CCDR • November 5, 2020 • Vol. 46 No. 11/12 Page 409 OVERVIEW Assessing the impact of varying levels of case detection and contact tracing on COVID-19 transmission in Canada during lifting of restrictive closures using a dynamic compartmental model Antoinette Ludwig1*, Philippe Berthiaume1, Heather Orpana2,3, Claude Nadeau4, Maikol Diasparra4, Joel Barnes4, Deirdre Hennessy4,5, Ainsley Otten4,6, Nicholas Ogden1 Abstract Background: The coronavirus disease 2019 (COVID-19) pandemic began with a detected cluster of pneumonia cases in Wuhan, China in December 2019. Endemic transmission was recognized in Canada in early February 2020, making it urgent for public health stakeholders to have access to robust and reliable tools to support decision-making for epidemic management. The objectives of this paper are to present one of these tools—an aged-stratified dynamic compartmental model developed by the Public Health Agency of Canada in collaboration with Statistics Canada—and to model the impact of non-pharmaceutical interventions on the attack rate of COVID-19 infection in Canada. Methods: This model simulates the impact of different levels of non-pharmaceutical interventions, including case detection/isolation, contact tracing/quarantine and changes in the level of physical distancing in Canada, as restrictive closures began to be lifted in May 2020. Results: This model allows us to highlight the importance of a relatively high level of detection and isolation of cases, as well as tracing and quarantine of individuals in contact with those cases, in order to avoid a resurgence of the epidemic in Canada as restrictive closures are lifted. Some level of physical distancing by the public will also likely need to be maintained. Conclusion: This study underlines the importance of a cautious approach to lifting restrictive closures in this second phase of the epidemic. This approach includes efforts by public health to identify cases and trace contacts, and to encourage Canadians to get tested if they are at risk of having been infected and to maintain physical distancing in public areas. Affiliations 1 Public Health Risk Sciences Division, Public Health Agency of Canada, St-Hyacinthe, QC 2 Centre for Surveillance and Applied Research, Public Health Agency of Canada, Ottawa, ON 3 School of Epidemiology and Public Health, University of Ottawa, Ottawa, ON 4 Health Analysis Division, Statistics Canada, Ottawa, ON 5 Department of Community Health Sciences, University of Calgary, Calgary, AB 6 Public Health Risk Sciences Division, Public Health Agency of Canada, Guelph, ON *Correspondence: antoinette.ludwig@canada.ca Suggested citation: Ludwig A, Berthiaume P, Orpana H, Nadeau C, Diasparra M, Barnes J, Hennessy D, Otten A, Ogden N. Assessing the impact of varying levels of case detection and contact tracing on COVID-19 transmission in Canada during lifting of restrictive closures using a dynamic compartmental model. Can Commun Dis Rep 2020;46(11/12):409–21. https://doi.org/10.14745/ccdr.v46i1112a08 Keywords: COVID-19, case detection, contact tracing, dynamic compartmental model, Canada This work is licensed under a Creative Commons Attribution 4.0 International License. Introduction The coronavirus disease 2019 (COVID-19) pandemic is a global health threat on a scale that was not seen in a century. The first cases of a cluster of pneumonia in Wuhan, China were reported to the World Health Organization (WHO) on December 31, 2019 with the cause of the outbreak identified as a novel coronavirus (now called severe acute respiratory syndrome coronavirus 2; SARS-CoV-2) on January 7, 2020 (1). Cases were soon detected outside China, with the first case of COVID-19 identified in Canada on January 25, 2020 in a resident who had returned from Wuhan, China (2,3). As of September 16, 2020, there have been 28.6 million confirmed cases of COVID-19, and over 900,000 deaths, globally (4); within Canada, there have been 139,747 confirmed cases and 9,193 deaths (3). A number of researchers have developed dynamic models of COVID-19 transmission to explore the effects of public health interventions for Canadian jurisdictions, including in Ontario (5–7) and British Columbia (similar findings have been mailto:antoinette.ludwig%40canada.ca?subject= https://creativecommons.org/licenses/by/4.0/ https://creativecommons.org/licenses/by/4.0/ https://creativecommons.org/licenses/by/4.0/ OVERVIEW CCDR • November 5, 2020 • Vol. 46 No. 11/12Page 410 found in personal communications, Anderson et al. Estimating the impact of COVID-19 control measures using a Bayesian model of physical distancing. medRxiv 2020), while many provinces and territories have released the results of COVID-19 modelling (8–12). Given the observed variation in the risk of severe outcomes of COVID-19 by age (13,14), and the need to consider differences in contact and transmission rates amongst age groups (15,16), age stratification is an important consideration for dynamic models of COVID-19. As of early July 2020, only a minority of the models for Canada or its provinces presented in the peer-reviewed or pre-print literature are age-structured (similar findings can be found in personal communications, Tuite et al. Reduced COVID-19-Related Critical Illness and Death, and High Risk of Epidemic Resurgence, After Physical Distancing in Ontario, Canada. medRxiv 2020). In Canada, public health intervention strategies including physical (social) distancing, case detection