key: cord-0764299-z6hnk56l authors: Mandayam Rangayyan, Y.; Kidambi, S.; Raghavan, M. title: Tracking deaths can provide an indicator of latent COVID19 cases date: 2021-06-05 journal: nan DOI: 10.1101/2021.06.02.21258217 sha: 0c2e409e8a0dcc3c520dec66b5f5e1f6ae2a2bc1 doc_id: 764299 cord_uid: z6hnk56l Background: With countries across the world facing repeated epidemic waves, it becomes critical to monitor, mitigate and prevent subsequent waves. Common indicators like active case numbers can flatter to deceive in the presence of systemic inefficiencies like insufficient testing or contact tracing. Test positivity rates are sensitive to testing strategies and cannot estimate the extent of undetected cases. Reproductive numbers estimated from logarithms of new incidences are inaccurate in dynamic scenarios and not sensitive enough to capture changes in efficiencies. Systemic fatigue results in lower testing, inefficient tracing and quarantining thereby precipitating the onset of the epidemic wave. Methods: We propose a novel indicator for detecting the slippage of test-trace efficiency based on the numbers of deaths/hospitalizations resulting from known and hitherto unknown infections. This can also be used to forecast an epidemic wave that is advanced or exacerbated due to drop in efficiency. Results: Using a modified SEIRD epidemic simulator we show that (i) Ratio of deaths/hospitalizations from an undetected infection to total deaths converges to a measure of systemic test-trace inefficiency. (ii) This index forecasts the slippage in efficiency earlier than other known metrics. (iii) Mitigation triggered by this index helps reduce peak active caseload and eventual deaths. Conclusions: Deaths/hospitalizations accurately track the systemic inefficiencies and detect latent cases. Based on these results we make a strong case that administrations use this metric in the ensemble of indicators. Further hospitals may need to be mandated to distinctly register deaths/hospitalizations due to previously undetected infections. Keywords: Covid19 Epidemic Epidemiology Mathematical model Death rates Compartmental epidemiology models like SIS,SIR,SEIR and SEIRD model the effects of changing dynamics in an epidemic in the form of transitions through a sequence of compartments [1, 2, 3, 4] . These transitions are a result of changes in number of individuals in each state as the individual subjects move from susceptible to getting exposed, infected and finally recover or die. The reproductive number R0 in an epidemic is the mean number of infections an infected person can cause in a fully susceptible population during the lifetime of a person's infection [5] . R0 indicates the attack rate or spread of infection with values greater than 1 indicating build-up and values less than 1 indicating fade out of the disease [6, 5, 7] . This metric is useful in gauging the risk of an epidemic [8] and when estimated in real time can determine the effectiveness of intervention strategies like lock downs and isolation that change the transmission dynamics [6, 8] . Modified SEIRD model [9] uses the epidemic simulator as tool for administration and governance. It uses compartments in two parallel tracks representing the quarantined and unquarantined population which makes it relevant in the days of COVID 19 pandemic. This model demonstrated the utility of using simulators for predicting the number of infections in both the quarantined and unquarantined arms of the model in the normal course and in response to a variety of administrative actions, thereby estimating the effectiveness of administration reforms. These models empower the policy makers and health workers to understand the model parameters better and take necessary and timely interventions. It is well known that testing helps flatten the curve while undetected and latent cases spur on a full blown epidemic. The epidemic simulations [9] helped to quantify this effect as a measure of inefficiency. Reasons for undetected cases are many. People who are asymptomatic or with limited access to Page 2 of 15 All rights reserved. No reuse allowed without permission. the preprint in perpetuity. for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display The copyright holder this version posted June 5, 2021. ; https://doi.org/10.1101/2021.06.02.21258217 doi: medRxiv preprint Tracking latent COVID19 cases healthcare (forming a large part of the population) might go undetected easily and hence the number of confirmed, recovered and deceased cases that are reported everyday can be an underestimate of the true figures [10, 11, 12] . Further insufficient testing, contact tracing or quarantining may contribute to this inefficiency. Amidst all the chaos of asymptotic cases, under-reporting etc, death is an unmissable event in an epidemic. The number of deaths in an epidemic provides a realistic picture of the extent of infection still latent in the population [13, 14] . While it is intuitively recognized that detection of infection postmortem or at first presentation at intensive care units are an indicator of the gravity of situation, this has never been quantified or studied as a measure or indicator of relevant quantities. Current reporting practices do not capture 'infections detected postmortem' or 'previously undetected infections presenting at ICU' separately from the detected infections. We propose that these metrics are vital indications of the health of a community or society and can be an early indicator of an emerging epidemic wave. Using the epidemic simulator described in [9] , we demonstrate the utility of such metrics in early detection of an epidemic wave that is hastened or exacerbated by inefficiency [9] on account of insufficient testing, tracing or containment measures. We use the symmetry in the two arms of the model [9] along with the fact that death of either kind is unmissable, to estimate the inefficiency (or latent spread) of an epidemic. We show here that recording the number of 'postmortem detection of infection' as a proportion of total deaths can be a good metric. The ratio of 'previously undetected infections at hospitalization' to total hospitalizations would also serve a similar purpose. We hereby make a case for modifying the Standard Operating Procedures to make this book keeping possible. The Modified SEIRD model described in [9] uses two symmetric, parallel arms to represent the quarantined and free populations. The