key: cord-0859266-raelqb6j
authors: Martinez-Loran, Erick R; Naveja, J Jesus; Bello-Chavolla, Omar Yaxmehen; Contreras-Torres, Flavio Fernando
title: Multinational modeling of SARS-CoV-2 spreading dynamics: Insights on the heterogeneity of COVID-19 transmission and its potential healthcare burden
date: 2020-04-17
journal: nan
DOI: 10.1101/2020.04.14.20064956
sha: e87480778faffce009192a7d51ca0b9b66038712
doc_id: 859266
cord_uid: raelqb6j

Background: Modelling and projections of COVID-19 using a single set of transmission parameters can be an elaborated because the application of different levels of containment measures at different stages of the worldwide COVID-19 outbreak. Methods: We developed a piecewise fitting SEIR methodology to fit the progress of the COVID-19 that can be applied on any of the 185 countries listed in John Hopkins Coronavirus Resource Center. The contagious contact rate, the rate of removal and the initially exposed population were obtained at three different stages of the pandemic for a set of 18 countries, and globally for the total number of cases worldwide. The active number of infections and the removed populations were fitted simultaneously to validate the SEIR model against the available time series reports on the number of confirmed infections, recoveries and deaths. We evaluate the effect of a reduction of contagious contact rate on the level of burden put on local healthcare infrastructure considering different levels of intervention. As a guideline for future public health interventions, we also estimated the maximum number of future cases and its potential peak date. Findings: We project that the peak in the number of infections worldwide will take place after the third quarter of 2020 with a decline rate that might extend beyond 2020. For 12 out of the 18 countries analyzed, we observe that, following the trend at the date of this study, the number of severe infections will surpass their healthcare capacity. For a 90% reduction scenario of the contagious contact rate, four out of the 18 countries analyzed will undergo a significant delay in the peak of infection, extending the course of the epidemic further than our simulation window (365 days). Interpretation: We identify three stages for the COVID-19 transmission dynamics, which suggest that it is highly heterogeneous between countries and its contagious contact rate, is currently affected by both local responses of the public health interventions and to the population's adherence to the measures. Funding: No funding received.

The SARS-CoV-2 virus responsible for the coronavirus disease 2019 (COVID- 19) emerged in Wuhan, China at the end of 2019. Early situation reports from the World Health Organization (WHO) database indicated that most of the regions with more than a thousand cases of SARS-CoV-2 infection exhibited an exponential progression in the number of cases after the first three weeks of the first confirmed case. 1 The first reports of the epidemic suggested an alarming death rate of ~3%, which has increased with the time up to more than 5% 2 . As of April 2020, the COVID-19 pandemic has globally reached more than 1,350,000 confirmed cases and 80,000 deaths 3 . However, the lethality rate and the number of confirmed cases notably differs between countries, 2 indicating distinct effects on the disease severity and transmission rate. Recent reports from Chinese COVID-19 cases have provided valuable information at the early stages of the epidemic and thus a general guidance to control the propagation within China has been considered in other countries. 4, 5 The control measures aimed at reducing the contact rate, such as social distancing policies and isolation of infected populations, have proven to be effective in managing the epidemic. Nevertheless, difficulties in the implementation of strict measures have led to a fast increase in the number of cases. 6, 7 For instance, Europe and the US have surpassed the number of fatalities in China despite the strict policies on social distancing that were adopted weeks ago. Due to the heterogeneity of the spread, it is expected that the healthcare systems of most economies will face a considerable burden in the coming months because of the COVID- 19 outbreak. 8 In the present circumstance of the COVID-19 spread, understanding of the dynamics of this epidemic is necessary to forecast and control the transmission of the disease, as well as to evaluate the effectiveness of potential interventions in modifying its degree of infectiousness. 5 In particular, the first report for the transmissibility of COVID-19 estimated a basic reproduction number (R) ranging from 2.24 to 3.58 based on the time series of two other well-known coronavirus diseases (MERS and SARS). 9 However, the main goal of several studies was focused on the prediction of the trend of the epidemic as it expanded across mainland China, limiting the comparability of disease courses worldwide. Despite considerable efforts to model COVID-19 epidemic courses, the local dynamics of transmission is currently not well described for other countries.

