hpcc-systems/covid19

https://covid19.hpccsystems.com

HPCC Systems Covid 19 Tracker

An open data lake solution for research and collaboration to track and report the progress of Covid 19 virus.

This system was built around a Production Data Lake Architecture (see Data Lake Whitepaper) allowing incremental value extraction, easy incorporation of new data sources, and rapid transition to production.

The goal of the project is to provide unique insights into the state and progress of the pandemic for each reporting location. This system is for the benefit of researchers, health workers, government agencies, and the general public. Data is presented in a balanced, digestable form, allowing individuals sufficient information and context to make reasonable decisions, rather than relying on news sources that are often sensationalized or politicised. It includes a "Hot Spots" module that identifies locations (e.g. Countries, States, Regions, Counties) that are experiencing the worst outbreaks at the current time. This could potentially aid in triage for various health organizations around the world.

With user-friendly interface and informative infection indicators, HPCC Systems Covid-19 Tracker is released to the public https://covid19.hpccsystems.com.

Background

The COVID-19 crisis moves at a very quick pace. Changes in social behavior can result in rapid changes to the overall picture. Monthly analysis would be obsolete by the time the analysis was available. Daily results are too noisy to be useful for decision making. We therefore chose weekly analysis as the optimal time frame to understand the situation. While we present the data on a daily, weekly, and cumulative basis, the primary analysis of the current situation is based on a sliding 7 day window.

We start by trying to understand the spread rate of the virus in a particular population (i.e. location). Epidemiology uses an effective reproductive growth rate known as "R" to represent the speed of spread. R defines the number of people a single individual is likely to infect over the course of their infection. Infections spread exponentially, and R represents the base of the exponent. An R value of 1.0 would represent a steady state in the number of active infections – each person would infect one other person, so the overall infection rate (number of active infections) would not change. An R value greater than 1 means that the infection is growing among the population, while an R value below 1 indicates that the infection is subsiding. With an R of 2.0, an infection would double the number of new cases every ten days or so. The higher the R value, the faster the doubling rate. Likewise, an R of .5 would halve the number of new cases every ten days.

We can’t observe R in practice, so we try to approximate it from the number of confirmed cases and the number of deaths due to the virus. The approximation based on confirmed cases we designate Case Growth (cR). The approximation based on deaths, we designate as Mortality Growth (mR). These numbers do not perfectly reflect R, but they are the best proxies available. cR is biased by the changing availability and policies around testing. If we had randomized testing, we could better approximate R. If we only test hospitalized patients, then cR will understate R. If the testing policy is shifting, then cR may either under or overstate R. mR, on the other hand, is a more objective indicator. It is less affected by policy, but may be biased by changes in medical care, such as improved treatments over time. mR also lags cR, so it is not as timely an indicator. By combining mR and cR, we get a better overall approximation of R.

By approximating R, we can quickly assess the situation in a given location. As an infection spreads within a location, one of two situations typically arises:

• The infected people will be quarantined and their contacts traced and also quarantined. If this is successful, the infection is said to be Contained, and R will quickly decrease.
• Containment fails, either due to late detection, failure to trace all contacts, or insufficient resources to enact the containment. In this case, the infection will spread uncontrolled until social behavior (e.g. social distancing) causes it to be controlled. This process is known as Mitigation.

By following changes in R, we can quickly see how the infection is responding to Containment or Mitigation. In the early Emergent stages of the infection, we commonly see R values greater than 3, which indicate a very fast exponential growth. As the infection is contained, or social distancing is deployed, R quickly falls to between 1 and 2, which can still be very rapid growth. At R = 2, the cases will double every 10 days. As the case growth increases, people tend to become more and more careful until R falls below 1. At this point the active infections stop increasing and gradually begin to decrease. We expect that this will tend to make people less careful, and we expect to see oscillation above and below 1. If social distancing can be maintained for a longer period, then the infection can be ultimately re-contained.

Causal Model

We use an evolving model of the cause and effect relationships between observed and unobserved (latent) variables to inform the definition and interpretation of metrics. This model lets us visualize the ways in which measurements are confounded by hidden variables, and possible ways to de-confound the meanings. Judea Pearl [3] has demonstrated that people are extremely good at building causal models. It may be that the human mind is largely a causality processing machine. Given any occurrence, we can quickly assess potential causes and downstream effects. Pearl has further defined an algebra for determining whether causes can be de-confounded, and which variables need to be controlled for in order to achieve the de-confounding, given a causal model [4].