and isolation, contact tracing and quarantine of contacts, among others (16,17) have been implemented with the aim of slowing the spread of the epidemic, reducing peak health care demand, reducing the possibility of infection for those most at risk of severe outcomes of the disease and reducing the overall number of deaths (18). In order to implement and optimize effective interventions, decision-makers in Canada need information on the relative impact of these measures. They also need to assess scenarios for lifting restrictive closures (e.g. stay-at-home orders, workplace, school and university closures, which may have severe economic and non-COVID-19 health impacts), while avoiding resurgence of the epidemic (often termed a “second wave”) in a Canadian population that remains largely naïve to this infection. The objectives of this paper are 1) to present an aged-stratified dynamic compartmental model developed by the Public Health Agency of Canada in collaboration with Statistics Canada and 2) to model the impact of non-pharmaceutical interventions (NPIs) including case detection/isolation, contact tracing/quarantine and changes in the level of physical distancing associated with lifting restrictive closures, on the attack rate of COVID-19 infection in Canada. Simulations of the epidemic Model presentation An age-stratified dynamic deterministic compartmental model using the susceptible, exposed, infected, removed framework, was developed and applied to the Canadian population stratified into six age groups. Model states are presented in Figure 1. Transmission between individuals can occur within or between age groups at rates influenced by the daily contact number, based on the matrix projected for Canada by Prem et al. (19). Individuals in quarantine were assumed to interact with a maximum of one person daily during the course of the quarantine. As the model aimed to explore the epidemic over a short time period (730 days), the model had a closed Detected isolated Latent Susceptible Not detected and not in quarantine Latent in quarantine Latent in the general population Infectious (pre/a)- symptomatic in quarantine Susceptible Infectious detected (asymptomatic or mild symptomatic) in the general population Infectious detected, with severe symptoms, in hospital sorting Infectious detected, with severe symptoms, before going to hospital Hospitalized in general care service Hospitalized with vent Hospitalized in ICU Hospitalized who can’t access vent Hospitalized who can’t access ICU Recovered Dead Legend Infectious not detected (asymptomatic or mild symptomatic) in the general population Infectious (pre/a)- symptomatic in the general population Severe case who don’t access hospital general care services Infectious not detected (asymptomatic or mild symptomatic) in quarantine In quarantined Process by which the hospital system is overwhelmed In hospital Figure 1: Diagram of the states and flows of the model Abbreviation: ICU, intensive care unit The susceptible state is the brown box; yellow boxes are latent infection states, blue boxes are detected and isolated case states; green boxes are quarantined contact states; orange boxes are undetected and non-quarantined or isolated case states; red boxes are hospitalized case states, the purple box is the recovered case state, and the grey box indicates deaths. The orange triangles indicate processes by which hospital systems may be overwhelmed if the need for hospital services exceeds available resources CCDR • November 5, 2020 • Vol. 46 No. 11/12 Page 411 OVERVIEW population with no births or non-COVID-19 related deaths, with a population comprising susceptible people at the beginning of the epidemic. Cases who recovered were assumed not to be susceptible to re-infection during the time period of the model (730 days). The model also assumed the infectivity of presymptomatic infectious individuals who become symptomatic was the same as that of symptomatic individuals, as well as individuals who remained asymptomatic throughout the course of infection. Assuming that all detected cases went into isolation, so case detection was a proxy for isolation (see Table 1). See Appendix A for a description of population flows in the model. While the model includes compartments for hospitalizations, intensive care unit (ICU) admissions, those in ICU on ventilators, and deaths, here are the results of the model for number of cases only. Model equations can be found in Appendix B. Parameterization and initialization of model Assuming that the first community transmission of SARS-CoV-2 in Canada was February 8, 2020. The simulations were run for the entire Canadian population (N=37,894,799 inhabitants), stratified in six age groups as shown in Appendix A Table S1 and Table S2 (19,20). Parameter values were set according to observed data for Canada (when available) and values in the literature (see Table S2 in Appendix A), obtained in a scan of the COVID-19 literature (published and pre-published) conducted daily by the Public Health Agency of Canada. Searches to retrieve relevant COVID-19 literature were conducted in Pubmed, Scopus, BioRxiv, MedRxiv, ArXiv, SSRN, Research Square and cross-referenced with the literature on the WHO COVID-19 literature list, and COVID-19 information centers run by Lancet, BMJ, Elsevier and Wiley. Literature with relevant prioritized outcomes were identified from the daily scan and parameter values were recorded in a