it is not appropriate to apply a standard statistical test it due to inflated Type I error. We then used Dutilleul's approach based on temporal Moran's I correlograms to reduce the degrees of freedom taking into account positive autocorrelation in both time series 17 . These interventions resulted in a significant increase in the isolation indicator from about 25% to ca. 55% within a one-week period ( Figure 1A Even so, despite the similarity of the overall pattern of the time-series, when we correlate Rt and the isolation indicator at a fixed data, there is a relatively low correlation (r = -0.281). However, it is indeed necessary to consider a time-lag to reveal a relatively high negative correlation, and it is possible to find a much higher correlation of -0.696 at time lag 8 (so that higher number of transmissions in the middle of the time window is . CC-BY-NC 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 July 29, 2020. . https://doi.org/10.1101/2020.07.28.20163493 doi: medRxiv preprint 6 indeed associated with low isolation 8 days before; as we used a 7 day time window, it closely matches the 5 average days of incubation of the virus). The relationship may be slightly non-linear (Figure 2 ), although Spearman rank correlation is not that different from linear correlation (-0.645). O power fit (i.e., log-transformation in both variables) increased only slightly the correlation to -0.72. The first class autocorrelation using Moran's I autocorrelation coefficient in both variables is around 0.5, decreasing to zero after ca. 21 days, and thus Dutileull's approach suggest that correlation between the two series should be effectively tested with about 20 degrees of freedom (and even in this case these correlations are significant at P < 0.01). . CC-BY-NC 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 July 29, 2020. . CC-BY-NC 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 July 29, 2020. . https://doi.org/10.1101/2020.07.28.20163493 doi: medRxiv preprint In the scatterplot shown in Figure 2 we were not able to identify any systematic effects or trends in regression residuals, although there was a reinforcement of the behavioral measures from middle April onwards (although we are not aware of the effectiveness of such measures and do not have a quantitative account of their effects). There is a real interest to evaluate the local dynamics of disease transmission, as this is the main parameter that drives the spread of COVID-19 in a region. Several analyses have shown, as expected, that social distancing measures effectively reduce the reproduction number (Rt) parameter 6, 7 . However, it is actually difficult to evaluate the true effects of such measures in a more realistic fashion, as there may be several confounding and interactions between broad-scale isolation related to mobility and more local and "behavioral" aspects at very local an individual scale, including hygiene measures, mask use and social awareness as a result of the pandemic 18, 19 , as well as a more effective contact tracing and early detection of cases 20 . . CC-BY-NC 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 July 29, 2020. . https://doi.org/10.1101/2020.07.28.20163493 doi: medRxiv preprint We identified for Goiás State a relatively high negative correlation of -0.696 (increasing to -0.72 at log-scale) between the estimated Rt and isolation indicator obtained from mobile phone data. Our empirical results match those reported for São Paulo State, where the Rt decreases from about 2 to 1 after strict social distancing interventions were implemented in mid-March 2020. Similar findings were also reported for broad-scale analysis of other countries 6, 9 . However, our results show that this high correlation between Rt and isolation index suggests a more continuous relationship between these variables, as recently calculated for United States 6 , rather than a more discrete variation of extremes (i.e, if isolation increases to 50% the Rt decreases to 1.0, as shown for São Paulo state 21 , France 22 and Europe 7 , and used for initial modeling in Brazil 10 ). Even more interestingly, the negative correlation between isolation and Rt appears only if a time-lag is created, which is indeed expected considering current knowledge of COVID-19 disease and in particularly its incubation time. This correlation may seems clear to our case in Goiás perhaps due to the rich behavior of the time series, with an initial increase in the isolation indicators shortly after the start disease transmission locally, followed by a more continuous reduction in the isolation indicator, and finally by a stabilization at around 38% in late May. We expect an even richer dynamics as the State has now implemented intermittent lockdown with cycles of 14 days, although not yet followed by all municipalities. Even so, it is also important to note that this correlation between Rt and isolation indicator must be better detected in early phases of the COVID-19 expansion, and it will tend to disappear as the epidemic size increases and the peak of transmissions occurs because Rt will be also more strongly affected by the reduction of number of susceptible individuals in the population. In conclusion, about 50% of the variation in the mean number of transmissions expressed by Rt in the Goiás state is explained by broad-scale isolation indicator measured by mobile phones. Although there is a relatively large amount of unexplained variation, we do not have additional variables related to more local measures that could improve our understanding of disease transmission. Considering the amount of variation explained and the randomness of the residuals of the relationship between isolation and Rt, we understand that using isolation indicators obtained from mobile phones can be a good surrogate for COVID-19 transmission in a given population, and can be used for modeling purposes as well as routine epidemiological analyses. More importantly, it and can be . CC-BY-NC 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 July 29, 2020. . https://doi.org/10.1101/2020.07.28.20163493 doi: medRxiv preprint quite useful for anticipating the need for early interventions, an important and critical issues in public health. . CC-BY-NC 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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