Introduction

India witnessed a huge part of the population affected by the COVID-19 virus in 3 waves from March 2020 to March 2022 [1] leading to a major crisis in saving lives, handling healthcare resources as well as suffering economic losses. Several administrative measures like lockdowns, social distancing, quarantining etc were implemented to curb the spread of these infections. These strategies should be invoked appropriately based on insights from epidemiological models. In the recent outbreak of COVID-19 parameters like the reproductive number (R0), serial interval, incubation period, transmissible period, proportion of confirmed cases in the population, proportion of deaths in critical cases and beta are some salient parameters used for modeling [2–4]. While these are some epidemiological parameters, COVID-19 is also characterized by many biological parameters like variance in transmissibility period and immunological strength across different age groups and viral strains, effect of vaccination etc [4, 5]. But these parameters are hard to study in an ongoing epidemic [5]. The authors highlight the complications of fitting the model to reported cases, as the cases can be distributed unevenly geographically. This would mean that there would be a sizeable population having latent infections that escapes being reported. Hence the authors suggest that hospitalizations and deaths are more reliable [5]. This way deaths and hospitalizations that get diagnosed with the infection are from the pool of latent infections thus acting as an indicator of latent infections.

The reasons for undetected cases are many. People who are asymptomatic or with limited access to 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 [6–8]. Further insufficient testing, contact tracing or quarantining may contribute to this inefficiency. Very few techniques like PCR and antibody tests are used to estimate the number undetected infections in a particular population [9]. These techniques are highly randomized and can only estimate the undetected cases at specific time point making the data very sparsely sampled [9].

Metrics like number of Active cases and deaths are looked at for studying the case growth patterns in different Indian states and ranking them based on severity of the spread [10]. A good amount of time has elapsed before some insights can be drawn from these metrics. [11] describes the correlation between reproductive rate and test positivity rates showing how testing failed to catch up with the reproductive rate. Further contact tracing is also biased to the serial interval in symptomatic people [4] Despite being capable of predicting an impending wave, these metrics are sensitive to testing strategies and cooperation by the population in different states making them unreliable.

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 [5, 12, 13]. 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 the 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.

Modified SEIRD model [14] describes most of the above parameters in its model and uses the epidemic simulator as a 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 [14] helped to quantify this effect as a measure of inefficiency.

Using the epidemic simulator described in [14], we demonstrate the utility of such metrics in early detection of an epidemic wave that is hastened or exacerbated by inefficiency [14] on account of insufficient testing, tracing or containment measures. These metrics that ensure robust surveillance of the pandemic and yet have a low cost of compliance are especially advantageous in scenarios of pandemic fatigue that is prevalent currently. We use the symmetry in the two arms of the model [14] 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.

Methods

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 [15–18]. 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 [19]. 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 [19–21]. This metric is useful in gauging the risk of an epidemic [2–4, 22] and when estimated in real time can determine the effectiveness of intervention strategies like lock downs and isolation that change the transmission dynamics [20, 22].

The Modified SEIRD model described in [14] 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 Fig 1 [14].

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Fig 1. Figure adapted from [14] describes the fraction of population flowing through each compartment in the parallel arms of the modified SEIRD model.

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These transitions provide a metric called the intervention inefficiency that is interpreted as the ineffectiveness of interventions; or the fraction of infections that are undetected. The inefficiency being a fraction in [0, 1] is the complement of efficiency [14]. (1) where,

a -The fraction of infection spread through contacts,

q -Fraction of infections detected through random testing and self reporting,

c -Fraction of infections detected through contact tracing.

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. Owing to the limitations in estimating the number of undetected cases in the population as seen in the introduction, we use the model simulations to obtain the number of undetected cases and the population falling in different compartments of the model. We thus hypothesize that calculating the ratio of unreported deaths to total deaths is a good indicator of inefficiency. Alternatively if the compartments D and Dq are replaced by H and Hq for hospitalisation of hitherto undetected infection and hospitalization of a known infection, the inefficiency can also be interpreted as ratio of ‘previously undetected infections at hospitalization’ to total hospitalizations.

