Is Wu Ever Going to Provide Descriptive Forecasts Again

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Research Commodity

COVID-19: Short term prediction model using daily incidence data

• Hongwei Zhao,
• Naveed Due north. Merchant,
• Alyssa McNulty,
• Tiffany A. Radcliff,
• Murray J. Cote,
• Rebecca S. B. Fischer,
• Huiyan Sang,
• Marcia G. Ory

x

• Published: April 14, 2021
• https://doi.org/10.1371/journal.pone.0250110

Figures

Abstruse

Groundwork

Prediction of the dynamics of new SARS-CoV-2 infections during the electric current COVID-nineteen pandemic is critical for public health planning of efficient health intendance allocation and monitoring the effects of policy interventions. We describe a new approach that forecasts the number of incident cases in the nearly hereafter given past occurrences using only a small number of assumptions.

Methods

Our approach to forecasting future COVID-nineteen cases involves 1) modeling the observed incidence cases using a Poisson distribution for the daily incidence number, and a gamma distribution for the series interval; ii) estimating the effective reproduction number assuming its value stays constant during a curt time interval; and 3) cartoon futurity incidence cases from their posterior distributions, assuming that the current transmission charge per unit volition stay the same, or modify past a certain degree.

Results

Nosotros apply our method to predicting the number of new COVID-nineteen cases in a single country in the U.S. and for a subset of counties within the land to demonstrate the utility of this method at varying scales of prediction. Our method produces reasonably authentic results when the constructive reproduction number is distributed similarly in the hereafter as in the past. Large deviations from the predicted results can imply that a change in policy or some other factors take occurred that have dramatically altered the disease transmission over time.

Conclusion

We presented a modelling approach that we believe tin can be hands adopted by others, and immediately useful for local or state planning.

Citation: Zhao H, Merchant NN, McNulty A, Radcliff TA, Cote MJ, Fischer RSB, et al. (2021) COVID-19: Short term prediction model using daily incidence data. PLoS 1 16(4): e0250110. https://doi.org/10.1371/periodical.pone.0250110

Editor: John Schieffelin, Tulane University, Usa

Received: November 18, 2020; Accepted: March 30, 2021; Published: April fourteen, 2021

Copyright: © 2021 Zhao et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in whatever medium, provided the original author and source are credited.

Data Availability: We used data from public available source, namely, COVID-xix Data Repository by the Center for Systems Scientific discipline and Engineering (CSSE) at Johns Hopkins University https://github.com/CSSEGISandData/COVID-nineteen.

Funding: The author(s) received no specific funding for this work.

Competing interests: The authors have declared that no competing interests exist.

Introduction

Since the World Health Organization declared a pandemic for the novel SARS-CoV-2 2019 virus (COVID-xix) on March 11, 2020 [i], the Americas, Europe, Southward-Eastward Asia and Eastern Mediterranean regions have the most documented cases [2]. Globally, nationally, and at every sub-governmental level, there is a demand to monitor the electric current caseload and project the rate and nature of the spread to guide public health awareness, preparedness, and response. Societies have to bargain with many pressing issues such every bit ensuring acceptable supplies of personal protective equipment, considerations about the adequacy of the health care workforce and other wellness care resources, as well every bit how to balance restrictive prophylactic guidelines with keeping businesses open and the economy audio. For a novel communicable diseases, it is especially important to forecast time to come cases based on what has happened in the firsthand past.

Prediction for the number of cases in a pandemic and implications for health care needs and resources have received a lot of attention in the scientific world [3–5], regime agencies [half-dozen–8], and in media lately [nine–11]. With the plethora of models, in that location is likewise growing scrutiny [12] about the accuracy of different models, and an appreciation that model parameters need to be refined based on evolving knowledge nearly the affliction trajectory and factors impacting infection and transmission rates.