Causal Model

Using the above model, we were able to show, for example, that changes in the rate of growth of reported cases is a reasonable proxy for Social Behavior (i.e. Social Distancing). This let us develop the Social Distance Indicator (SDI) metric, which is described in later sections.

Looking at the diagram above, we see that Social Behavior (e.g. Social Distance) is an unobserved variable. We can't measure it directly, but perhaps we can observe its effects on other variables.
We see that the primary effect of Social Behavior is on the number of Active Infections. This is also an unobserved variable but it, in turn, effects Reported Cases, an observable variable. When we look at the myriad influences that drive Reported Cases, it seems unlikely that we can unconfound it enough to use it as a proxy for Social Distance. Let's look at each of these influences, both direct and indirect, and see if it's possible. I reorder them to ease the narrative:

• Original Exposure Count -- If we use the differential version (dCases/dT), then this
• Time since first exposure
• Case Reporing Policy
• Test Policy and Coverage
• Weather / Climate
• Population Density
• Social Behavior
• Population age and health

This generally provides barriers to interpretation, as meaning (a causal concept) is confounded by the multiple influences. Perhaps we eliminate some of those factors

Epidemiological Model

The system embeds a classical epidemiological model known as SIR [1]. The SIR model predicts the changes in Susceptibility, Infection, and Recovery using a set of differential equations. This allows us to estimate quantities such as Active Infections, Recovered Infections, Percent Immunity, Time-to-peak, Deaths-at-peak, and Time-to-recovery.

In practice, the SIR model gives us a good estimate of Active versus Recovered infections, but predictive power is limited due to rapidly changing social and societal behaviors. In animal epidemiology, the growth rate (R) is typically identical to the Basic Reproductive Rate (i.e. R0) of the virus. In human society, there are both innate and orchestrated responses to a pandemic that cause R to rapidly diverge from R0. Changes in behavior such as quarantines, social distancing, and enhanced hygiene can quickly dampen the growth rate. Returning to normal behavior can rapidly increase the rate. Therefore any predictions of growth must model the expected changes in human behavior, which is beyond the scope of the current system.

Data Filtering

In the first iteration of the system, we noticed some unexpected swings in R values. Upon analysis, it was discovered that many locations will make corrections to their cumulative case and death data retroactively, either due to changes in reporting policy or correction of previous errors. This sometimes results in cumulative values shrinking, and differential values (e.g. growth) turning negative. Other times, this results in large numbers of cases that occurred previously being dumped into a single day’s data. Both situations can badly distort differential growth calculations. In fact, these adjustments are irrelevant for growth calculations as well as any other calculations that are based on sequential changes (such as the Active Cases calculation) since they are anachronous – not received in the order that they actually occurred. These adjustments, while detrimental to sequential calculations, are important to cumulative values.

We therefore added a Smoothing Filter that calculates an alternate time series for Cases and Deaths with most of the effect of these anachronistic changes removed. This greatly improved the stability and dependability of the sequence dependent metrics, while still allowing use of the original time series for sequence independent metrics. This filter process is described below under Metric Details.

The Smoothing Filter described above has done a good job of eliminating anachronous data dumps, while having little impact on the natural time series. If differential values such as R were computed on the raw time series, severe distortions would result.

The charts below show the original time series data as well as the filtered results at two levels -- the county of Bergen, New Jersey, USA, and the state of New Jersey. “deltaCases” is the difference in Cases from period T-1 to period T. “deltaDeaths” is the equivalent for Deaths. “filtNewCases” and “filtNewDeaths” are the adjusted versions of the delta time series based on the Smoothing Filter.

Smoothing Filter - County Level

Note that the anachronous spike in deaths (red line), and the negative spikes in delta cases (green line) have been effectively removed from the filtered series. Also note that toward the end of the green line several anamolous spikes have also been attenuated. Early in the history of deltaDeaths (red line), the series was very noisy, likely the result of sporadic test results arrivals. This noise was also reduced in the filtered series.