This paper uses a measure D_ratio to describe the ratio of unreported deaths to the total number of deaths obtained from the deceased compartment. (2)

While the structure of the compartment model itself guarantees that the D_ratio will asymptotically converge to the inefficiency when parameters of the model are constant, we wish to explore the utility of D_ratio in scenarios where inefficiency is varying dynamically. In order to test our hypothesis, we probe the relationship between the D_ratio 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.

Convergence of D_ratio to true inefficiency and lag in convergence

The experiments are simulated by seeding the model with an initial set of parameters as described in the Table 1. These parameters are obtained from the understanding of the COVID-19 disease as on April 27th 2020 such that the set of parameters such as mean infection time and mean latency time seem epidemiologically plausible. Population is set to 10 million to keep it realistic to a city in India. 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. We can largely classify the parameters as static parameters that don’t change in the course of epidemic simulation and dynamic parameters that are time varying and are manipulated throughout the simulation to fit the model to some particular data. Sensitivity analysis has been performed on these static parameters namely The mean infection time (inf_t), the mean latency time (lat_t), population, and fraction of infections through direct contact (a). Beta and influx are time varying parameters that were modified during the course of the epidemic to simulate different scenarios in the experiment.

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Table 1. The model parameters used for simulations.

https://doi.org/10.1371/journal.pone.0283081.t001

Interventions are introduced at two instances of time t1 and t2 having corresponding intervention inefficiencies of Inefficiency1 and Inefficiency2. Each of these Inefficiencies are varied from 0 to 1 in steps of 0.05, and their corresponding time series of D_ratios are plotted, thereby exploring the ability of a variety of change patterns.

If the interventions are ineffective, the D_ratios increase and similarly when the interventions contain the spread of infection more effectively the D_ratios tend to decrease. Hence the Intervention Inefficiency becomes the true value of the D_ratios. The lag with which the D_ratios converge with the prevalent inefficiency value is a good indicator of the utility of this metric. Hence the experiments run with various intervention inefficiencies are noted for observations. The time to convergence is defined as (3) where,

T_{latest intervention} represents the the day on which the latest intervention was made,

T_convergence is the first day in a block of five days where the D_ratio is within ±5% of true inefficiency.

Results

The ratio of unreported deaths to total deaths converge with their true value of inefficiency

It may be observed from Fig 2 that the D_ratio tracks the true value of inefficiency as the inefficiency changes dynamically. The metric tracks the true inefficiency on both the increasing and decreasing excursions. While the time to converge varies, the changes in D_ratio follow a largely exponential trajectory. As a result, changes in the metric of interest are large at the onset of change and becomes progressively slower. This suggests that the D_ratio can be a good metric for detecting sudden changes in underlying inefficiency.

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Fig 2. Variation of intervention inefficiency and D_{smooth ratio} with time.

The 4 plots show the trends in D_ratio over window periods of 10, 50 and 100 days when the inefficiencies are increased and decreased in different temporal orders. Metrics calculated with all window sizes show high day to day variation when the death numbers in either arm is very low. However, metrics with smaller window sizes are more prone to this daily variation. It is observed that D_ratio when smoothed over a small window of 10 days, converges faster but has a lot of variance due to daily fluctuations in numbers. Whereas D_ratio 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.

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Convergence time to true inefficiency is directly proportional to differences in inefficiencies

The heatmap in Fig 3 shows the relationship between magnitude of change in inefficiency and the number of days for D_{smooth ratio} 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 inefficiencies are small and increase with difference between inefficiencies. This diagonal is flanked on both sides by a series of symmetric bands that progressively widen with increase in the inefficiencies. The broader bands of fast convergence in the bottom-right indicates that the metric performs progressively better and is advantageous in higher inefficiencies when the situation most warrants it. The convergences 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 D_{smooth ratios} beyond the 5% margins used to define convergence in our definition.

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Fig 3. Correlation between intervention Inefficiency₁, Inefficiency₂ when D_{smooth ratio} is calculated over a 50 day window and the number of days for D_{smooth ratio} to converge with Inefficiency₂ is plotted on a heatmap.