The susceptible-exposed-infected-removed (SEIR) compartmental model has been recently used to model the progression of the epidemic in China. 4 Models of higher complexity to extrapolate information from early stages of the outbreak may not necessarily be more reliable in making predictions due to the larger number of model parameters to be estimated. 10 The SEIR model has been successfully used to model many other infectious diseases, 5, 9, [11] [12] [13] and can offer an adequate tradeoff between accuracy and complexity (e.g. between compartmental models of less complexity like the susceptible-infected-removed (SIR) model 14 and models of larger number of compartmental interactions, like the one described by Arenas et al. 2020 15 ). This makes the SEIR model suitable to estimate COVID-19 rates by fitting the time series of the infected population. While it is common practice to fit only the infected compartment, 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 April 17, 2020. . https://doi.org/10.1101/2020.04.14.20064956 doi: medRxiv preprint removed population should also be considered when fitting, because its evolution determines the extent to which a decline in the number of infections will occur throughout the course of the epidemic. In this work, we use the SEIR model without vital kinetics (i.e., assuming a constant population size) to simultaneously fit the progression of active infections and removed populations for selected countries. We present a piecewise methodology that allows us to compare the progression of the epidemic at different stages and make comparisons of the infectiousness across countries. We use the extracted epidemic parameters to make relevant projections on the dynamics of the disease in forthcoming months. Information about the local dynamics of the epidemic can be useful to anticipate the impact of public policy interventions, including social distancing as well as to project healthcare supply needs in the short-term.

The time series of the COVID-19 were extracted from official reports provided by the Johns Hopkins Coronavirus Resource Center (hereafter JHCRC), starting from January 21st to April 12th, 2020. 16, 17 In our multinational modeling of SARS-CoV-2 spreading, we selected 18 countries corresponding to a ~10% of the total number of countries reported in JHCRC. The particular choice of countries was made based on the consistency of the data with the SEIR model (R 2 > 0.8), and taking into account a number of confirmed cases larger than one per 100k, with a number of total deaths exceeding 200. Country-level data on population size was extracted from the latest report by the Department of Economic and Social Affairs of the United Nations. 18 The lethality rates were used to assess the status of the COVID-19 outbreak for all the analyzed countries;

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The copyright holder for this preprint this version posted April 17, 2020. . https://doi.org/10.1101/2020.04.14.20064956 doi: medRxiv preprint we computed the current lethality rate (in %) as the quotient of deaths by COVID-19 divided by confirmed cases in last reported values as obtained from JHCRC. To evaluate the burden that the pandemic lays on the country-level healthcare system, we used the number of hospital beds and acute care beds based on data extracted from the World Bank Database. 19 

The SEIR model

The total population is considered to be constant and is partitioned into four disjoint groups, namely: susceptible, ( ); exposed, ( ); infected, ( ), and recovered, Equivalently, dividing all terms by ( ):

( ) + ( ) + ( ) + ( ) = 1,

And the system of ODEs is given by:

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The copyright holder for this preprint this version posted April 17, 2020. We solve the coupled system for the SEIR model using SciPy's implementation of the explicit Runge-Kutta method of order 8 (DOP853); 22 this enables us to estimate the transmission rate ( ), recovery rate ( ), and the initially exposed population ( 0 ≡ ( = 0)) by fitting the progression of ( ) and ( ). We use the trust-reflective non-linear leastsquares method to minimize the residuals between the SEIR model and the data as . 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 April 17, 2020. 

To assess COVID-19 dynamics at different epidemic stages, we fitted ( ) and

( ) piecewise and optimized the interval ranges until the value of 2 was higher than 0.8.

To compare changes in epidemic curves where at least two inflection points were identified, we composed a ratio of transmission rates ( = +1 / ), for = 1,2,3 being the interval number (i.e. stages). This estimate can reflect the changes in the COVID-19 epidemic as induced by public health policies. Functional prediction bands ( ) = ( ) ± ( ) were obtained using ( ) =(variance)×(inverse of the t-student cumulative distribution).

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A fundamental question for decision makers in countries where the pandemic is developing consists of whether their healthcare systems will be coped with the increasing demands posed by SARS-CoV-2 [27] [28] [29] [30] . To add this practical perspective into our analysis, we included: a) the number of hospital beds per capita as reported in official sources, and b) split the number of confirmed COVID-19 cases according to the reported proportions to which 80% of the infected will likely develop mild symptoms only (not requiring hospitalization), 15% would display severe disease (requiring to stay at the hospital) and 5% would reach a critical state (requiring admission to the Intensive Care Unit) 31 .

