key: cord-1009283-wl0c4qpy
authors: Wilson, N.; Parry, M.; Verrall, A. J.; Baker, M. G.; Schwehm, M.; Eichner, M.
title: When Can Elimination of SARS-CoV-2 Infection be Assumed? Simulation Modelling in a Case Study Island Nation
date: 2020-05-20
journal: nan
DOI: 10.1101/2020.05.16.20104240
sha: da14deb28306557a5be41730f34147a926079ed3
doc_id: 1009283
cord_uid: wl0c4qpy

Aims: We aimed to determine the length of time from the last detected case of SARS-CoV-2 infection before elimination can be assumed at a country level in an island nation. Methods: A stochastic version of the SEIR model CovidSIM v1.1 designed specifically for COVID-19 was utilised. It was populated with data for the case study island nation of New Zealand (NZ) along with relevant parameters sourced from the NZ and international literature. This included a testing level for symptomatic cases of 7,800 tests per million people per week. Results: It was estimated to take between 27 and 33 days of no new detected cases for there to be a 95% probability of epidemic extinction. This was for effective reproduction numbers (Re) in the range of 0.50 to 1.0, which encompass such controls as case isolation (the shorter durations relate to low Re values). For a 99% probability of epidemic extinction, the equivalent time period was 37 to 44 days. In scenarios with lower levels of symptomatic cases seeking medical attention and lower levels of testing, the time period was up to 53 to 91 days (95% level). Conclusions: In the context of a high level of testing, a period of around one month of no new notified cases of COVID-19 would give 95% certainty that elimination of SARS-CoV-2 transmission had been achieved.

Some nations are attempting to eliminate the SARS-CoV-2 pandemic virus as in the case of New Zealand 1 and for Australia this has been articulated as a potential option. 2 It might also be the goal for the island jurisdiction of Taiwan and for South Korea, which has well controlled land borders (though neither of these places appears to have actually specified this goal).

Once a nation can declare itself having achieved elimination status it can potentially phase out restrictive disease control measures within the country, while maintaining tight border controls with quarantine for incoming travellers. It could also permit quarantine-free travel with other COVID-19 free nations, as envisaged by the Prime Ministers of Australia and New Zealand in terms of a trans-Tasman "bubble". 3 Similarly, the leaders of Austria, Greece, Israel, Norway, Denmark, the Czech Republic, Singapore, Australia and New Zealand "agreed that as each begins to ease restrictions they could capitalise on low infection rates by creating tourism safe zones". 4 We selected New Zealand as a case study island nation as it has an elimination goal, 1 has good border controls and is making steady progress towards elimination with occasional days in May 2020 with no new cases reported. 5 Some work has already been done on the elimination topic in New Zealand, with a modelling group 6 reporting that a "90 day period at Level 4 [intensive lock-down restrictions] leads to containment to very low levels by the end of the 90 day period". "This scenario leads to elimination in approximately 50% of stochastic realisations". Another study 7 estimated the probability that regions within New Zealand might have achieved elimination, with the District Health Board region with the highest number of days free of notified cases (Wairarapa at 16 days as of 18 April 2020) having a 92% probability of having eliminated the pandemic virus. However, none of this work has defined time periods for differing levels of probability for elimination being achieved at a whole country level. Estimating these periods was therefore the aim of this simulation study.

To run "time to elimination" analyses for New Zealand, we used a stochastic SEIR type model with key compartments for: susceptible [S], exposed [E] , infected [I] , and recovered/removed [R] . The model is a stochastic version of CovidSIM which was developed specifically for COVID-19 (http://covidsim.eu; version 1.1). Work has been published from previous versions of this model, 8 9 but in the Appendix we provide updated parameters and differential equations for version 1.1. A similar simulation approach was taken previously for a poliomyelitis elimination study. 10 The stochastic model was built in Pascal and 10,000 simulations were run for each set of parameter values.

The parameters were based on available publications and best estimates used in the published modelling work on COVID-19 (as known to us on 13 May 2020). Key components were: a starting position of 10 infected cases, the assumption of effective border control with no new imported cases, 80% of infected COVID-19 cases being symptomatic, 39.5% of cases seeking medical consultation in primary care settings, and 4% of symptomatic cases being hospitalised (see Table A1 in the Appendix for the full set of parameters used). The level of testing of symptomatic cases in primary care and for respiratory cases being tested when hospitalised (both at 95% coverage with test sensitivity of 89% 11 ), was as per a fairly optimal surveillance system conducting 7,800 tests per million people per week (slightly less than the level in New Zealand as per mid-May 2020 at 8, 190 tests per million people per week 12 ). Identified cases were transferred to supervised isolation which was assumed to be 95% effective. We considered different levels of transmission with the effective . 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 May 20, 2020. . https://doi.org/10.1101/2020.05.16.20104240 doi: medRxiv preprint 3 reproduction number (Re) of SARS-CoV-2 to be 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 (with extinction still occurring in the last case [Re = 1.0] due to accumulation of immune individuals after infection). These levels of Re were assumed to represent the summated total of pandemic-related physical distancing (voluntary and mandated), travel restrictions, hygiene behaviours, mask use, voluntary staying at home when unwell, and contact tracing resulting in quarantine of contacts.