The days to converge is the least on the diagonal and is largely symmetric. Transitions in the range of inefficiencies 0.2 through 1 converge within a period of 60 days and the range from 0.4 through 1 within 50 days. The empty(grey) cells indicate it takes more number of days to converge than the period of simulation or the cases are extremely low to show up in the D_{smooth ratio}. In general it may be seen that in the high inefficiency range where it is critical to react fast, the convergences are faster, thus emphasizing the utility of this metric.

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Smoothed D_ratio can detect onset of laxity earlier than other metrics

Fig 4 compares the responses of metrics such as daily increase in active cases and daily deaths with the D_ratio calculated over a ten day window. It may be noticed that the change in inefficiency causes an increase in R 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 R_t had occurred by means of increased β 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 D_ratio captures the imbalance between the detected and undetected arms and hence indicates the changes underneath. The daily change in the D_ratio can be an indicator of the noise in the estimation of D_ratio. While full convergence of D_ratio to the true inefficiency may take time, it is seen from Fig 4 that within a span of about 20 days it converges to the new inefficiency and at 10 days already shows clear indications of rise in inefficiency as evidenced by sudden high increase and moderate variance.

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Fig 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 β, 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 D_ratio is already evident in 10 days from the day inefficiency increases and stabilizes within a period of 20 days. Complete convergence as defined in Fig 4 comes around 35 days. It may thus be seen that the maximum convergence times of D_ratio metrics are comparable to the early rises in active case load based metrics. Thus windowed D_ratio based metrics are ideally suited as triggers for initiating mitigation.

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Mitigation by tracking the D_ratio reduces or truncates the epidemic wave intensity or delays it sufficiently

As the number of daily active cases in a pandemic remains low for a long period of time, it is natural for some laxity to creep in the regulations and protocols followed. This results in an increase in the inefficiency as indicated in Fig 5(a) thereby precipitating or advancing an impending latent wave. Intervention resulting in decreased inefficiency can be triggered by one or more indicators. The interventions triggered after observing the conventional metrics like significant rise in the number of daily active cases would easily cost 60 days of valuable time. The earliest response monitoring the situation aggressively would also take no less than 40 days (Fig 5(b) and 5(c)]. Despite reducing the deaths and active cases, both these scenarios [Fig 5(b) and 5(c)] leave very little time to prepare or react resulting in quite a number of infections and deaths. Intervention based on sudden deviations of the metric D_ratio plays a seminal part here in averting the wave or pushing the wave much farther ahead in time as indicated in Fig 5(d), where the inefficiency is lowered based on the increase in D_ratio. As seen in Fig 4, D_ratio can detect the true inefficiency in about 20–30 days with certainty as witnessed by very low daily variations in D_ratio. The metric can clearly forewarn although with with slightly lower certainty (moderate daily variation) within 10 days. Using D_ratio the maximum time to track the inefficiency transition is given by the heatmap in Fig 3 and the earliest response time is about a half or third of it as observed in Fig 4. The benefits of reacting based on this metric is demonstrated in Fig 5(d). The peak active case load and death are reduced significantly. The early warning also provides the administrative bodies sufficient time to plan the interventions, resources and logistics needed to mitigate or tide over it.

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Fig 5.

Left to right: (a) Inefficiency increases, but no counter measures are taken. Result is a peak active case load of 300 000 in a 10 million population and causing close to 75 000 deaths. (b) Inefficiency is lowered when the daily active cases significantly increase above 40,000. This measure reduces the daily active cases by nearly 50% and deaths by 75%. (c) By monitoring rise in daily active cases closely, lowering the inefficiency when they rise above a smaller threshold of 15 000 active cases daily, the peak and deaths both reduce considerably. (d) Instead when the inefficiency is lowered as the D_ratio begins to increase, the peak active cases and deaths are averted.