The unlike approaches to modeling and forecasting infectious disease epidemics tin be characterized as: 1) mechanistic models based on SEIR (referring to Susceptible, Exposed, Infected, and Recovered states) framework [13]; or its modified version [fourteen–16]; two) time serial prediction models such as ARIMA [17], Grey Model [18], and Markov Chain models [19]; and three) amanuensis type models (i.e. simulating individual activities for a population) [20]. Even within each category, there are unlike types of approaches attempted. For SEIR models, there are deterministic models involving differential equations, and stochastic models entailing probability distributions. There are models that are designed to brand long-term forecasts, and models that are all-time used for brusk-term predictions. For this paper, nosotros primarily focus on short-term predictions based on SEIR concepts intended to forecast incidence cases for the adjacent two to three weeks.

The SEIR model is an extension of the classical SIR model [21], and both SEIR and SIR models are foundations for many epidemiological modeling techniques. The model's force lies in its simple approximation of a complex process. For example, a typical SIR model specifies that at a certain time t, the population (with size Northward) can be classified as people who are susceptible S(t), infected I(t), and recovered R(t) according to the post-obit serial of differential equations: where β and λ represent the manual rate and recovery rate, respectively.

In theory, the population size for each state equally a time series can exist used to estimate the parameters in the model according to the system of equations. In practice, modelers rarely have an accurate count of people at each stage, and the parameters could change with time. The problem has been tackled using dissimilar approaches. For example, Zhu and Chen [22] considered a statistical transmission model for early phase of COVID-19 outbreak; Wu et al. [23] incorporated the possibility of people moving out of the compartments due to migration in the modified SEIR model. However, both approaches made the supposition that the transmission rate was constant. In many states within Us, or in many counties, we have seen a rapid change of the manual rate caused by public behavior and public policy, therefore, it is not realistic to use a model with a constant transmission rate over a long catamenia of time.

Although many approaches to predicting infectious disease transmission have appeared in literature, we accept non plant one method that can be used readily for a solar day-to-24-hour interval short-term forecast purpose. Godio et al. [24] used SEIR models for predicting epidemic evolution past means of a stochastic solver, which allows a time-dependent transmission rate. They model the transmission rate as a function of community mobility. This approach is more than flexible than the constant transmission charge per unit assumption. Yet, it still cannot capture other dynamic aspects of the surroundings that impact the transmission rate, such as masks mandates, and adoption of contact tracing, early testing and isolation. Alternatively, Friston et al. [25] proposed a dynamic causal model framework for COVID-19, where they tried to include every variable that "matters" in the spread of the affliction. This model suggested that individuals had four different characteristics: location, infection status, testing results, and clinical status (i.due east., how sick they are). Each of these four characteristics independent four different states, and individuals could move from one state to another country over time. The chief challenge was that at that place were many parameters used in the model, and identifying authentic initial estimates of all the parameters is difficult for a novel infectious affliction with not-specific symptoms and potentially many asymptomatic cases.

The objective of this paper is to provide a method that can be reliably used to brand predictions for the epidemic development in the adjacent two to 3 weeks, based on the observed incidence cases merely. Due to the relative small pct of death in the whole population, we will ignore the death information in our modeling. The motivation for this work originated from pragmatic planning questions posed by local and country officials charged with allocating resources and ensuring population health. Members from the Texas A&M University Schoolhouse of Public Health started to monitor and forecast COVID-nineteen cases at the kickoff of the pandemic, so used the projected cases to support predictions for hospitalization and related wellness resources utilization.

Methods

Assuming that we have observed a time serial of COVID-19 incidence cases up to a time t, our goal is to make predictions of incidence cases in the next two to three weeks. In an platonic scenario, all data sets would be calibrated to the time of infection (an admitted impossibility). However, publicly available information sets most often reverberate the date of reporting, which may exist the date of reporting to the local health department, but more frequently reflects the date of reporting up the chain, such as to the State wellness department. As such, day-to-day variations of reported incidence cases often reflect not the true variation of the disease infection but reporting capacity. In addition, a large data dump might occur considering of attempts to process backlogged data. Therefore, we propose to perform a smoothing average of data (due east.g. iii-day weighted average) before performing any analysis. In the event of a large data dump, we also need to make adjustment to the information and distribute the cases over time. These aligning to public databases would non only improve model treatment but also exist valuable for our interpretation and awarding.