transition rates from one compartment to another are proportional to the extent of contact tracing and self-reporting in each of the respective compartments. These transition rates are described in Figure 1 for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display It is observed that c and q play a significant role in altering the inefficiency. The ratio of unreported cases to total number of cases can be captured in any of the compartments of the model at I or beyond, to measure the inefficiency. Since death is an unmissable event in an epidemic, the data for it is more easily and accurately available than in any other compartment. We the preprint in perpetuity. for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display The copyright holder this version posted June 5, 2021. ; https://doi.org/10.1101/2021.06.02.21258217 doi: medRxiv preprint Tracking latent COVID19 cases interpreted as ratio of 'previously undetected infections at hospitalization' to total hospitalizations. This paper uses a measure to describe the ratio of unreported deaths to the total number of deaths obtained from the deceased compartment. While the structure of the compartment model itself guarantees that the will asymptotically converge to the inefficiency when parameters of the model are constant, we wish to explore the utility of in scenarios where inefficiency is varying dynamically. In order to test our hypothesis, we probe the relationship between the and the intervention inefficiency and their growth trends in a simulated epidemic with changing intervention inefficiencies. In particular we are interested in exploring the scenarios where a drop in efficiencies due to systemic fatigue in a prolonged epidemic can exacerbate a wave in infections. The experiments are simulated by seeding the model with an initial set of parameters as described in the Table 1 . This is done to ensure the model simulates a realistic number of cases in each of the compartments and it also furnishes an identical backdrop for all the experiments. All rights reserved. No reuse allowed without permission. the preprint in perpetuity. for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display The copyright holder this version posted June 5, 2021. where, represents the the day on which the latest intervention was made, is the first day in a block of five days where the is within ±5% of true inefficiency. The can be calculated in multiple ways; by summing over the entire epidemic period, or over windows of several days. The experiment was run over different window periods where the were smoothed over the window length to omit the baggage of deaths that occurred much earlier in time. This led to the term ℎ defined as : where, i represents the 'i'th day, n represents the number of days chosen in the window period. All rights reserved. No reuse allowed without permission. the preprint in perpetuity. for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display Laxity in contact tracing and testing are common during a long ongoing epidemic due to systemic fatigue or ignored clusters. This leads to increase in inefficiency and case numbers are subdued or increase only mildly when the epidemic starts to rise. Thus it blindsides the system to a wave building up. We simulate such a case with inefficiency1 = 0.5 and an inefficiency2 rising to 0.7 which results in a wave. A response to this situation results in a decrease in inefficiency to 0.3. The timing of the response and its effect on the impending wave are explored. In this scenario we also explore the resultant rise in and active cases and their relative utility in predicting and mitigating the impending latent wave. The ratio of unreported deaths to total deaths converge with their true value of inefficiency It may observed from Figure 2 the preprint in perpetuity. for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display faster but has a lot of variance due to daily fluctuations in numbers. Whereas over a 100 days window length is smoother, but takes longer to make inferences due to slower convergence. Although sensitive to noise, 10 day window period gives the fastest convergence followed by 50 and 100 day periods. changing and reforming administrative policies. The heatmap in Figure 3 shows the relationship between magnitude of change in inefficiency and the number of days for ℎ over a 50 day window to converge with the latest inefficiency. The bright diagonal band shows that convergence is the fastest when the difference between the inefficien- All rights reserved. No reuse allowed without permission. the preprint in perpetuity. for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display The copyright holder this version posted June 5, 2021. ; https://doi.org/10.1101/2021.06.02.21258217 doi: medRxiv preprint Tracking latent COVID19 cases Figure 4 : The graph considers the rise in active cases due to two scenarios, both of which result in identical changes in reproduction number R. When the rise in R is due to an increase in , the active case increase yields a sharper curve giving a true indication of underlying cases. However, when the the increase in R is due to increase in test-track-trace inefficiency, the rise in active cases are slower and in fact even decrease over the short term as the increasing cases are missed due to high inefficiency. A noticeable increase in active cases can only be seen past 30-40 days after the change. However, the increase in is already evident in 10 days from the day inefficiency increases and stabilizes within a period of 20 days. Complete convergence as defined in Figure 4 comes around 35 days. It may thus be seen that the maximum convergence times of metrics are comparable to the early rises in active case load based metrics. Thus windowed based metrics are ideally suited as triggers for initiating mitigation. gences are slower when absolute number of deaths are low in either arm (detected or undetected) as seen when either of the inefficiencies is small. Such situations result in high variance of ℎ beyond the 5% margins used to define convergence in our definition. All rights reserved. No reuse allowed without permission. the preprint in perpetuity. for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display Figure 4 compares the responses of metrics such as daily increase in active cases and daily deaths with the calculated over a ten day window. It may be noticed that the change in inefficiency