data-extraction form. Model parameters are reassessed weekly according to new research. The choice of the literature source was made according to the relevance and quality of the publication. Estimates were chosen to reflect the most likely value based on minimum and maximum estimates from studies identified from the literature scanning process, using geography, date of study, sample size and target population as criteria in the choice of the retained literature. Estimates from Canada or similar countries, those with more recent study dates, larger sample sizes and more representative samples were prioritized. A simple calibration of the probability of successful transmission (beta) of SARS-CoV-2 from an infectious person to an uninfected person when they make contact was obtained (Figure 2). This was achieved through iterative trials that compared a target curve based on reported cases from February 8 to May 4, 2020 (21), and simulation results for the same period. The target curve was obtained from increasing the observed count by 25% (assuming later in the epidemic reported cases underestimate the actual number by 25%: personal communication, Dougherty et al., September 15, 2020), and moving the entire curve to be one week earlier (assuming each case was reported one week later than symptom onset). The number of reported cases in the target curve and the number of simulated cases were compared visually to ensure that the parameter values for the simulations were reasonable before assessing the impacts of NPIs. Initial values for each model state were set according to the number of cases reported in Canada at February 8, 2020, which was seven cases. The epidemic was initiated with 10 latent individuals, 20 presymptomatic individuals and two individuals with mild symptoms in the general population. The values were chosen to be higher than the observed number of cases to reflect both likely underdetection of cases, as well as the lag between the moment of exposure and the detection and declaration of cases. All other model state variables were set to zero. Case detection/ isolation Contact tracing and quarantine 0.30 0.40 0.50 0.60 0.70 0.80 Contact rate reduced by 50% after day 88 0.30 53.57 51.68 49.66 47.49 45.15 42.62 0.40 44.21 41.06 37.61 33.84 29.71 25.24 0.50 31.92 27.10 21.86 16.35 11.09 7.06a 0.60 16.46 10.82 6.61a 4.34a 3.25a 2.66a 0.70 4.69a 3.35a 2.68a 2.29a 2.05a 1.88a 0.80 2.33a 2.06a 1.88a 1.75a 1.65a 1.58a Contact rate reduced by 33% after day 88 0.30 68.68 67.41 66.04 64.56 62.95 61.20 0.40 62.54 60.37 57.95 55.26 52.24 48.84 0.50 54.22 50.68 46.65 42.02 36.70 30.61 0.60 42.70 37.17 30.77 23.49 15.67 8.86a 0.70 26.68 18.89 11.18 6.02a 3.82a 2.88a 0.80 8.34a 4.69a 3.23a 2.56a 2.19a 1.96a Contact rate reduced by 16.7% after day 88 0.30 76.56 75.65 74.66 73.58 72.41 71.13 0.40 72.20 70.63 68.87 66.89 64.66 62.13 0.50 66.27 63.67 60.67 57.19 53.10 48.29 0.60 57.92 53.73 48.74 42.77 35.59 27.03 0.70 45.80 39.18 31.21 21.85 12.20 6.03a 0.80 27.95 18.53 9.65a 4.96a 3.28a 2.57a Table 1: Variation of the attack rate (at day 730) for different levels of case detection/isolation, contact tracing/quarantining and physical distancing, after day 88, May 4, 2020 a Scenarios where epidemic control maintained attack rate below 10% (green) OVERVIEW CCDR • November 5, 2020 • Vol. 46 No. 11/12Page 412 The model was implemented in R using RStudio, using the following packages: adaptivetau; deSolve; dplyr; DT; forcats; ggplot2; htmlwidgets; lhs; magrittr; openxlsx; plotly; readxl; scales; tidyr; and triangle. Code is available upon request to the authors. No ethics approval was required as all data were based on surveillance reports publically available from the Public Health Agency of Canada and published literature sources. Simulations of non-pharmaceutical interventions A total of 108 possible epidemics were simulated to assess the impact of different levels of case detection/isolation and contact tracing/quarantine under three scenarios for different levels of contact rates due to changes in physical distancing following de-escalation of restrictive closures as of May 4, 2020 (day 88). The study design is represented in Figure 3. From day 0 until day 88, all three scenarios are identical and involved constant levels of case detection/isolation (a conservative 40% of cases detected) and contact tracing/quarantine (40% traced and quarantined) while physical distancing (and thus the contact rates) varied according to the following: 1) an initial period of 40 days during which the level of daily contacts corresponded to what is normally observed in the general population; 2) a seven-day period during which the daily contact rate was gradually reduced by 50% to represent the implementation of physical distancing associated with the start of implementation of restrictive closures in Canada; and 3) a period of 40 days (from day 47 to day 87) over which physical distancing due to the restrictive closures maintained contact rates at 50% below pre-COVID-19 levels. From day 88 (the date of lifting restrictive closures), there were three scenarios for physical distancing: 1) physical distancing was kept such that contact rates remained 50% less than pre-COVID-19 levels (i.e. restrictive closures are not lifted); while in 2) and 3) restrictive closure were lifted to allow contact rates to increase, respectively, to 33% or 16.7% below pre-COVID-19 levels until the end of the simulation. Six levels of case