Smoothing Filter - State Level

The above chart illustrates the filter operating at a higher level (the state of New Jersey). Note that statewide the Deaths adjustment at 06/25 indicates nearly 1800 one day deaths compared to an average of around 50. This is effectively filtered out along with several anomalously high and low spikes.

Infection State

The levels of cR and mR along with some other data, allow us to classify an outbreak according to its stage:

• Spreading -- Number of active infections is rapidly increasing (R >= 1.5) and the scale of the infection is probably beyond containment.
• Emerging -- Number of active infections is rapidly increasing (R >= 1.5), but is small enough to potentially contain.
• Stabilizing -- Infection slowly growing (1.1 <= R < 1.5).
• Stabilized -- Number of active infections is approximately stable (.9 <= R < 1.1).
• Recovering -- Number of active infections is shrinking (R < .9), but is still beyond containment.
• Recovered -- Number of active infections is shrinking or stable, and scale is containable.

These define the potential values of the Infection State at a given location.

Metrics

Given a reasonable estimate of R, cR, and mR, we can begin to infer some other metrics that further illuminate the nature of the infection. Metrics are developed to provide insight into the dynamic state of the infection within a location. They may illustrate temporal changes as well as contemporaneous relationships within the data.

Contagion Risk is the likelihood of meeting at least one infected person during one hundred random encounters.

The Case Fatality Rate (CFR) is the likelihood that someone who tests positive for the virus will die. This is useful for comparing medical conditions between locations with a similar testing and reporting protocol and testing constraints. It is somewhat confounded by changes in testing availabilty. It almost always overstates the fatality of the infection and should not be confused with the Infection Fatality Rate.

The Infection Fatality Rate (IFR) is the likelihood that someone who catches the infection will die. This is a very elusive number due to the difficulty in estimating the actual number of infections in a population. This can be retroactively assessed via antibody testing, or approximated through calibrated adjustments.

Cases Per 100K combines location population data with the COVID-19 reported data to look at the proportion of a population that has tested positive for the virus. Ths is useful to normalize the infection rates across populations of different sizes. We use "per 100,000" as our scaling factor since it is an easier number to work with than the tiny numbers one would get using a per capita calculation.

Deaths Per 100K looks at the death rate per 100,000 population at a given location.

Immune Percent identifies the percentage of the population which has recovered from the infection and are presumed to be immune. As a larger proportion of the population becomes immune, the spread of the virus is dampened until at some level so called "herd immunity" is attained. At that point, it is difficult for the infection to continue as there are too few non-immune targets.

The Heat Index is a composite metric that combines a number of relevant metrics to indicate the relative level of attention a given location needs. This index is calibrated such that values greater than 1 indicate that attention is likely needed.

Indicators are a type of metric that can have negative or positive values. We define our indicators such that negative values imply negative outcomes. Indicators highlight both the direction and relative magnitude of change.

The Social Distance Indicator (SDI), based on change in Case Rate (cR), provides insight into the level of social distancing being practiced by a population. All other things being equal, a reduction in R is caused by an increase in social distancing, while an increasing R is indicative of reduced social distancing. This can be somewhat confounded by changes in testing policy and availability, but in practice is a good short term indicator.

The Medical Indicator (MDI) is based on changes in the ratio of Case Rate (cR) to Mortality Rate (mR). If all else is held constant, this ratio would settle at a consistent value, as the rate of increase in deaths would be proportional to the rate of growth in cases. Therefore, a decrease in the ratio signals that something has changed for the worse. In practice, this can be caused by a number of factors: 1) Testing is not growing as fast as the infection, 2) Medical Care is worsening or 3) Rapid changes in R combined with the time lag of deaths can cause skew between the two. If we adjust for the time lag, then either of the first two causes can be considered medical care issues. Thus decreases in this ratio will result in a negative Medical Indicator.

The Short Term Indicator (STI) is a predictive indicator that attemtps to determine if the infection is likely to get worse (negative values) or get better within a few days.

The Early Warning Indicataor (EWI) predicts major shifts (inflection points) in the momentum of the infection. It is meaningful when an infection is moving from a neutral or recovering state to a spreading state. It is also meaningful when an infection is transitioning from growth to stability.