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Performance of D_ratio and other metrics on real world data

The performance of D_ratio is compared with other metrics like daily active cases and daily new cases on a real world epidemic to demonstrate the practical application of the metric. It is observed that a wave is precipitated when beta and influx of migrant population increases and c decreases significantly. The D_ratio, daily active cases and daily new cases are all compared by taking a n-day rolling average for different values of n (n = 7,10,15,25,50). As demonstrated in Figs 6–8 the metric D_ratio always lags the daily active cases and daily new cases when averaged over a 25 day rolling window thereby validating its utility in the purpose of planning mitigation strategies. These results have been validated for rolling windows of different lengths as well. These results prove the advantages of a metric like D_ratio in real world scenarios giving the administrative bodies a minimum of 10–15 days to prepare for an upcoming wave and also to bring in interventions by keeping a tab on the underlying model parameters.

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Fig 6. Delhi as on 22nd June 2022.

(a) Real COVID-19 data and simulated data showing confirmed cases, recoveries and deaths. It is observed that simulations match the real case growth to a great extent. (b) The intervention inefficiency underlying the epidemic is plotted along with the ratio of deaths from undetected infections to total number of deaths (D_ratio), daily new cases and active cases. The dashed vertical lines correspond to the potential time points when an intervention can be made based on the respectively coloured D_ratio, daily active cases and daily new cases. D_ratio predicts an upcoming wave ahead of other metrics when the wave is precipitated due to a drop in efficiency (decreasing values of ‘c’—the fraction of infections detected through contact tracing). (c) The model parameters beta, fraction of infections that get detected through contact tracing—’c’, the fraction of infections spread through migrant population—’in_phi*pI’ are tuned to fit the model to real data.

https://doi.org/10.1371/journal.pone.0283081.g006

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Fig 7. Karnataka as on 22nd June 2022.

(a) Real COVID-19 data and simulated data showing confirmed cases, recoveries and deaths. It is observed that simulations match the real case growth to a great extent. (b) The intervention inefficiency underlying the epidemic is plotted along with the ratio of deaths from undetected infections to total number of deaths (D_ratio), daily new cases and active cases. The dashed vertical lines correspond to the potential time points when an intervention can be made based on the respectively coloured D_ratio, daily active cases and daily new cases. D_ratio predicts an upcoming wave ahead of other metrics when the wave is precipitated due to a drop in efficiency (decreasing values of ‘c’—the fraction of infections detected through contact tracing). (c) The model parameters beta, fraction of infections that get detected through contact tracing—‘c’, the fraction of infections spread through migrant population—’in_phi*pI’ are tuned to fit the model to real data.

https://doi.org/10.1371/journal.pone.0283081.g007

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Fig 8. Uttar Pradesh as on 22nd June 2022.

(a) Real COVID-19 data and simulated data showing confirmed cases, recoveries and deaths. It is observed that simulations match the real case growth to a great extent. (b) The intervention inefficiency underlying the epidemic is plotted along with the ratio of deaths from undetected infections to total number of deaths (D_ratio), daily new cases and active cases. The dashed vertical lines correspond to the potential time points when an intervention can be made based on the respectively coloured D_ratio, daily active cases and daily new cases. D_ratio predicts an upcoming wave ahead of other metrics when the wave is precipitated due to a drop in efficiency (decreasing values of ‘c’—the fraction of infections detected through contact tracing). (c) The model parameters beta, fraction of infections that get detected through contact tracing—‘c’, the fraction of infections spread through migrant population—’in_phi*pI’ are tuned to fit the model to real data.

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Sensitivity of D_ratio to model parameters

The sensitivity analysis for D_ratio is performed for the static model parameters that don’t vary during the epidemic. The performance of D_ratio is tested by varying model parameters like mean infection time (the duration of infection in an individual) and the mean latency time (the period between an individual contracting the infection and when one spreads it to others). The days when D_ratio, active cases and daily new cases are higher than their respective maximum value in the last 20 days is used to trigger an alert predicting an upcoming wave. The number of days by which D_ratio predicts the epidemic wave earlier than active cases and daily new cases are tabulated in the Tables 2 and 3. Although it is found that D_ratio is sensitive to these model parameters, it is seen that it is still a better indicator as compared to active cases and daily new cases thereby validating its utility.