Moreover, we have performed three kinds of projections: first, following the best fit of the SEIR model at the latest stage of the time series, and other two other projections assuming a 50% and 90% decrease in the spreading of the disease, as assessed by the β parameter. As a metric of the level of burden that the epidemic will lay on the health care systems, we define the health care stress as the ratio between the number of infection cases that require hospitalization at the peak of the disease and the number of available beds as reported by the World Bank database.

The current officially reported lethality for COVID-19 is approximately 3.4% 1 .

However, the data fitted indicates a global lethality rate of about 6.17%; this number considers only confirmed cases and could be an overestimation over reporting biases for symptomatic and high-risk cases. A cluster of European countries (UK, Italy, Spain and France) whose calculated lethality rate range from 10.3 to 12.7% and their number 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 April 17, 2020. . https://doi.org/10.1101/2020.04.14.20064956 doi: medRxiv preprint confirmed cases exceeds 100 cases per 100k is visibly the most affected region ( Figure   1 ). Germany, Austria, Switzerland and the US reported >100 cases/100k and their lethality rate similar or lower to than China (4.021%). South Korea, Singapore, Australia and Canada also cluster together, being countries with a lower lethality (< 3%) and confirmed cases lower than 100 per 100k. Brazil, Ecuador and Iran have higher lethality rates than China and their number of confirmed cases is currently still increasing (>10 per 100k). Finally, Japan and Mexico show a number of confirmed cases lower than 10 per 100k; however, the lethality rate for Mexico (6.4%) is higher than that of China. In this study, Mexico shows the lowest number of confirmed cases per 100k habitants. Although this relationship among lethality rate and confirmed cases could be an indication that the pandemic has different dynamics of transmissibility when comparing countries to each other, it must be kept in mind that those countries have responded heterogeneously to COVID-19, both in testing and in the enforcement of public policies.

The number of active infections and removed individuals shows an apparent change in both transmission and removal rates, leading to a crossover in February 28, with a transitory decline in the number of active infections, followed by a second crosspoint around March 16, when the number of active infections takes over the number of recoveries (Figure 2) . These features can be regarded because of a lag between the pandemic's onset across different regions of the globe, which also introduces an additional heterogeneity due to local reporting and containment policies, and demonstrates that SEIR modelling of individual countries is required to address the heterogeneity of the COVID-19 pandemic.

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The first crossing point between the infected and removed curves, where the number of recovered cases surpasses active infectious cases is currently not observed for most of the countries studied, with a clear exception for China, South Korea and Austria (see Supplementary Material). This is because (1) several countries are still at the early stages of an exponential spread, and (2) an apparent lag between the application of the social distancing measures and the effective change in the rate of the expansion of the epidemic. Because of the inherently high effectiveness of the transmission of SARS-CoV-2, it is expected that the pandemic will extend for months.

According to the current trend, we project that the peak in the number of infections worldwide will take place after the third quarter of 2020 ( Figure 2C) . When assessing the projection of COVID-19 cases worldwide, we simulated the same scenarios over different ranges of (see Table 1 ), indicating the potential of reduced transmission by the initiation of public policy measures. As observed in Figure 2D , an earlier peak of infection and a reduced burden on healthcare systems can be achieved by targeting drastic reductions on transmission using social distancing measures.

So far, European countries still lead in the number of confirmed cases and COVID-19 deaths per capita, followed by the United States (Figure 1, Table 1 ). Most countries, with the exception of Japan and Mexico, have managed to slow down the spreading of the epidemic, as revealed by lower 3 values, as well as 1,2 values<1 (Figure 3) . In the case of Mexico, the modelling might be limited due to the implementation of a sentinel surveillance model, which samples only a few of all SARS-CoV-2 infections; therefore, the effect of public policy measures might not be accurately estimated using our model 32 . The sharpest declines in spreading rates were observed for Austria, China and South . 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 April 17, 2020. . https://doi.org/10.1101/2020.04.14.20064956 doi: medRxiv preprint Korea. Notably, Austria was an early responder of the epidemic, enforcing more stringent restrictions before its neighbors, and as a result it is reportedly now preparing to lift lockdown. 33 Removal rates are also increasing in many countries, which goes along with increases in the estimations of lethality rates, probably it might also be related with a shortening in recovery times or to an increase in recovery rates as the pandemic progresses.