Vaccine Metrics

The following metrics are designed to track vaccination data:

Vaccines Distributed indicates the cumulative number of vaccines that have been distributed to a location. This data is currently only available for US states.

Vaccines Administered shows the cumulative number of vaccine doses that were administered (i.e. injected) at the location.

People Vaccinated indicates the cumulative number of people who have received at least one vaccine dose.

People Fully Vaccinated shows the number of people who have received all of the required doses of any vaccine, whether single dose or multi-dose (not available for all locations).

Population Vaccinated Pct is the percent of the population that has recieved all of the required doses of any vaccine (not available for all locations).

Vaccines Administered Pct is he percent of the distributed vaccines that have been administered. This data is currently only available for US states.

In addition to the cumulative vaccination data above, the system also produces daily and weekly vaccination data.

Surge detection

The system tracks ebbs and flows in the infection rate to show multiple "surges" or "waves" of infection. We define a surge as a transition from a shrinking state to a growing state. We track the start dates, peaks, and durations of each surge. Knowing the surge number and start date helps in understanding the oscillations that a location goes through over the life of the infection.

Commentary

The metrics above paint a fairly clear picture of the state of the infection in any location at any given time. Interpreting them, however, requires a detailed understanding of the meaning of each metric and the range of values that it can assume.

We therefore created an interpretive commentary that describes the state of the infection for each location. This commentary combines the various metrics with expert qualitative assessment to form as complete a picture as possible, depending on the Infection State. For example:

“As of Aug 20, 2020, US-FLORIDA has improved to a Recovering state from a previous state of Stabilized. The infection is slowly decreasing (R = 0.81). There are currently 49,270 active cases. New Cases are currently 30,750 per week, down 62% from a peak of 79,920 per week. New Deaths are currently 1,035 per week, down 0% from a peak of 1,035 per week. This is the 4th surge in infections, which started on the week of May 29, 2020. With 1,035 new deaths, this is the worst week so far for deaths during this surge. The Contagion Risk is very high at 49.9%. This is the likelihood of meeting an infected person during one hundred random encounters. It appears that the level of social distancing has increased significantly, resulting in lower levels of infection growth. The Case Fatality Rate (CFR) is estimated as 1.7%. This is much lower than the average CFR of 3.6%. Preliminary estimates suggest that 7% of the population may have been infected and are presumed immune. This is not enough to significantly slow the spread of the virus. This preliminary estimation also implies an Infection Fatality Rate (IFR) of roughly 0.6%. The Short-Term Indicator(STI) suggests that the infection is likely to slow somewhat over the next few days.”

The commentary consists of several sections, each centered on the interpretation of one or more metrics:

• Infection State and Previous state if changed
• Number of active cases and implications
• Surge information
• Contagion Risk and qualitative assessment
• Social Distancing assessment
• Medical Conditions
• Case Fatality Rate
• Immune Percentage
• Hot Spots information (if on Hot Spots list)
• Predictive Indicators

Sections may be omitted if they are not relevant to the current scenario.

Data Pipeline

Our data pipeline is a One-Stop-Shop scalable solution from seemless data collecting, ingestion, ETL, analytics to governing and monitoring built on top of HPCC Systems. Each component of the pipeline is running as a job in HPCC Systems cluster. These jobs are scheduled to run automatically once the new incoming data is received without human intervention. Below is an introduction of each component of the pipeline.

• Collection: In our pipeline, the source data is automatically collected by monitoring and pulling the new data from data source and automatically uploaded to HPCC Systems cluster for Data Ingestion.

• Ingestion: once the data are collected and automatically uploaded for ingestion, the ingestor will automatically search the newly uploaded files and ingested to the system for ETL.

• ETL: By transforming, enhancing and cleaning the data, the processed data including Covid19 metrics are stored in HPCC Systems Data Lake and ready for data scientist and researchers to apply data analytics to extract useful information.

• Analysis: As introduced in the Metrics section, SIR model and Covid-19 indicators are developed in HPCC System for Covid19 analysis and prediction. The built-in Machine Learning Library of HPCC Systems is a great tool for data scientist and researcher to conduct data analytics and statistic inference as well. It includes but not limited to regression bundles, classification bundles, clustering bundles and Deep Learning bundle as well.