In each stochastic simulation, the delay since the last detected cases was stored on a daily basis together with the information as to whether infection was still ongoing or was extinguished. The probability that extinction had occurred if no cases have been reported for a given number of days was calculated by dividing the number of such delays during extinction by the total number of such delays (ie, with ongoing transmission or with extinction). Other scenarios considered the impact of higher starting numbers of infected cases, and lower levels of attendance for medical consultations in primary care and also for the level of testing.

It was estimated to take between 27 and 33 days of no new detected cases for there to be 95% probability of epidemic extinction for effective reproduction numbers (Re) in the range of 0.5 to 1.0, combined with effective case isolation ( Table 1 ; the shorter durations relate to low Re values as depicted in Figure 1 ). This range was 37 to 44 days (around 5 to 6 weeks) for the 99% probability level. In scenarios with lower levels of symptomatic cases seeking medical attention and lower levels of testing, the time period was up to 53 to 91 days (second scenario in Table 1 ; Figure 2 ; for the 95% level of probability). Starting the simulations with 100 or 1000 initially infected cases instead of 10, made no meaningful difference ( Figure 2 ). This was expected because while there are 1000 or 100 infected individuals in the population, the frequency of very short case-free intervals of up to a few days at most are very frequent whereas long case free intervals of weeks are virtually impossible. Only after the number of cases has dropped to very low numbers, case-free periods of weeks may occasionally occur despite ongoing transmission. Also only for such long case-free periods is there an ambiguity whether extinction has occurred or not, whereas nobody would assume that extinction has occurred if no cases have been reported for two or three days. . 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 May 20, 2020. . https://doi.org/10.1101/2020.05.16.20104240 doi: medRxiv preprint Figure 1 : Probability that pandemic virus extinction has occurred according to different Re values. The chart shows extinction probabilities if no new COVID-19 cases have been reported for a given number of days (10,000 simulations starting with 10 infectious cases for each value of Re). The curves from left to right relate to Re = 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, respectively. Figure 2 : Probability that pandemic virus extinction has occurred according to different numbers of initial cases and testing proportions. The chart shows extinction probabilities if no new COVID-19 cases have been detected for a given number of days (effective reproduction number Re=0.8; 10,000 simulations each scenario). The three black curves on the left (nearly undistinguishable) give the results obtained when starting the simulations with 10 (solid), 100 (dotted) or 1,000 (dashed) infections, respectively. The dark grey curve shows the result when only 30% of COVID-19 patients seek medical attention and only 60% of them are tested (Scenario 1). The light grey curve on the right shows the result when only 20% seek medical attention and only 30% of them are tested (Scenario 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.

The copyright holder for this preprint this version posted May 20, 2020. . https://doi.org/10.1101/2020.05.16.20104240 doi: medRxiv preprint

These simulations suggest that with an effective surveillance system (high levels of testing symptomatic cases with cough and fever and testing of respiratory cases being hospitalised), it is possible to develop high assurance that an elimination goal has been achieved in around four to five weeks of no cases being detected (Figure 1 ). Of course this modelling assumes that Re values are being successfully suppressed (at Re ≤ 1.0), which may be feasible if there are both rigorous public health control measures (contact tracing, case isolation etc) and people maintain some levels of behaviour change in the peri-elimination period (hand and respiratory hygiene, mask use, working from home where feasible, staying home when unwell etc).

The time period for no new cases we have identified of four to five weeks is similar to a provisional "28 days since the onset date of the last known infection" that has been suggested for New Zealand previously. 13 This is also the span of two maximal incubation periods (14 days, which is being used for determining the length of quarantine for incoming travellers in New Zealand). A 28 day period for elimination has also been proposed for the Australian setting. 2 Nevertheless, it is possible that the 99% level of probability provides a better safety margin (ie, the 37 to 44 day period we have estimated). This would be more appropriate if there are uncertainties with the distribution of testing by geographical region and socio-demographic group. It might also be considered more appropriate by policy makers wanting to reduce international travel restrictions between COVID-19 free nations (see Introduction).