Our arroyo to forecasting future COVID-19 cases involves two chief steps. Kickoff, nosotros model the observed incidence cases using similar ideas as appeared in Cori et al. [26]. Bold a Poisson distribution for the daily incidence number, and a gamma distribution for the serial interval, we are able to estimate the parameter (i.east. the effective reproduction number R _{due east} ) in the model. In the forecasting step, we depict future incidence cases from their posterior predictive distributions, assuming that the current R _e volition stay the same, decrease 5%, or increase 5%. The upper 95% posterior credible intervals for increased R _e scenario together with the lower 95% posterior apparent intervals (CI) for decreased R _eastward scenario constitute our prediction intervals. The detailed clarification of our methods can be found in S1 Appendix.

Some basic assumptions are necessary for using our methods. In order to determine the value of the effective reproduction number R _e , we made the assumption that R _e has a prior gamma distribution with a shape parameter of 1 and a scale parameter of five, similar to Cori et al. [26]. We as well causeless that the serial interval has a discretized gamma distribution [26] with a mean of 3⋅95 and a standard divergence of iv⋅24 [27]. These hyper-parameters are generally fixed in our model and in our projection.

One parameter that we permit to vary is the time interval τ which we utilise to get reliable estimates of R _e . In essence, we assume that R _e is constant during this interval [t − τ + i, t] and then that we can become a reliable gauge of R _eastward (t) at time t. From our experience, τ = 7 days or τ = 12 days are recommended, the option of which depends on the incidence numbers (smaller incidence cases require a larger τ) and the actual dynamic change of the transmission rate (a smaller τ tin can capture the alter improve). A detailed discussion of the assumptions and parameters used for our model is provided in the "Choosing Model Parameter" section in S1 Appendix.

Awarding to COVID-19 information sets

We first demonstrate how to apply our methods for predicting COVID-19 cases in Texas, a large and diverse state in the US with a population size of approximately 29 million. We utilize information from the COVID-xix Data Repository past the Middle for Systems Science and Applied science (CSSE) at Johns Hopkins University. Every bit of November 15, 2020, the total number of reported cases was 1,059,753, corresponding to an attack charge per unit of 38⋅0 per 1,000 people.

We emphasize the importance of agreement how the case reports can be influenced by authoritative problems, and the demand to adapt our model accordingly. For instance, on September 21, 2020 there was a reported 14,129 cases for Harris county due to processing of backlogged information on that 24-hour interval. This artificial spike would influence the gauge of R _e , and consequently, the prediction going forward. Therefore, we reassigned those cases from Harris county according to the following rule: We showtime imputed the number of cases on that day using the average number of cases in the past seven days. Then we evenly spread the extra cases over the previous 31 days including that index day of September 21. The modified series would be treated equally the observed series in our subsequent modeling assay. Another modification we made was to shine the data serial. Due to the loftier variability of the daily cases, and the fact that there was frequently a delay in reporting especially during the weekends, nosotros smoothed the data using the post-obit algorithm, similar to Sun et al. [28]: where T is the final time point in the data series upon which a forecast is to exist made. The smoothed information series were the data nosotros used for generating our prediction models.

Equally mentioned in the detailed "Methods" department in S1 Appendix, nosotros beginning used the method of Cori et al. [26] to judge the reproduction number R _e (t) for different time t based on the smoothed incidence information in Texas, with a cut off date of November 15, 2020, and an interval of τ = seven days. (Results using τ = 12 days are presented in S1–S3 Figs). The smoothed data series, the estimated R _e (t), and its 95% confidence intervals (CI) are shown in Fig 1.