• Governing/Monitering: The data governing and job monitering is managed by Tombolo, HPCC Systems Data Catalog tool. When job failes, Tombolo will instantly identify the failure and automatcially send email notification to system administrator for the failure. For data governing, the pipeline on HPCC Systems is defined as workflow in Tombolo, as shown in Fig Tombolo COVID-19 Workflow . Each run of the workflow is an instance and the status of each job is recorded, as show in Fig Tombolo Workflow Instances and Fig Tombolo Instance Detial. If any job failed, it will automatically send an email notification to the adminitrators.

Data Governing

The main data sources are John Hopkins University (daily cases and deaths), US Census Bureau (US population), UN DESA (World population). The data lake data and the workflow can viewed using HPCC Systems Data Catalog tool Tombolo (version 0.5) at:

https://tombolo.hpccsystems.com [please login using CovidTracker/HPCCSystems as the user name and password]

Tombolo Application

A node in the workflow can be selected and double clicked to view the details. The following is an example of the details of a metrics file:

Tombolo Workflow

User Interface

The system provides a friendly web-based interface for viewing COVID-19 data and metrics. World, Country, and Regional maps are color coded to represent any of various selectable attributes of the infection at those locations. Clicking on any given location brings up a set of pages that provides details about that location -- from raw statistics to charts to advanced metrics and commentary.

The user interface provides several ways to navigate:

• Map View shows aspects of the infection through color codings on a map. The map can be color coded by a number of attributes including Infection State, New Cases, New Deaths, Cases per 100K, Deaths per 100K, Total Cases, Total Deaths, Vaccine Utilization, and Population Percent Vaccinated. On the Map View, users can drilldown to any level of location. Currently supported Views include World View, Country View, Province/State View, City/County View.

Country Map View

State Map View

• Stats View shows the summary statistics and metrics of each location. The location can be world level, country level, province/state level or city/country level. The statistics include but limited to daily new cases, daily new deaths, cumulative cases and cumulative deaths. It also includes all the metrics introduced in the previous section. The metrics are displayed in a bar chart.

Stats View

• Vaccine Data View shows the vaccination status at a location.

Vaccine Data View

• Trend View shows the trend of infection rate, weekly new cases and weekly new deaths. The details of theses definitions can be found in the previous section.

Trend View – Infection Trend

Trend View – New Cases and New Deaths Trend

• Hotspots View orders the locations by Heat Index, showing a triage list of locations and a description of their state. All details can be seen by clicking on any of the Hotspot locations.

Hotspots View

Additionally, the user interface provides the ability to move back and forward in time, to look at map views and / or statistics at any level, and during any point in the pandemic, to better understand the development and evolution of the pandemic.

Furthermore, a button is provided to animate the evolution of the pandemic, automatically moving from week to week, and showing any aspect (e.g. Contagion Risk, Infection State, Vaccine Administration). This live animation is intended to complement the static views to provide insights into how the pandemic evolves over time.

Appendix

Our metrics are based on below assumptions and definitions.

Constants

• Infection Period(IP) -- The average length of time during which an individual remains infections. This is currently set to 10 days.
• Infection Case Ratio(ICR) -- The average ratio of Actual infections to cases. This is a gross estimate of the ratio of all infections (Asymptomatic, Subclinical, Clinical) to Confirmed Cases. Although this is treated as a constant for rough estimation, it is known that this number varies over time as well as location, based on testing availability. This is currently set to 3.0 based on estimates by Penn State [2]
• Metric Window (MW) -- The number of days over which growth metrics are calculated. This is currently set to 7.
• minActiveThreshold -- The minimum fraction of the population with active infections in a location to be considered beyond containment. This is currently set to 0.0003.
• hiScaleFactor -- A scaling factor for Heat Index that provides a threshold for the Hot Spots list. This is calibrated such that Heat Index >= 1.0 identifies locations requiring attention. This is currently set to 5.0.

Input Statistics

• Cases -- Cumulative cases for a given location.
• Deaths -- Cumulative deaths for a given location.
• Hospitalizations -- Cumulative hospitalizations for a given location.
• Positive -- Cumulative number of positive tests for a given location.
• Negative -- Cumulative number of negative tests for a given location.
• Population -- The number of individuals living in a given location.