causes an increase in value from 1.57 to 2.20 thereby precipitating a wave. However responding in the wake of conventional metrics like daily increase in active cases or log changes in active cases are only visible after a time lag as the lower efficiencies result in a large fraction of cases to be undetected. If the same change in had occurred by means of increased instead of an increased inefficiency, the daily increase in active cases would have increased faster, with a possibility of early detection. When inefficiencies increase due to decreased testing or contact tracing, the daily increase in active cases is rather subdued in the short term, masking the impending wave. Although deaths cannot go unnoticed, rise in deaths can take even longer to show up sufficiently to raise an alarm. However, the preprint in perpetuity. for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display The copyright holder this version posted June 5, 2021. ; https://doi.org/10.1101/2021.06.02.21258217 doi: medRxiv preprint Tracking latent COVID19 cases warning also provides the administrative bodies sufficient time to plan the interventions, resources and logistics needed to mitigate or tide over it. All rights reserved. No reuse allowed without permission. the preprint in perpetuity. for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display Constantly monitoring an epidemic is extremely crucial as even small laxity in test-track-trace efficiencies has great potential to precipitate a wave. This situation can be analysed with the help of parameters like reproductive number, daily increase in active cases, test positive ratios etc. But these parameters are largely dependant on testing strategies and the nature of sampling, whereas monitoring deaths are unmissable events in an epidemic and are capable of explaining the underlying situation quantitatively. This paper proposes a metric based on death reports(or equivalently hospitalizations reported) to monitor the inefficiency in test-track-trace performance. We show that being deaths resulting from hitherto undetected infections as a fraction of all deaths is sensitive to the changes in the inefficiencies prevalent in the system and reflects these changes quicker than any other conventional indicators. Our work also highlights the potential reduction in the peak active case load and deaths when mitigation measures are triggered by the metric . The proposed metric and inferences drawn, if employed as part of standard reporting procedures can enable the government to stay better equipped to predict a loss in efficiency and a resulting wave. The benefits can accrue by way of stronger mitigation and prevention of the wave at best or better preparation of hospital infrastructure (beds, ventilators, test kits etc) at the least. Generalizing this method, the inefficiency thus defined could have been obtained from any of the compartments in the Modified SEIRD model [9] by taking the corresponding numbers from the two parallel arms for reported and unreported cases respectively. As deaths are usually reported at hospitals or government bodies, adequate data can be collected which is not guaranteed in other compartments of the model (namely S,E,I,R). Further these and can be used interchangeably as and representing the hospitalized cases or cases requiring intensive care with no loss of generality. would in this case mean hospitalization of a patient already diagnosed with the infection and would mean the hospitalization of a patient due to severe symptoms but diagnosed with the infection post hospitalization. This extrapolation of results helps in arriving at the analysis faster and more importantly without risking a death. This model assumes that the rates of death are the same in both the arms -detected and undetected. But in reality it is plausible that the undetected arm could have a lower probability of I->D transition Page 13 of 15 All rights reserved. No reuse allowed without permission. the preprint in perpetuity. for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display The copyright holder this version posted June 5, 2021. ; https://doi.org/10.1101/2021.06.02.21258217 doi: medRxiv preprint Tracking latent COVID19 cases than the detected arm. These different rates would show up as a scaling factor of . However, even in such scenarios the gradient of the rise in compared to the previous epoch would still give indication of the impending wave earlier than the other indicators used currently. In light of the above results, we strongly propose that policy makers and healthcare administrators consider the inclusion of metric as part of their decision making framework. Since it is likely that hospitals already have this data, implementing this proposal would only demand certain changes in the book keeping of already available data, posing minimal overheads. By closely monitoring the trends in this metric it is possible to detect the changes in the laxity in regulations and take corrective measures much earlier and also gain ample time to work on the strategies and procurement of required resources to overcome the wave. A contribution to the mathematical theory of epidemics Transmission dynamics and control of severe acute respiratory syndrome A simulation of a COVID-19 epidemic based on a deterministic SEIR model. Front Public Health A conceptual model for the coronavirus disease 2019 (COVID-19) outbreak in Wuhan, China with individual reaction and governmental action A brief history of R0 and a recipe for its calculation Unraveling R0: considerations for public health applications On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations Perspectives on the basic reproductive ratio Using epidemic simulators for monitoring an ongoing epidemic Clinical characteristics of asymptomatic and symptomatic patients with mild COVID-19 Estimation of the asymptomatic ratio of novel coronavirus infections (COVID-19) Estimating mortality from COVID-19: scientific brief Evaluating the massive underreporting and undertesting of COVID-19 cases in multiple global epicenters Public Health Agency of Sweden. The infection fatality rate of COVID-19 in Stockholm -Technical report All rights reserved. No reuse allowed without permission. the preprint in perpetuity.for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display The copyright holder this version posted June 5, 2021. ; https://doi.org/10.1101/2021.06.02.21258217 doi: medRxiv preprint