It is clear from Fig 1 that there were unlike stages of COVID-19 spread in Texas. Due to the large number of incidence cases, the 95% CI for the constructive reproduction number R _{due east} are quite narrow. During the calendar month of Apr, the case counts were kept very low due to a statewide Shelter-in-Place lodge that was enacted by the Governor. The estimated R _{due east} was close to i⋅0 around mid-April. Beginning May 1, 2020 Texas started phased reopening process, with many restrictions lifted in early on June, right subsequently the Memorial Day holiday. The daily incidence cases began to increase dramatically after Memorial Mean solar day weekend, and continued throughout June, reaching a acme daily incidence of about 13,000 in early on July. During this period, R _{due east} gradually increased to a value of i⋅325. A statewide mask mandate was implemented on July three, 2020, and a couple of weeks subsequently that, we started to see a downward tendency in the incidence cases. The reproduction number slowly decreased to below 1⋅0 towards the cease of July and during August. Unfortunately, the trend reversed starting in early on September, with cases increasing once again and a reproduction number to a higher place one.0. The uptick was perchance due to Labor Mean solar day weekend gatherings and widespread reopening of in-person options for schools and colleges for the Fall 2020 semester. The epidemic was then kept under control for a while until Mid-October, when COVID-19 cases started to increase dramatically both statewide and nationwide.

For illustration purposes, we applied our prediction method at 4 equally spaced fourth dimension points that were two months autonomously: April fifteen, June xv, August 15, and October 15. We plotted three projection lines corresponding to the predicted mean values when the transmission rate (or equivalently the reproduction number R _e ) stayed the same, increased 5%, or decreased 5%. We also plotted the prediction intervals (shaded areas) based on the upper 95% CI limits for the five% increasing R _e and the lower 95% CI limits for the 5% decreasing R _e scenario. The predicted daily cases and cumulative cases, together with their prediction intervals for the next three weeks are shown in Figs 2 and 3 separately.

Fig 2. Texas predicted incidence cases using seven-solar day intervals.

3 solid lines stand for the predicted cases corresponding to current rate of transmission sustained, 5% increment in transmission rate, and 5% decrease in transmission charge per unit. The shaded areas bespeak prediction intervals.

https://doi.org/ten.1371/journal.pone.0250110.g002

Fig 3. Texas predicted cumulative incidence cases using 7-day intervals.

3 solid lines correspond the predicted cases corresponding to current rate of transmission sustained, v% increment in transmission charge per unit, and 5% decrease in manual rate. The shaded areas indicate prediction intervals.

https://doi.org/ten.1371/journal.pone.0250110.g003

As expected, our predictions performed differently at dissimilar times. On April 15, our forecast assuming constant transmission charge per unit matched the observed information very well. On June 15, when R _e was increasing apace because of the business reopening process and the Memorial Day holiday weekend, the observed cases savage betwixt our predicted curves assuming the same transmission charge per unit and five% increase in manual charge per unit. On August 15, we saw a gradual subtract in transmission rate due to a statewide mask mandate, and the forecast with 5% decrease in transmission rate matched the observed information closely. Finally, on October xv, we started to see an increasing tendency once again, and the forecast assuming 5% increase in transmission charge per unit worked well.

Secondarily, we chose to test the applicability of our model to a smaller geographic region within Texas. We applied our method to predicting the number of cases for the Brazos Valley (BV), a group of vii counties in Texas (i.e., Brazos, Robertson, Burleson, Madison, Grimes, Leon, and Washington counties), which collectively comprise the Bryan-Higher Station metropolitan surface area and neighboring counties. The center is Brazos County, where Texas A&M Academy is located. This surface area is approximately 100 miles from both Austin and Houston and has a younger population than Texas as a whole. Several healthcare entities and a public health authority in the BV needed timely and accurate forecasts to support planning for local COVID-xix cases.

The BV incidence cases and the estimated reproduction number R _eastward (t) using 12-day intervals are presented in Fig four. Due to pocket-sized incidence cases in BV, the CIs for R _e were quite wide, making forecasting for BV more than challenging. The trend for BV was influenced past the local context and so it did not always follow the trend in Texas. In addition, due to a relative small-scale population size (approximately 229,000), and sudden population modify caused by college students' moving out (in late-March corresponding to the Stay-at-Habitation order) and and so back to the region (in mid-Baronial to correspond with the get-go of the Fall semester), we saw more than variability in the incidence cases for BV. Therefore, we chose to use 12-day intervals for our modeling approach, merely we also provided results using vii-day intervals in S4–S6 Figs for additional information. All other parameters were the same as appeared in the land model, and we made predictions on the same days as we did for the state model. The predicted daily incidence cases and cumulative incidence cases for BV are shown in Figs five and half-dozen separately.