detection/isolation (from 30% to 80% in 10% increments) and six levels of contact tracing/quarantine (from 30% to 80% by 10% increments) were simulated for each one of the three scenarios of physical distancing, for a total of 108 simulated epidemics. Outcome measures The attack rate was the primary outcome of the simulation experiments, consisting of the cumulative number of infected people over the entire initial population, for the entire 730 days of the epidemic, or at the end of the simulation period if the epidemic was not completed. Simulations longer than two years were considered as unrealistic given the assumption that recovered individuals do not return to the susceptible state during the simulation. Currently, there is not enough scientific evidence to confirm post-infection immunity in all recovered cases, or the duration of immunity any individual may achieve from a COVID-19 infection (22–24). Attack rates below 10% were considered corresponded to a condition of “epidemic control” of COVID-19 in Canada, below which the healthcare system was less likely to be overwhelmed. A analysis of sensity of the attack rate to an increase or decrease of the transmission coefficient (beta) by 10% (using the formula Sensitivity=((Vi - V0)/V0)/(|(Ti - T0)/T0|) (25) was performed, where V0 is the attack rate without changes to input data [T0] and Vi is the attack rate with a given increase or decrease of input [Ti]). Day 40 March 17th Day 47 March 24th Day 88 May 4th 40% of case are detected 6 levels of case detection rate (30% to 80%, by 10%) 6 levels of contact tracing rate (30% to 80% by 10%) 40% of detected cases’ contacts are traced and quarantined C as e de te ct io n/ is ol at io n P hy si ca l d is ta nc in g C on ta ct tr ac in g an d qu ar an tin in g Easing physical distancing - 3 levels: 50%/33%/16.7% less contact than normal Maintaining physical distancing Implementing physical distancing (50% less contact than normal) No physical distancing Day 0 Feb 8th 0 5 10 15 0 20 40 60 80 100 120 Time A ve ra g e co nt ac t ra te in t he g en er al p o p ul at io n Start of epidemic in Canada Figure 3: Simulation study design showing initial period of epidemic (before day 88) During implementation of, and while maintaining physical distancing, along with a consistent level of case detection/isolation and contact tracing/quarantine; and second period of epidemic (after day 88) with varying levels of physical distancing (red at 16.7%, blue at 33% and green at 50% less contact than normal), case detection and contact tracing 0 10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 0 10 20 30 40 50 60 70 80 90 C um ul at iv e ca se s Time (days) Observed cases Corrected observed cases Infectious simulated Figure 2: Comparison of observed cases in Canada from February 8 (day 1) to May 4, 2020 (day 88) Corrected cases (assuming one week of delay between infection end detection, and a level of underreporting of 25%) corresponding to the target curve, and simulated cumulative infectious cases with the age-stratified model CCDR • November 5, 2020 • Vol. 46 No. 11/12 Page 413 OVERVIEW Outcomes Attack rates of the 108 simulations are presented in Table 1 and illustrated in Figure 4; both table and figure show how the attack rate reduction evolved according to the different levels of NPI. Results showed that relaxing physical distancing at day 88 (40 days after its implementation) had a significant impact on the attack rate in all the simulated epidemics, with the attack rate varying between 1.6% and 76.6%. The extent of the impact of the easing of physical distancing varied according to the values of the other control measures already in place; i.e. the case detection/isolation rate and the contact tracing/quarantine rate. An attack rate below 10%, which was considered here to represent epidemic control, was much more frequent when the contact rate was kept at 50% level below normal after day 88, compared with lower levels of physical distancing. Additionally, a level of case detection/isolation of 70% or more allowed for control of the simulated epidemics at all levels of contact tracing above 30% when physical distancing is maintained at 50% below normal levels. However, the level of case detection and contact tracing needed to control the epidemic increased markedly if physical distancing was not maintained to reduce contact rates. The results also suggest that the relative impact of case detection/isolation on the decrease of the attack rate appeared to be higher than that of contact tracing. Even with contact tracing at levels as high as 80%, 50% of cases had to be detected to control the epidemic when physical distancing kept contact rates 50% lower than pre-COVID-19 levels. An even higher level of case detection was required when physical distancing was lifted to allow contact rates to rise to 16.7% or 33% below pre-COVID-19 levels. The sensitivity analysis for beta showed that the average percent change for the attack rate was lower than 10% in most scenarios, increasing with increasing beta (8.1%; SD=9.2%; data not shown) and decreasing with decreasing beta (4.1%; SD=2.9%). When beta was increased, the number of combinations of case detection and contact tracing rates resulting in an attack rate less than 10% reduced by half (from 32 to 16) while decreasing beta resulted in an increase (from 32 to 43) in the number of combinations resulting in an attack rate less than 10% (see Appendix