Adjusted Cases and Deaths

Various locations will occasionally produce anachronous data. That is, data that is not arriving in correct time sequence. This typically occurs when there is a change in reporting policy for the location, or when errors were found in the reporting process and corrections are applied retroactively. In these cases, it is common for large batches of cases or deaths to be suddenly dumped into a single days reporting. Likewise, downward corrections are occasionally seen, that can cause the cumulative values to become non monotonic. These occurrences can dramatically distort resulting metrics, especially those that depend on the difference in cumulative totals among periods, such as growth rate computations. To compensate for this, we subject the source data to a smoothing filter. This produces a set of alternate inputs that have removed these spikes and reversals. These alternate values can then be used to calculate more consistent differential values.

This filter is applied to the incoming data, both Cases and Deaths. It limits any daily change to between the MW-day moving MIN of the series and 1.25 * the MW-day moving MAX of the series. It then reconstructs a new adjusted time series based on these restricted changes. A change greater than 1.25 from day to day implies a growth rate(R) greater than 10, which is larger than any expected maximum real growth rate, At the same time, the filter removes any negative changes, by bounding the newCases and newDeaths to greater than or equal to zero.

• newCases(T) = MAX(Cases(T) - Cases(T-1), 0)

• casesMax(T) = MAX(newCases(T-MW - 1), newCases(T-MW), ... ,newCases(T-1))

• casesMin(T) = MIN(newCases(T-MW - 1), newCases(T-MW), ... ,newCases(T-1))

• adjustedNewCases(T) = IF(newCases(T) > 1.25 * casesMax(T), 1.25 * casesMax(T), IF(newCases(T) < casesMin(T) / 1.25, casesMin / 1.25, newCases(T)))

• adjustedCases(T) = adjustedNewCases(1) + adjustedNewCases(2) + ... adjustedNewCases(T)

• newDeaths(T) = MAX(Deaths(T) - Deaths(T-1), 0)

• deathsMax(T) = MAX(newDeaths(T-MW - 1), new Deaths (T-MW), ... ,newDeaths(T-1))

• deathsMin(T) = MIN(newDeaths (T-MW - 1), newDeaths (T-MW), ... ,newDeaths (T-1))

• adjustedNewDeaths (T) = IF(newDeaths(T) > 1.25 * deathsMax(T), 1.25 * deathsMax(T), IF(newDeaths(T) < deathsMin(T) / 1.25, deathsMin / 1.25, newDeaths(T)))

• adjustedDeaths(T) = adjustedNewDeaths(1) + adjustedNewDeaths(2) + ... adjustedNewDeaths(T)

Metrics

These are calculated based on an MW (e.g. 7) day sliding window. T refers to the current day, while T-MW refers to MW days previous. Note: please see the definition of adjCase from section Adjusted Cases and Deaths.

• cR -- The effective case growth rate. cR = ((adjustedCases(T)– adjustedCases(T-MW)) / (adjustedCases(T-MW) - adjustedCases(T-2MW)))^(IP/MW)

• mR -- The effective mortality growth rate. mR = ((adjustedDeaths(T)– adjustedDeaths(T-MW)) - (adjustedDeaths(T-MW) - adjustedDeaths(T-2MW)))^(IP/MW)

• R -- Estimate of the effective reproductive rate. This is based on a geometric mean of cR and mR. Some constraints are placed on the values to reduce the effect of very noisy data. R = √((MIN(cR,mR + 1.0) * MIN(mR,cR + 1.0)))

• Active -- The estimated number of active (i.e. infectious) cases. Active = adjustedCases(T) - adjustedCases(T-IP)

• Recovered -- The number of cases that are considered recovered. Recovered = Cases - Active - Deaths

• ContagionRisk -- The likelihood of encountering at least one infected person during 100 random encounters. ContagionRisk = 1 - (1-(Active / Population))^100

• Case Fatality Rate (CFR) -- The likelihood of dying given a positive test result. CFR = adjustedCases(T - IP) / adjustedDeaths(T)

• Infection Fatality Rate (IFR) -- The likelihood of dying, having acquired an infection. This is a gross approximation assuming a constant ICR. IFR = CFR * ICR

• immunePct -- The fraction of the population that has recovered from the infection and are considered immune. immunePct = Recovered * ICR / Population