Fig five. Brazos Valley predicted incidence cases using 12-twenty-four hour period intervals.

Three solid lines represent the predicted cases corresponding to current rate of manual sustained, 5% increase in manual rate, and 5% decrease in transmission rate. The shaded areas bespeak prediction intervals.

https://doi.org/10.1371/journal.pone.0250110.g005

Fig vi. Brazos Valley predicted cumulative incidence cases using 12-twenty-four hour period intervals.

Three solid lines stand for the predicted cases corresponding to current rate of manual sustained, 5% increment in transmission rate, and 5% decrease in transmission rate. The shaded areas indicate prediction intervals.

https://doi.org/10.1371/journal.pone.0250110.g006

On April 15, our prediction bold the same transmission charge per unit sustained agreed well with the observed cases. On June 15, when the transmission rate increased quickly, the prediction upper bounds followed approximately the observed curve. Our forecast based on by history did not capture the increased instance numbers at the end of Baronial when school started, since we had an influx of cases due to thousands of students moving to Brazos county from all over Texas. Starting October xv, although by trend suggested increasing incidence cases, the observed data matched more than closely with the prediction lower bounds. Our model and method produced reasonably accurate results when the R _e value is distributed similarly in the future as it is in the past. Large deviations from the predicted results can imply that a change in policy or some other factors take occurred that have dramatically altered the R _e value over time.

Conclusion

We take proposed a method that generates predictions for the number of COVID-xix infectious affliction cases in the future, based on what estimates of R _e are like at the current time. The major strength of our approach lies in its simplicity, which makes information technology easy to implement with a small squad of modellers. As such, nosotros have incorporated information technology as part of a dashboard (https://covid19-modeltrac.shinyapps.io/TX-BV-ModelTrac/#section-tx-forecasts), where it can automatically generate forecasting values every twenty-four hours for a future view of three weeks using publicly-available data. This transparent and straightforward approach ways that the method can be hands adopted by others who want to do similar predictions to help inform local or state-wide decision using public data sources. Our predicted case numbers tin can also exist used as data inputs aslope other information for predicting health care utilization and wellness outcomes such as hospitalizations, intensive care unit (ICU) occupancy and corresponding ventilator use, and anticipated fatalities. These projections should exist performed routinely to plan for surges and avert overwhelming health resources. In Texas for case, hospitals are collectively working together using surge projections to identify and refer patients to bachelor infirmary beds [29].

A limitation for whatever infectious affliction prediction model is the complexity inherent in how data are nerveless. Communicable diseases reporting has long been plagued with many challenges. It is important to acknowledge that our model, every bit many others, relies on detection of infections through testing and reporting. In reality, the journeying of a simple data element, from infection to tabulation, has many obstacles and nuances forth the way. Some major complexities of the information include: policies almost testing algorithms (east.thousand. which suspect cases are tested); if screenings or surveillance is conducted, which diagnostic exam is acceptable or required for reporting; accessibility and availability of testing; administrative issues such as reporting requirements, procedures, and infrastructure. These elements can vary widely by locale and among populations within a locale. Thus, the available information are probable to represent some fraction of infections. Agreement the underlying caveats and how local situations contribute to limitations is essential to evaluating the model output. Nonetheless, the opportunity for practical awarding of our model to provide insight for cess, planning, and policy-making remains invaluable.