C). Discussion Summary of key findings This work highlights, in order of importance, that ensuring a relatively high level of detection/isolation of cases and tracing/ quarantine of potentially infected cases while maintaining some personal physical distancing will all be necessary to avoid a resurgence of the epidemic in Canada. Comparison with other studies These results are in accordance with an example presented in Ogden et al. (26), based on a deterministic compartmental model that was not age stratified. Additionally, similar studies that assessed the impact of NPIs for Canada as a whole, or for a specific Canadian province, have come to similar conclusions (5,27,28) (similar findings have been found in personal communication,Tuite et al. Reduced COVID-19-Related Critical Illness and Death, and High Risk of Epidemic Resurgence, After Physical Distancing in Ontario, Canada. medRxiv 2020 and in Eastman et al. Mathematical modeling of COVID-19 containment strategies with considerations for limited medical resources. medRxiv. 2020). Even if a direct comparison between results in different studies is difficult because of differences in details of the modelling study design (study region, epidemic start date, inclusion or not of stochasticity and epidemic outbreak metric), they all concluded that control of the epidemic requires a combination of three things: 1) maintenance of some level of physical distancing (for a minimum of 10 months according to Tuite et al. (5)); 2) enhanced detection of cases; and 3) tracing and quarantine of contacts, to minimize the attack rate. Strengths and limitations A major strength of this study is that it provides a clear signal of the potential impact of lifting restrictive closures (represented in this study by release of physical distancing), which began in many jurisdictions within Canada around mid-May 2020. The results of the simulation experiments presented here demonstrated that during the lifting restrictive closures, public health decision-makers and practitioners will need to maintain continued vigilance to avoid the resurgence of the COVID-19 epidemic (a "second wave"), through the maintenance of a high level of case detection and contact tracing and some level of physical distancing. A further strength of this work is that the 0 10,0000 20,0000 30,0000 40,0000 50,0000 60,0000 70,0000 80,0000 0 100 200 300 400 500 600 700 N um b er o f in fe ct ed Time (days) Contact rate reduced by 50% after day 88 Contact rate reduced by 33% after day 88 Contact rate reduced by 16.7,% after day 88 Figure 4: Simulation of the epidemic for three scenarios after day 88, May 4, 2020 Case detection/isolation at 70%, contact tracing/quarantine at 50% and contact rate reductions of 50%, 33% or 16.7% below pre-pandemic levels. Values for days before 88 are described in Figure 3. The y-axis includes all individuals in the infectious states—presymptomatic, symptomatic (hospitalized or not) and asymptomatic OVERVIEW CCDR • November 5, 2020 • Vol. 46 No. 11/12Page 414 chosen model states are comprehensive and account for the main disease statuses, including latent and presymptomatic states. Additionally, the model accounts for the age structure in the Canadian population, which is an important element of transmission risk heterogeneity (29). Finally, modeling the case detection level instead of the ratio of asymptomatic cases has allowed to circumvent the difficulty of obtaining precise information on the number of asymptomatic cases, which is a still a challenge for COVID-19 modelling. A limitation of this study, which applies to most mathematical modelling work, is that translating the levels of NPI modelled into the real world is not always easy for the public health stakeholders and can be open to interpretation. In this study, we used our current best estimates for parameter values; however, these values may change as knowledge of COVID-19 increases. The preliminary sensitivity analysis that was conducted shows that the results were relatively robust to changes in beta (the transmission coefficient); therefore, the attack rate values obtained here should be considered as illustrative of the principle that increased case detection and contact tracing, as well as maintenance of some physical distancing, will be needed to control the epidemic as restrictive closures are lifted. Additionally, the model does not account for delays between onset of symptoms and case detection or between case detection and contact tracing/quarantining. It is recognized that these delays exist and have been reported elsewhere in the world (30). In the United States and the United Kingdom, it has been shown that these delays are subject to significant variation depending on the study population, the strength of symptoms and the vulnerability of the person, though no published estimates of these delays are yet available for Canada (Personal communication, Lawless et al. Estimation of Symptomatic Case Counts and the COVID-19 Infection Curve Through Reporting Delay Adjustment: An Observational Study of Ontario Surveillance). Finally, the contact matrices used are the result of projections for Canada based on data from other countries in Europe and corrected for socio-demographic and health factors (19). Actual contact rate data for Canada would strengthen future versions of this model. Implications and next steps his study underlines the importance of a cautious approach to lifting restrictive