A limitation of our work is that we didn't perform scenario analyses that captured differing performance of the contact tracing systeminstead we assumed that effective routine contact tracing was part of the low Re values. A more sophisticated model (eg, an agent based SEIR model) would be needed to separate out the effect of contact tracing. Another limitation was that we didn't consider extreme scenarios such as residual transmission amongst groups of school children where infection is more likely to be asymptomatic or only mildly symptomatic (ie, this could result in further delays in detection).

In the context of a high level of testing, a period of around one month of no new notified cases of COVID-19 would give 95% certainty that elimination of SARS-CoV-2 transmission had been achieved.

The authors have no competing interests. . 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 May 20, 2020. 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 May 20, 2020. 

The kind of epidemiologic events and the duration between two consecutive events are calculated using random numbers. The simulations start with a susceptible population with a given number of infected individuals ("index cases"). The individual infection stages of these index cases are picked at random, taking into consideration the different lengths of the latent, prodromal, early and late infectious period. In each simulation, the sum of all the rates that change the current state of the system is calculated as   is chosen, and the first transition in the order whose cumulative rate is larger than 2 r is performed. If, for example, the event is an infection, one individual is removed from the group of susceptible individuals and added to the group of latent individuals of stage 1. If a transition is scheduled to take place to an individual in stage 3 L , a third random number is calculated to determine whether the case is diagnosed and isolated or whether the case progresses to 4 L . New rates are calculated after each step, and the procedure is repeated. A more detailed description of the transformation of differential equation models to stochastic models can be found in Gillespie (1976) . 14 Parameters . 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 May 20, 2020. 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 May 20, 2020. The initial status of these cases was randomly selected taking into consideration the durations of the different stages.

Infections that lead to sickness 80% We used the same proportion (80%) of symptomatic cases as per a Chinese study, 16 and as per an Australian modelling study. 17 This value is higher than the 57% value found in an Icelandic study 18 but this study did not involve long-term follow-up of the asymptomatic cases (ie, some of the asymptomatic cases might subsequently have developed symptoms). But it is also lower than that found in another Chinese study (at 94% symptomatic). 19 Sick people who seek medical attention in primary care

We used the result from the NZ Flutracking surveillance system for people with "fever and cough" in the weekly surveys who report seeking medical attention for these symptoms. 20 This is very similar to international estimates for people with influenza who seeking medical attention at 40% eg, as used in other modelling. 8 Sick people need hospitalisation

At the time of writing on 3 May 2020, there were 8 people hospitalised in NZ with COVID-19 (out of a total of 201 actively infected cases, ie, 4.0% 21 ). Of note is that modellers in the United Kingdom (UK) have used 4.4% (of all infected cases), 22 and for modelling in the United States 3%, 5% and 12% have been proposed. 23 The length of hospitalisation was assumed to be 10 days which is similar to other modelling work eg, 10 There is as yet insufficient data on this for COVID-19, so we used an assumed value for influenza (SD = 25%; 0.25 days), Erlang distribution). Symptomatic period 10 days (split into 2 periods of 5 days each)

The WHO-China Joint Mission report stated that "the median time from onset to clinical recovery for mild cases is approximately 2 weeks and is 3-6 weeks for patients with severe or critical disease". 26 But given that mild cases may have been missed in this particular assessment, we used a slightly shorter total time period of 10 days (SD = 25%; 2.5 days), Erlang distribution).

Effective reproduction number (Re) 0.5, 0.6, 0.7, 0.8, 0.9, 1.0

In the peri-elimination phase of pandemic control, we assumed Re values in this range to ensure extinction occurred in the simulations. Extinction still occurred when simulations started with Re = 1.0 due to the accumulation of immune individuals in the course of the simulations, gradually reducing Re(t) to values slightly below 1. These levels of Re were assumed to represent the summated total of pandemic-related physical distancing (voluntary and mandated), travel restrictions, hygiene behaviours, mask . 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 May 20, 2020. There is uncertainty around this value but we used the same estimate as in recent UK modelling. 22 This has biological plausibility as while there is similarity in viral loads between asymptomatic and symptomatic COVID-19 patients, 27 it would be expected that those who are fully symptomatic (with a cough etc.) would be more likely to transmit infection. Of note is an estimate from the Diamond Princess cruise ship outbreak, that 17.9% of COVID-19 infections were from asymptomatic individuals (95% credible interval 15.5-20.2%). 28 But it is unclear how generalisable this finding is given the crowded cruise ship conditions and the typically elderly nature of the passengers. Contagiousness during the two symptomatic periods 100% and 50%