• Infection State (IState) -- A qualitative metric that models the state of the infection. It will assign one of the following states to the infection within a location: 1) INITIAL, 2)RECOVERED, 3) RECOVERING, 4) STABILIZED, 5) STABILIZING, 6) EMERGING, 7) SPREADING. These are assigned based on a series of cascading predicate tests. The first true predicate assigns the state. prevState = IF(not EXISTS(Istate(T-1), SetStat(1),

                   IState = MAP(
                                R > 1.5 and Active / Population < minActiveThreshold => EMERGING,
                                R > 1.5 => SPREADING,
                                R > 1.1, STABILIZING,
                                R > .9, STABILIZED,
                                R > .1 OR Active / population > minActiveThreshold, RECOVERING,
                                Cases > 0, RECOVERED,
                                INITIAL
                              )
  

• HeatIndex(HI) -- A composite metric that takes into account scale, growth rate, social distancing, medical conditions, and Contagion Risk. This metric is scaled such that values >= 1.0 are considered Hot Spots needing attention. Heat Index = LOG(Active) * (MIN(cR, mR + 1) + MIN(mR, cR+1) + MI + SDI + ContagionRisk) / hiScaleFactor

Note: See below for definitions of SDI and MI

Indicators

Indicators are zero based, with negative numbers indicating negative outcomes, and positive numbers positive outcomes.

• Social Distance Indicator (SDI) -- Based on the ratio of the current cR to the previous cR. dcR = cR(T) / cR(T-MW) SDI = IF(dcR > 1, 1-dcR, 1 / dcR - 1)

• Medical Indicator (MI) -- Based on the ratio of case growth (cR) to mortality growth (mR). cmRatio = cR / mR MI = IF(cmRatio > 1, cmRatio - 1, 1 - 1 / cmRatio)

• Short-term Indicator (STI) -- A short term directional predictor (period 2-3 days)
  cSTI = adjustedNewCases(T) / ((adjustedNewCases(T-MW) + adjustedNewCases(T-MW+1) + ... + adjustedNewCases(T)) / MW) mSTI = adjustedNewDeaths(T) / ((adjustedNewDeaths(T-MW - 1) + adjustedNewDeaths(T-MW)+ ... +newDeaths(T-1)) / MW) STI0 = (cSTI + mSTI) / 2 STI = IF(STI0 > 1, 1-STI0, 1 / STI0 - 1)

• Early Warning Indicator (EWI) -- EWI is a pseudo-predictor. It uses predictable changes in the ratio of newCases to newDeaths to detect major inflections. It generates a positive signal when R (as computed above) is likely to transition from above one to below one within one to two weeks. It generates a negative signal in advance of R transition from below one to greater than one. It is not a true predictor in that it detects that the inflection has already occurred, but did not show up in the computed R because of its lagging mR component. EWI0 = SDI - MI EWI = IF(SDI < -.2 AND MI > .2, EWI0, IF(SDI > .2 AND MI < -.2, EWI0, 0))

References

[1] Kermack, W. O., & McKendrick, A. G. (1927). A contribution to the mathematical theory of epidemics. Proceedings of the royal society of london. Series A, Containing papers of a mathematical and physical character, 115(772), 700-721.
[2] Silverman, J. D., Hupert, N., & Washburne, A. D. Using influenza surveillance networks to estimate state-specific case detection rates and forecast SARS-CoV-2 spread in the United States.
[3] Judea Pearl. "Causality: Models, Reasoning, and Inference", Cambridge University Press, 2000, 2008, Kindle edition.
[4] Judea Pearl, Madelyn Glymour, Nicholas P. Jewell. “Causal Inference in Statistics”, John Wiley and Sons, 2016.

Data Attribution

[1] Dong, Ensheng, Hongru Du, and Lauren Gardner. "An interactive web-based dashboard to track COVID-19 in real time." The Lancet infectious diseases 20.5 (2020): 533-534. https://github.com/CSSEGISandData/COVID-19
[2] Hasell, J., Mathieu, E., Beltekian, D. et al. A cross-country database of COVID-19 testing. Sci Data 7, 345 (2020). https://doi.org/10.1038/s41597-020-00688-8 https://github.com/owid/covid-19-data
[3] World Population Prospects 2019. Available at https://population.un.org/wpp/