closures. It appears that maintaining some level of physical distancing (for example, by limitations on the size of gatherings, maintaining a two metre distance, or maintaining a social bubble) or other non-pharmaceutical measures (such as wearing non-medical masks) combined with high levels of case detection and contact tracing are key components of epidemic control. It this context, it seems important to support strategies aimed at encouraging people to get tested when they may have been exposed to suspected or confirmed COVID-19 cases, encouraging people to respect isolation instructions as well as strategies that support personal protection measures, such as mandating the use of non-medical masks in indoor public settings (31), in order to offset the risk of infection from the increase of physical proximity of citizens that comes with re-opening. Conclusion This paper presents an aged-stratified dynamic compartmental model for the transmission of COVID-19 in Canada. As well, these results provide estimates of the impact of NPIs, including case detection/isolation, contact tracing/quarantine and changes in the level of physical distancing, on the COVID-19 attack rate, for a period of time after mid-May 2020, when lifting of restrictive closures began at a national level. The model and analyzed scenarios demonstrate that case detection/isolation and contact tracing/quarantine, along with reduced rates of contact through some form of physical distancing, will be essential for future control of the COVID-19 epidemic. Authors’ statement AL, PB and NO — Conceptualization AL, PB, AO, HO — Data curation (parameter values) AL, PB, CN, DH, JB, MD — Analysis AL, PB, HO — Writing–original draft AL, PB, NO, AO, HO, CN, DE, JB, MD — Writing–review and editing NO — Supervision AL, PB — Contributed equally to this work Competing interests None. Acknowledgements The authors would like to thank the Knowledge Synthesis team members within Public Health Risk Sciences Division of Public Health Agency of Canada. Their daily literature scans and summarization of SARS-CoV-2 publications contributed to the quick preparation of the work presented here. Funding This work was supported by the Public Health Agency of Canada. CCDR • November 5, 2020 • Vol. 46 No. 11/12 Page 415 OVERVIEW References 1. World Health Organization. Novel coronavirus (2019-nCov) Weekly Epidemiological Update and Weekly Operational Update. September 14, 2020 Weekly Epidemiological Update. Geneva (Switzerland): WHO; 2020. https://www.who.int/docs/default-source/coronaviruse/ situation-reports/20200914-weekly-epi-update-5.pdf?sfvrsn= cf929d04_2&download=true 2. Silverstein WK, Stroud L, Cleghorn GE, Leis JA. First imported case of 2019 novel coronavirus in Canada, presenting as mild pneumonia. Lancet 2020;395(10225):734. DOI PubMed 3. 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After the latent period, the individuals become infectious without developing symptoms— for individuals who will develop symptoms, this corresponds to a presymptomatic state (states Iq_pres or I_pres depending on whether the individual is quarantined or not). For individuals who will remain asymptomatic, the state we call presymptomatic simply corresponds to the first phase of their infectious period, until they may be detected, or not. Individuals are then either detected (a fraction of mild symptomatic individuals, asymptomatic individuals and all with severe symptoms) or not (most of the asymptomatic and a fraction of the mild symptomatic). Detected individual with mild symptoms or who are asymptomatic are isolated at home, while detected individuals with more severe symptoms enter the hospitalization section of the model. Undetected individuals, either with mild symptoms or who are completely asymptomatic are not isolated and are considered to continue to contribute to the epidemic for as long as their infectious period, at which point they recover. Once in the hospital states, depending on severity, individuals move to one of three possible compartments: a general non-emergency ward, an intensive care unit (ICU) if they are a severe case, or an ICU unit with ventilation for the most critical patients. The model accounts for lack of care for severe cases in the situation where hospital capacity is overwhelmed. Each severe case can either die or recover. State definitions can be found in Table S1. Appendix A: Model flow, compartment definitions, parameter definitions and values Table S1: Model compartment definitions and values State Definitions Initial values S Susceptible Stratification by age group, StatCan Population estimates July 1, 2019 (32) Ages 0–10 estimate of 3,982,527 Ages 10–20 estimate of 4,146,397 Ages 20–40 estimate of 10,286,131 Ages 40–60 estimate of 10,069,708 Ages 60–75 estimate of 6,315,255 Ages 75+ estimate of 2,789,244 Lq Latent in quarantine 0 Table S1: Model compartment definitions and values State Definitions Initial values L Latent in the general population (not in quarantine) 10 I_pres Infected presymptomatic in the general population (and first infectious period for asymptomatic) 20 Iq_pres Infected presymptomatic in quarantine (and first infectious period for asymptomatic) 0 Iqnd Infected in quarantine not detected (asymptomatic or mild symptom) 0 Ind Infected non-detected (asymptomatic or mild symptom) in the general population 2 Idam Infectious detected asymptomatic or with mild symptoms in the general population 0 Idss