In the first five days of symptoms, cases were considered to be fully contagious. In the second five-day period, this was assumed to be at 50%. The latter figure is highly uncertain, but is broadly consistent with one study on changing viral load. 29 Prevented fraction of contacts for isolated cases 95% effectiveness This value is not precisely known for NZ but isolation of known cases is thought to be fairly well supervised and there has been high public support for pandemic control measures which may improve adherence to such constraints. Data from the NZ arm of the Flutracking surveillance system was used. This indicates that approximately 3% of respondents in the period from April to October report "fever and cough" in the weekly surveys. 20 Of these 39.5% report seeking medical attention for their symptoms. However, we assumed a lower annual rate of 2% to account for the period outside of the influenza season (eg, Flutracking reporting is closer to 1% for weekly "fever and cough" at the start of May when the surveillance system begins for the year). In the NZ population of 5 million this would suggest 14,300 new cases developing "cough and fever" per day of whom 5640 would be expected to seek medical attention. Coverage in patients with respiratory symptoms who seek medical attention in primary care

These coverage values were further adjusted for the test sensitivity of 89% (see below). With 95% coverage and 89% test sensitivity, 84.55% of cases would be detected. Combined with hospital testing (see below) this resulted in a testing level of 7,800 tests per million per week (Submitted manuscript).

Coverage in hospitalised patients with respiratory symptoms 95% coverage As above.

A meta-analysis has reported this as 89% (95%CI: 81 to 94%). 11 This sensitivity is not ideal as while infection can be in the lungs, the sampling is from the nasopharynx, which may contain lower levels of virus at some stages of infection. Specificity is close to 100% for the PCR test.

Delay from symptom onset 5 days plus 1 day for the There is a delay between symptom onset and the performance of the test for SARS-CoV-2. For the first part of the delay we considered a study in . 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 May 20, 2020. . https://doi.org/10.1101/2020.05.16.20104240 doi: medRxiv preprint Parameter Value/s used Further details for parameter inputs into the modelling until a test has been performed and the result has become available testing delay Beijing, China, which reported the interval time from between illness onset and seeing a doctor was 4.5 days. 31 Another Chinese study of 710 patients with pneumonia 32 reported that those dying had a median duration from onset of symptoms to radiological confirmation of pneumonia of 5 (IQR: 3-7) days.

For the testing delay we noted that the aim in NZ is to obtain the result of the tests in under 24-hours regardless of the primary care or hospital setting. But this may not always be the case for rural and small town settings. In our simulations, test results were available on average 5.94 days after symptom onset (SD: 1.36 days).

New Zealand's elimination strategy for the COVID-19 pandemic and what is required to make it work

COVID-19 Roadmap to Recovery: A Report for the Nation. The Group of Eight Ltd

Trans-Tasman bubble: Jacinda Ardern gives details of Australian Cabinet meeting

What is the future for travel and migration in age of Covid-19?

No new cases. (Media release). NZ Ministry of

A stochastic model for COVID-19 spread and the effects of Alert Level 4 in Aotearoa New Zealand

Estimating the probability of New Zealand regions being free from COVID-19 using a stochastic SEIR model

Modelling the potential health impact of the COVID-19 pandemic on a hypothetical European country

Potential health impacts from the COVID-19 pandemic for New Zealand if eradication fails: Report to the NZ Ministry of Health

Eradication of poliomyelitis: when can one be sure that polio virus transmission has been terminated?

Diagnostic Performance of CT and Reverse Transcriptase-Polymerase Chain Reaction for Coronavirus Disease 2019: A Meta-Analysis

New Zealand Ministry of Health. [Data on 7-day rolling average up to 14

The need for a robust scientific definition for the elimination of COVID-19 from New Zealand

A general method for numerically simulating the stochastic time evolution of coupled chemical reactions

Statistics New Zealand

Epidemiology and transmission of COVID-19 in 391 cases and 1286 of their close contacts in Shenzhen, China: a retrospective cohort study

Exit strategies: optimising feasible surveillance for detection, elimination and ongoing prevention of COVID-19 community transmission

Spread of SARS-CoV-2 in the Icelandic Population

Modes of contact and risk of transmission in COVID-19 among close contacts

Ministry of Health. COVID-19 -current cases

Impact of nonpharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand

Worst-case estimates for U.S. coronavirus deaths

Novel coronavirus 2019-nCoV: early estimation of epidemiological parameters and epidemic predictions

Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV2)

WHO-China Joint Mission. Report of the WHO-China Joint Mission on Coronavirus Disease

SARS-CoV-2 Viral Load in Upper Respiratory Specimens of Infected Patients

Estimating the asymptomatic proportion of coronavirus disease 2019 (COVID-19) cases on board the Diamond Princess cruise ship

Virological assessment of hospitalized patients with COVID-2019

. 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 May 20, 2020. . 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 May 20, 2020. . https://doi.org/10.1101/2020.05.16.20104240 doi: medRxiv preprint