Two distinct values of are defined per country to reflect changes in for the three fitted intervals (Figure 3) 

Assuming that the treatment and prevention of the disease is not affected by other means that are not accounted by the model, then the projections suggest a very strong decrease of the spreading of the disease necessary in most countries to avoid surpassing the healthcare system capacities. Our results also suggest that more stringent measures are still required in most countries; only a few exceptions were observed for Australia, . 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 April 17, 2020. . https://doi.org/10.1101/2020.04.14.20064956 doi: medRxiv preprint Austria, China, Iran and South Korea, which could either continue the same or even relax the containment measures to some controlled extent (Figure 4) . As expected, a monotonic decrease in the number of cases at the peak of the infection is observed with a decrease in the value of . For 12 out of the 18 countries analyzed, the current trend indicates that probably the number of severe infections will surpass the healthcare capacity ( Figure 4C ). According to our projections, Germany, South Korea, Spain and Switzerland would avoid a saturation of the health case capacity with just a 10% reduction in their . We observe that for four out of the 18 countries analyzed, a 50% reduction on the is enough to avoid the saturation of the available health care infrastructure.

We also see that a reduction of 90% in will be a failsafe intervention for all of the analyzed countries. For this level of intervention, it is expected that 11 out of 18 countries (not including Australia, Austria, China and South Korea, which seem to have already passed their infection peaks) reach their peak before the third quarter of 2020.

Additionally, it is observed that 5 out of the 18 analyzed will see a significant delay in the peak of the infection for a 90% reduction of extending the course of the epidemic further than the 365 day simulation window, namely, Brazil, Ecuador, Japan, the United Kingdom and the United States.

Multinational SEIR modeling of the COVID-19 pandemic demonstrates a significant heterogeneity of the disease across different countries; this suggests that there is no consistent public policy, which will be universally applicable, and that the course of the pandemic will likely be extended given that peak infection rates will occur at different times across countries. Our results suggest that the measures that most countries have . 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 April 17, 2020. . https://doi.org/10.1101/2020.04.14.20064956 doi: medRxiv preprint imposed so far have not been sufficient at the time they were enforced to contain the spread. In some scenarios, the likelihood of significantly reducing the number of cases and mortality rates would require significant additional measures to reinforce social distancing. Countries that acted earlier were benefited from the social lockdown; those countries facing a more challenging COVID-19 epidemic should enforce the most stringent measures to avoid overwhelming the capacities of their healthcare systems.

Should the situation progress as it has so far, our model projects that the global peak of confirmed cases will be reached by after the third quarter of 2020, though significant fluctuations of this timing are expected among countries. Our piecewise analysis also shows that the rate of spread and impact of COVID-19 has slowed down in most countries, and this fact will likely modify predictions with regard to the size and temporality of the peaks in coming weeks.

Our approach to estimate different stages of the COVID-19 pandemic would likely be better at reflecting changes in both government response and human mobility throughout the course of the epidemic. 34 Notably, our proposed metric evidences changes in transmission rates and elucidates country-specific changes in the rate of spread after implementation of public policy measures to contain the virus. The social distancing policy has been implemented heterogeneously across countries, most likely to reduce the socio-economic impact on vulnerable populations. 35 Preliminary data from China demonstrates that public health interventions including traffic restriction, social distancing, home quarantine, and universal symptom survey was temporally associated with reduced effective reproduction number of SARS-CoV-2: 36 this is confirmed in our data, whereby China showed significant reductions in values indicating containment 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 April 17, 2020. . https://doi.org/10.1101/2020.04.14.20064956 doi: medRxiv preprint SARS-CoV-2 spread. Austria and South Korea are additional examples of public health measures, which have effectively curbed the total number of cases and reduced the impact of the COVID-19 epidemic. 37, 38 Additional modelling efforts are required to retrospectively assess the effect of social distancing in curbing the pandemic; nevertheless, our results show that most countries in which social distancing has been implemented show a decrease in the rate of contact transmission. Moreover, the latter likely indicates that those countries with early phases of spread will also experience longterm benefits with more strict policies. Notably, our analyses show that stringent decreases in contact transmission of SARS-CoV-2 could lower the healthcare stress, and decrease the number of total cases. However, depending on the local progress of the pandemic, even a stringent reduction in could have the effect of either shortening the length of the disease, or prolong the time to reach the peak number of infections. The relevance of decreasing the contagious contact rate stems from the fact that the lethality could be exacerbated once the number of severe cases exceeds the healthcare capacity. 39 With respect to mobility, the citywide quarantine at Wuhan since January 23, 2020, had negligible effect on the epidemic trajectories for the rest of the country. 4 A 50% reduction in inter-city mobility leads to a negligible effect on epidemic dynamics. 4 Therefore, we concluded that accounting for inter-city and inter-country mobility in modeling countries where the epidemic is already present is not of main importance and could be mostly neglected. Given the heterogeneity of the COVID-19 pandemic, our projections should be helpful in understanding the effect of reducing under different circumstances.