Infected detected between onset of symptoms, that are severe, and going to the hospital 0 Iss_hosp Infected with severe symptoms who are in hospital sorting 0 H_g_OK Infected with severe symptoms who stay at the hospital in the general care service 0 H_ICU_ OK Infected with severe symptoms who stay at the hospital in ICU 0 H_vent_ OK Infected with severe symptoms who stay at the hospital with ventilation 0 H_g_ denied Infected with severe symptoms who are not able to access hospital care because of insufficient/overwhelmed local capacity 0 H_ICU_ denied Infected with severe symptoms who are not able to access ICU because of insufficient/ overwhelmed local capacity 0 H_vent_ denied Infected with severe symptoms who are not able to access ventilation because of insufficient/overwhelmed local capacity 0 R Recovered 0 D Dead 0 Abbreviation: ICU, intensive care unit OVERVIEW CCDR • November 5, 2020 • Vol. 46 No. 11/12Page 418 Parameter name Definition Value Evidence beta Probability of transmission when contact made with infectious person Ages 0–10 average value of 0.041 Ages 10–20 average value of 0.041 Ages 20–40 average value of 0.041 Ages 40–60 average value of 0.041 Ages 60–75 average value of 0.041 Ages 75+ average value of 0.041 Based on Stilianakis et al. (33) and adjusted using data from the beginning of the epidemic (Figure 2 in the article) lambda Proportion of exposed to detected infectious who are traced and quarantined (contact tracing/ quarantine) Value of 40% until day 87 From day 88 up to the end of the epidemic, the value varied according to control scenarios NA cgg Number of daily contacts between two individuals from the general population 6*6 matrix Average value of 12.6 from day 0 to day 40 (see below) Linear decrease of 50% from days 41 and 47 Value of 50% below normal from day 48 until day 87 From day 88 up to the end of the epidemic, the value varied according to control scenarios Based on Prem et al. (19) cgq Number of daily contacts between an individual from the general population and an individual from the quarantined population 6*6 matrix identical during all the duration of the simulation We assumed a person in quarantine is in contact with a maximum of one person each day during his/her quarantine period. The value of one was then standardized according to the total population size in each stratum 20sigma Latent period (days) 4.12 days Based on Li et al., 2020 (34) delta Proportion of presymptomatic infectious cases that will be identified (or detected) Value of 40% until day 87 From day 88 and to the end of the epidemic, the value varied according to control scenarios NA alpha Proportion of cases who develop severe symptoms Ages 0–10 average value of 0.02 Ages 10–20 average value of 0.02 Ages 20–40 average value of 0.04 Ages 40–60 average value of 0.10 Ages 60–75 average value of 0.30 Ages 75+ average value of 0.41 Based on Public Health Agency of Canada (21) tpres Period of time between onset of infectiousness and onset of symptoms in those developing symptoms OR first infectious period for asymptomatic 2 days Based on He et al., 2020 (35) Age group 0–10 10–20 20–40 40–60 60–75 75+ 0–10 0.47 0.09 0.26 0.14 0.03 0.00 10–20 0.06 0.61 0.17 0.15 0.01 0.00 20–40 0.07 0.11 0.53 0.26 0.02 0.00 40–60 0.07 0.15 0.34 0.40 0.04 0.00 60–75 0.09 0.09 0.26 0.28 0.27 0.02 75+ 0.10 0.14 0.18 0.31 0.17 0.10 Table S2: Model parameters, definition, values and evidence Age group 0–10 10–20 20–40 40–60 60–75 75+ 0–10 4.60 0.89 2.59 1.38 0.34 0.04 10–20 1.03 0.61 2.80 2.45 0.21 0.03 20–40 1.15 1.67 8.18 4.05 0.35 0.04 40–60 1.00 2.17 4.89 5.83 0.60 0.07 60–75 0.63 0.65 1.89 2.06 1.98 0.14 75+ 0.45 0.66 0.84 1.42 0.77 0.46 CCDR • November 5, 2020 • Vol. 46 No. 11/12 Page 419 OVERVIEW Parameter name Definition Value Evidence tsm Period of time between onset of symptoms and recovery for cases with mild symptoms OR second infectious period for asymptomatic 6 days Based on Wölfel et al., 2020 (36) and He et al., 2020 (35) tsph Period between symptom onset for cases with severe symptoms and being taken care of by the health system 3 days Based on Khalili et al., 2020 (37) pICU Proportion of hospitalized cases who require/access to ICU in hospital Ages 0–10 average value of 0.20 Ages 10–20 average value of 0.35 Ages 20–40 average value of 0.36 Ages 40–60 average value of 0.46 Ages 60–75 average value of 0.46 Ages 75+ average value of 0.19 Based on Public Health Agency of Canada (21) pvent Proportion of hospitalized cases who require/access to ventilation (Vent) 0 This will be updated in future models once age-specific data become available tsorting Period of time for sorting severe cases in hospital (before general service, ICU or Vent) 1 day We assume it takes one day on average between when a severe case arrives in the hospital and when the case is sorted to the appropriate service mg Mortality rate for severe cases in hospital that do not require ICU or Vent (general) Ages 0–10 average value of 0 Ages 10–20 average value of 0 Ages 20–40 average value of 0 Ages 40–60 average value of 0.02 Ages 60–75 average value of 0.14 Ages 75+ average value of 0.34 Based on Public Health Agency of Canada (34) mICU Mortality rate for severe cases dying in hospital (ICU) Ages 0–10 average value of 0 Ages 10–20 average value of 0 Ages 20–40 average value of 0.06 Ages 40–60 average value of 0.15 Ages 60–75 average value of 0.32 Ages 75+ average value of 0.57 Based on Public Health Agency of Canada (34) mVent Mortality rate for severe case dying in hospital (Vent) NA Not calibrated because this parameter has no impact on the results (e.g. attack rate) presented in this article thr Period of time between first day in hospital after sorting, and recovery or death 12 days Based on hospitalization and length of stay of COVID-19 cases (38–40) mg- Mortality rate for severe cases dying at home because they are not able to access hospital care NA Not calibrated because this parameter has no impact on the results (e.g. attack rate) presented in this article mICU- Mortality rate for severe cases dying in hospital because they are not able to access ICU NA Not calibrated because this parameter has no impact on the results (e.g. attack rate) presented in this article Table S2: Model parameters, definition, values and evidence (continued) Abbreviations: ICU, intensive care unit; NA, not applicable; Vent, ventilator OVERVIEW CCDR • November 5, 2020 • Vol. 46 No. 11/12Page 420 dS / dt = - S * beta * 1/N*[(1-lambda*delta) * ( cgg * (I_pres + Ind) + cgq * (Iq_pres + Iqnd)) + lambda * delta *( cgg * (I_pres + Ind) + cgq * (Iq_pres + Iqnd))] dLq / dt = S * beta *1/N* lambda * delta *( cgg * (I_pres + Ind) + cgq * (Iq_pres + Iqnd)) - Lq / sigma dL / dt = S * beta *1/N* (1-lambda *delta) * ( cgg * (I_pres + Ind) + cgq * (Iq_pres + Iqnd)) - L / sigma dIpres / dt = L / sigma - Ipres / tpres dIq_pres/ dt = Lq / sigma - Iq_pres / tpres dIqnd / dt = Iq_pres *( 1-delta) / tpres - Iqnd / tsm dInd / dt = Ipres *( 1-delta) / tpres - Ind / tsm dIdam / dt = (Iq_pres + Ipres)* delta* (1- alpha) / tpres - Idam / tsm dIdss / dt = (Iq_pres + Ipres)* (delta* alpha) / tpres - Idss / tsph dIss_hosp / dt = Idss / tsph - Iss_hosp / tsorting dH_g_OK/ dt = Iss_hosp * (1-pICU-pvent) / tsorting - H_g_OK / thr dH_ICU_OK / dt = Iss_hosp * pICU / tsorting - H_ICU_OK / thr dH_vent_OK / dt = Iss_hosp * pvent / tsorting - H_vent_OK / thr dH_g_denied / dt = 0 * Iss_hosp * (1-pICU-pvent) / tsorting - H_g_ denied / thr where 0 comes from the assumed infinite capacity. dH_ICU_denied / dt = 0 * Iss_hosp * (pICU) / tsorting - H_ICU_denied / thr where 0 comes from the assumed infinite capacity. dH_vent_denied / dt = 0 * Iss_hosp * (pvent) / tsorting - H_vent_ denied / thr where 0 comes from the assumed infinite capacity. dR / dt = Idam / tsm + Ind / tsm + Iqnd / tsm + H_g_OK * (1- mg ) / thr + H_g_denied * (1- mg- ) / thr + H_ICU_OK * (1- mICU ) / thr + H_ICU_denied *(1- mICU- ) / thr + H_vent_OK * (1- mVent ) / thr dD / dt = H_g_OK * mg / thr + H_g_denied * mg- / thr + H_ICU_OK * mICU / thr + H_ICU_denied * mICU- / thr + H_vent_OK * mVent / thr + H_vent_denied / thr Appendix B: Equations CCDR • November 5, 2020 • Vol. 46 No. 11/12 Page 421 OVERVIEW Appendix C: Sensitivity analysis for beta Case detection/ isolation Contact tracing and quarantine 0.30 0.40 0.50 0.60 0.70 0.80 Attack rate for a beta 10% higher than expected (beta=0.045) Contact rate still reduced by 50% after day 88 0.30 59.09352 57.4983 55.78916 53.9561 51.98852 49.87534 0.40 51.116 48.47224 45.58901 42.44803 39.03661 35.35465 0.50 40.72402 36.72655 32.39552 27.80149 23.12042 18.6755 0.60 27.68375 22.66857 17.92792 13.9703 11.07788 9.127013a 0.70 14.67835 11.41256 9.222685a 7.797606a 6.846839a 6.184861a 0.80 7.997407a 6.941327a 6.220808a 5.706796a 5.325164a 5.032136a Contact rate reduced by 33% after day 88 0.30 72.12056 71.03947 69.87305 68.6118 67.24506 65.76064 0.40 66.84949 65.00664 62.96262 60.688 58.14878 55.30608 0.50 59.74349 56.76575 53.38173 49.5269 45.13509 40.15337 0.60 49.97753 45.37923 40.1135 34.16619 27.6911 21.21683 0.70 36.56815 30.14937 23.41448 17.23498 12.63568 9.755943a 0.80 20.20915 14.69697 10.93404 8.667255a 7.296874a 6.418942a Contact rate reduced by 16.7% after day 88 0.30 78.97424 78.18379 77.33041 76.40654 75.40348 74.31118 0.40 75.19535 73.84808 72.34734 70.66763 68.77832 66.64237 0.50 70.09167 67.88819 65.35466 62.42254 59.0075 55.00747 0.60 62.96743 59.44347 55.27892 50.33294 44.45665 37.55202 0.70 52.71792 47.23034 40.70934 33.12933 24.9225 17.4795 0.80 37.83963 30.13374 22.10612 15.33652 11.01025 8.593437a Attack rate for a beta 10% lower than expected (beta=0.037) Contact rate still reduced by 50% after day 88 0.30 46.32687 44.1102 41.73141 39.17554 36.42638 33.46669 0.40 35.37861 31.69369 27.6635 23.2589 18.45491 13.23975 0.50 21.11151 15.51616 9.487262a 4.352624a 2.026998a 1.268084a 0.60 4.446911a 1.925112a 1.178985a 0.892557a 0.747114a 0.659919a 0.70 0.917685a 0.750175a 0.655133a 0.594146a 0.551763a 0.520622a 0.80 0.594963a 0.550296a 0.517993a 0.493555a 0.474428a 0.459053a Contact rate reduced by 33% after day 88 0.30 64.06551 62.56878 60.95033 59.19649 57.29164 55.21801 0.40 56.83411 54.26817 51.41448 48.22939 44.66162 40.65115 0.50 47.04398 42.87674 38.12076 32.67411 26.42855 19.2982 0.60 33.54144 27.06095 19.59878 11.19984 4.000164a 1.648817a 0.70 14.97949 6.498159a 2.127114a 1.165722a 0.858549a 0.713186a 0.80 1.48164a 0.962062a 0.758895a 0.652422a 0.587167a 0.543146a Contact rate reduced by 16.7% after day 88 0.30 73.32151 72.24328 71.07465 69.80463 68.42056 66.90782 0.40 68.1969 66.33559 64.25373 61.91416 59.27188 56.27203 0.50 61.2006 58.12787 54.57939 50.45286 45.61944 39.91796 0.60 51.36095 46.40851 40.51931 33.46741 25.00128 14.98944 0.70 37.11735 29.3243 19.98326 9.323668a 2.537434a 1.234962a 0.80 16.33694 6.198483a 1.832707a 1.050737a 0.794449a 0.670077a a Scenarios where epidemic control maintained attack rate below 10% (green)