Similar to the widely-adopted method for estimating R _e [26], we fabricated a few assumptions, east.grand. the incidence I(t) follows a Poisson distribution, with a mean parameter determined by a renewal function involving a serial function w(due south). The serial office is assumed to have a discretized gamma distribution. The reproduction number R _e varies with fourth dimension, but we assume that it is constant over a time interval (vii days, or 12 days) in gild to obtain a stable estimate for its posterior distribution. Nether these assumptions, we can predict the number of cases that could occur in the following two or iii weeks, allowing R _{due east} to stay the same, increment five%, or decrease 5%. The assumption that R _e behaves similarly in the future as it does now is a major assumption, and is probably inaccurate if we projection far into the future. However, nosotros believe information technology to be a reasonable approximation of the truthful procedure if we want to see what happens in the adjacent couple of weeks from the nowadays.

Because R _east is related to many factors, it can change dramatically. It is a function of transmission probability, which means it can be affected by a mask mandate. Information technology is too affected by the average number of contacts ane person has, hence, we expect that R _e might increase when in-person schoolhouse resumes. In addition, it depends on how many days on average i person is infectious afterward condign infected, which can exist reduced by contact tracing and early on isolation. The number of people that are susceptible or immune is also changing over time. Equally more people become infected and then go recovered, the constructive R _e should subtract over time if other factors stay constant. If we want to make more authentic forecasts, we should allow a hereafter R _e to be a part of all these different factors. Another way to think almost this is that if we make projections according to current values of R _e , and then any deviations from the current trend can exist attributed to factors non explicit in our model, such as a policy implementation, or behavior changes arising from reactions to electric current situation.

One contributing factor to R _e that can be considerately measured is mobility data. If mobility information could provide insight on how R _eastward may vary, incorporating the motility data in a prediction model can result in better predictions for R _e in the time to come, which in turn will result in better estimates for the number of incidence cases. Finding the trend of R _{due east} values in the future using other data sources is a direction of our future research.

In summary, we presented a modelling approach that we believe can be easily adopted by others, and immediately useful for local or state planning. Although many initially downplayed the long-term consequences of COVID-19 [thirty], it is at present clear that new surges are appearing in the United states of america as well as globally [31–33], and that the pandemic spread is likely to last for some other year or two [three]. Thus, public health and governmental responses will need to be guided by data that pinpoint where, when, and amid whom the new cases are occurring. This data can help guide public wellness messaging equally well as the nature and degree of regime responses to mandating public health practices or regulating business operations to limit spread. Timely projections regarding case counts are critical to planning for healthcare resources and assuring available care and best possible outcomes for populations facing the uncertainty of a rapidly emerging infectious disease during a pandemic response.

Supporting data

S2 Fig. Texas predicted incidence cases using 12-day intervals.

Three solid lines represent the predicted cases corresponding to current rate of transmission sustained, 5% increment in transmission rate, and five% decrease in transmission rate. The shaded areas betoken prediction intervals.

https://doi.org/ten.1371/journal.pone.0250110.s003

(TIF)

S3 Fig. Texas predicted cumulative incidence cases using 12-24-hour interval intervals.

Three solid lines represent the predicted cases respective to current rate of manual sustained, 5% increment in transmission charge per unit, and v% subtract in transmission charge per unit. The shaded areas indicate prediction intervals.

https://doi.org/10.1371/journal.pone.0250110.s004

(TIF)

S5 Fig. Brazos Valley predicted incidence cases using 7-day intervals.

3 solid lines represent the predicted cases corresponding to current charge per unit of transmission sustained, 5% increase in manual charge per unit, and 5% subtract in transmission rate. The shaded areas indicate prediction intervals.

https://doi.org/x.1371/journal.pone.0250110.s006

(TIF)

S6 Fig. Brazos Valley predicted cumulative incidence cases using 7-mean solar day intervals.

Three solid lines represent the predicted cases corresponding to electric current charge per unit of transmission sustained, five% increase in manual rate, and five% decrease in manual rate. The shaded areas bespeak prediction intervals.

https://doi.org/x.1371/journal.pone.0250110.s007

(TIF)

Acknowledgments

We are appreciative of the inspiration and insight nosotros take gotten from the Texas A&Thou Emergency Management Advisory Grouping, and Public Health Modelling Team.

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Source: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0250110

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