Unlike most SEIR models reported for COVID-19, we fit the data of both confirmed and removed cases, which provides higher confidence in our estimations. However, some . 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 April 17, 2020. . https://doi.org/10.1101/2020.04.14.20064956 doi: medRxiv preprint limitations to our analysis can significantly influence the model predictions. For instance, our analysis does not consider the fact that the number of confirmed cases could be underestimated. To address this issue, some countries such as South Korea, Germany and to some extent the US have enacted massive testing which has shown benefits in reporting the spread of the disease, 40 

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Ongoing data collection and epidemiological analysis are essential parts of assessing the impacts of mitigation strategies against SARS-CoV-2 pandemic. In this study, a multinational SEIR modeling considering three different epidemiological stages was used to compare the COVID-19 spreading dynamics. This allowed us to identify the effectiveness of the containment measures across 18 countries and determine the potential burden to the healthcare system, under the assumption of different levels of reduction of the contagious contact rate. Our estimations for the number of active infections place the global peak after the third quarter of 2020; however, several countries may experience a sharper decline within the coming weeks. We found that the peak number of infections monotonically decreases with the decrease in the contagious contact rate. Nevertheless, there is a mixed outcome in the duration of the epidemic since for some countries, the implementation of even more stringent containment measures would lead to a prolonged development of the COVID-19 epidemic. For all studied countries a 90% reduction in the contagious contact rate is required to avoid an excessive burden on the health care capacity. COVID-19 exhibits a heterogeneous spread for the countries studied, a fact that can be related to variations in both timing and efficacy with which the containment measures were implemented in each country. Our results provide informative guidelines to avoid healthcare overcapacity and weigh the long-term effects of more lenient policies. is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The copyright holder for this preprint this version posted April 17, 2020. . https://doi.org/10.1101/2020.04.14.20064956 doi: medRxiv preprint Figure 1 . Number of confirmed COVID-19 cases per 100k habitants versus the lethality rate (in %) for different countries. The lethality rate was calculated as the quotient of deaths by COVID-19 divided by the confirmed cases according to the report published on April 12, 2020, from JHCRC.

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The copyright holder for this preprint this version posted April 17, 2020. . https://doi.org/10.1101/2020.04.14.20064956 doi: medRxiv preprint Figure 2b shows the the selection of intervals used to fit the mode globally: (a) from the date of the first detected case to the point 1 indicated on the infections curve, (b) on the range indicated between the arrows labeled as 2 on the infections curve and (c) from the point labeled as 3 on the infections curve to April 12th 2020.

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The copyright holder for this preprint this version posted April 17, 2020. . https://doi.org/10.1101/2020.04.14.20064956 doi: medRxiv preprint (infectious rate) for each of the different intervals (c) Fitted removal rate ( ) for each of the different intervals (e) Ratio = +1 / between the different intervals, indicated as a measure of the effectiveness of the containment measures. For panels (b) through (d) missing values indicate that only two intervals were identified in the corresponding dataset. The scale of the vertical axis in (d) was adjusted to a maximum of 100. Nonetheless, Mexico overpasses this limit drastically, which could be attributed to a low early detection rate due to the implementation of a sentinel model for epidemiological surveillance (see Table 1 ).

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