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Table 2. Time lag between D_ratio and number of daily active cases (Days).

https://doi.org/10.1371/journal.pone.0283081.t002

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Table 3. Time lag between D_ratio and number of daily new cases (Days).

https://doi.org/10.1371/journal.pone.0283081.t003

Discussions

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 daily 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 D_ratio 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 D_ratio. 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 [14] 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 D_detected and D_undetected can be used interchangeably as H_detected and H_undetected representing the hospitalized cases or cases requiring intensive care with no loss of generality. H_detected would in this case mean hospitalization of a patient already diagnosed with the infection and H_undetected 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 than the detected arm. These different rates would show up as a scaling factor of D_ratio. However, even in such scenarios the gradient of the rise in D_ratio compared to the previous epoch would still give indication of the impending wave earlier than the other indicators used currently.

The results of this research indicate that D_ratio outperforms the active cases and daily new cases in predicting an upcoming epidemic wave when the epidemic is characterized by a low ‘c’ typically a scenario as is prevalent currently wherein the amount of testing has come down drastically and contact tracing has become virtually nil. Under these circumstances if an epidemic were to start due to potent imported contagious strain or by any other means, the results here show that it will be quite a while before the epidemic is actually caught using 7 day rolling average of daily new cases or active cases. On the other hand, just tracking the proposed metric D_ratio having a very low cost of compliance is a lot more feasible and can catch an upcoming epidemic wave early. Since our metric is specially sensitive at low values of ‘c’(infections caught from contact tracing) and ‘q’(infections caught from random testing), it is an ideal indicator of an epidemic wave because it imposes least socio economic cost but keeps the surveillance robust. For example, one could put a threshold on the D_ratio and escalate within the administration when it hits the threshold. The main advantage of this metric is that it does not force people to get tested, does not impose unnecessary lockdowns, does not disrupt the economics of the state or the country. Hence this scheme is better than tracking 7 day rolling averages of daily new cases or active cases in predicting an epidemic wave in scenarios described above. However when the epidemic wave is precipitated due to changes in beta and influx of population active cases and daily new cases are found to be better indicators of the impending wave. This is a limitation with regard to the utility of the metric.

The model assumes that a person once infected cannot be re-infected. This model doesn’t account for changes immunological changes, transmissibility changes due to reinfections, vaccination and mutations of viral strains. These are some limitations with regard to the design of the model.

Further, this model also assumes that the mortality rate is constant across waves during the epidemic and across various strains of viruses. But it has been noticed in reality that there can be different mortality rates in different waves, for different viral strains and also different in vaccinated set of population versus the ones without vaccination. This effect can be observed in the difference in the number of cases simulated in the third wave compared to actual data in Fig (6). It is evident from Fig (7) that the utility of D_ratio is still valid.

It has also been observed that the rate of transmission in each limb of the modified SEIRD model can be different based on the age groups, whether symptomatic or asymptomatic, vaccinated or not etc. Hence by incorporating more such endogenous viral parameters in the model it is possible to improve the performance and accuracy of the model.

This model falls short in explaining the changing dynamics in different geographical clusters within a state. Hence it is not possible to infer the localised cause for the surge in cases within a state. There could be a few districts with a denser spread of cases while a slightly farther set of districts might still be unaffected with only fewer cases. [23] talks about the pandemic as a chaotic dynamical system where the growth of the pandemic is unpredictable due to a vast set of changing parameters across countries. But this unpredictability affects all the metrics like daily active cases, daily new cases, and D_ratio equally as they are all inferred from the same field data of a specific region. Since the purpose of this metric is to indicate an impending wave in a region, the utility of the metric holds good regardless of the chaotic nature of the epidemic.

Ideally a model with all the above described parameters will provide a more comprehensive picture of the ongoing epidemic. But an epidemic due to a completely new pathogen can go full blown even before most of these variables are understood. We demonstrate that a model with a minimal set of parameters can still capture the D_ratio earlier than other conventional metrics. The advantage of such a model comes to light when non experts, people without domain knowledge can use the model to make timely interventions.

In light of the above results, we strongly propose that policy makers and healthcare administrators consider the inclusion of D_ratio 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.