Nowcasts
UC Irvine - Rt-estim
This Rt-estim-gamma model by Isaac Goldstein and Volodymyr Minin at UC Irvine and Jon Wakefield at University of Washington is a branching process inspired model where cases are modeled as noisy realizations of latent unobserved incidence. The number of diagnostic tests is incorporated as a covariate into the surveillance model to adjust for changes in testing volume over time.
Code Repository Raw Data Modeling methods
UC Irvine - Wastewater
This model by Isaac Goldstein and Volodymyr Minin at UC Irvine uses a modified compartmental model where viral pathogen genome concentrations are modeled as a noisy realization of a weighted sum of the number of infectious and recently recovered individuals.
Code Repository Raw Data Modeling methods
UCSF
ca-covid-r.infoThe UCSF model uses raw data from three sources: new cases by county from California Health and Human Services; wastewater readings from the Cal-SuWers network (“Wastewater (C)”), BioBot Analytics (“Wastewater (B)”) and WastewaterScan (“Wastewater (W)”). The Wallinga-Teunis technique is used to estimate reproduction numbers, corrected for right censoring of the case detection data.
Raw data Modeling methods
CDC Center for Forecasting and Outbreak Analytics
Rt estimates are derived from daily counts of new
COVID-19 hospitalizations.To estimate Rt, CDC fit Bayesian models to the data using the R packages
EpiNow2,
epinowcast, or using Stan models developed by the CDC Center for Forecasting and Outbreak Analytics (CFA).
Raw data Modeling methods
UC Santa Cruz
The County of Santa Cruz COVID-19 model is a probabilistic SEIR model with compartments for hospitalizations and ICU visits. Population-averaged COVID-19 data from three wastewater plants, along with hospitalization, ICU and death data, are used to inform model estimates using Bayesian techniques. These estimates include the effective reproductive number Rt and hospitalization projections, also available at the County of Santa Cruz Health Services Agency website.
County of Santa Cruz Health Services Agency website Model code repository
UC Davis Wastewater
Developed in collaboration with the Sophia and HCVT teams at UC Davis, this model estimates the Rt for COVID-19 using a sequential Bayesian method that models the test positivity rate (TPR) based on the concentration of SARS-CoV-2 RNA in wastewater (WW). This method is designed to adapt to changes in virus dynamics, which provides a comprehensive understanding of TPR trends. To model the TPR, a Bayesian sequential approach employs a Beta regression model with the concentration of SARS-CoV-2 RNA in WW as a covariate. This modeling approach provides TPR estimates which are used to calculate the Rt estimates.
Modeling methods Model code repository Raw data
Santa Clara County Wastewater
The Santa Clara County Wastewater Rt model is derived from the work of
Huisman et al., but includes several modifications. The model first fits an adaptive spline (
bs = 'ad' in
mgcv's
gam() function) to the normalized wastewater data to remove noise and recover the underlying trend of interest-- log-transformed input data undergoes smoothing using a TOBIT (censored normal) error distribution; dates with concentrations of 0 are treated as non-detects with censored outcomes, and the limit of detection is initially estimated using the lowest nonzero value in recent data. Smooth fits are used to detect outliers, i.e., observations with extreme residuals and thus unlikely to be in 95% of time series generated under the smooth model. Any outliers so flagged are resampled. Then the wastewater concentrations are converted into an estimated time series of infection events by deconvolving the smoothed wastewater signal with an estimate of the shedding load distribution. For deconvolution, following Huisman’s initial approach is used (available through
estimateR's
deconvolve_incidence() function) with a gamma-distributed incubation period with mean 3.58 days and SD 1.77 days, combined with a fecal shedding load distribution from the systematic review of Benefield et al., gamma distributed with mean 6.7 days and SD 7 days. Once the time series of infection events has been estimated, Rt is recovered based on an estimate of the generation interval distribution using standard renewal equation methods with the default priors for Rt in EpiEstim to have an expected value of 1. Rt estimates for each sewershed are converted to the overall county estimate using a population-weighted average. Inference is then conducted by calculating bootstrap quantiles and odds of agreement of epidemic trajectory with the point estimate based on original data.
Input data: PMMoV-normalized target gene concentrations in wastewater solids provided by
Wastewater SCAN.
Modeling methods Raw data
CDPH Wallinga Teunis
The Wallinga and Teunis method is based on the probabilistic reconstruction of disease transmission chains to estimate the number of secondary cases per infected individual. It is robust and only requires only case incidence data and the distribution of the serial interval (the time between the onset of symptoms in a primary case and the onset of symptoms of secondary cases) to estimate the % of cases from each day which were infected by cases on previous days. This data used for the estimate is derived from the CDPH line list of cases indexed by the date of symptom onset. The serial interval is given by a Weibull distribution with mean interval of 5.5 days. The methodology is implemented in the R programming language by the R0 package.
Modeling methods
CDPH Cislaghi
This method calculates R-effective as the number of newly diagnosed cases on day
s over the number of newly diagnosed cases on day
(s - T), where
T is the incubation time. CDPH uses officially reported California case data indexed by episode date, and an incubation period (
T) of 3 days. To smooth the curve and to avoid strong daily variations due to noise, R-effective was calculated as a seven-day moving average.
Modeling methods
CDPH Wastewater
estimateR PackageR forecast Package
Wastewater samples are collected and processed by WastewaterSCAN, an organization that partners with the Cal-SuWers Network to monitor wastewater at wastewater treatment plants in California. To reduce the effect of noise, the wastewater data is processed with spline smoothing followed by a square root transformation. To convert from viral shedding events in wastewater to a time series of infection events, the estimateR method uses a gamma delay distribution with a mean of 5 days and a standard deviation of 0.5 days (Huisman et al. 2022). Using the inferred infection time series, estimateR calculates the effective reproduction number by implementing a wrapper around the EpiEstim package (Scire et al. 2022). The generation time distribution input to EpiEstim is gamma distributed with a mean of 6.84 days, and a standard deviation of 4.48 days (Manica et al. 2022).
To account for lags introduced by deconvolution and wastewater data reporting, wastewater for each treatment plant is forecasted until the present day using a TBATS time series model (T: Trigonometric seasonality, B: Box-Cox transformation, A: ARIMA errors, T: Trend, S: Seasonal components) optimized by the forecast package. TBATS is an exponential smoothing model designed to forecast data with complex seasonal patterns (De Livera et al. 2011). This step provides a nowcasted, current-day estimate of the effective reproduction number. The effective reproduction number for each wastewater treatment plant is subsequently aggregated to the county level via population weighting.
CDC overview of wastewater surveillance
CDPH EpiEstim - ELR
EpiEstim uses a time series of daily infections generated by EpiNow2 from reports of positive PCR tests using ELR data as input, and a renewal equation based method to estimate R-effective over “sliding windows”. We assume R-effective will be constant over 7 day sliding windows. The serial interval is parameterized as an offset gamma distribution with a mean of 2.90 and a standard deviation of 1.64 days (Park et al. 2023).
Code repository Model vignette
CDPH EpiNow2
EpiNow2 uses a renewal equation-based model to estimate the time-varying reproduction number (R-effective) based on time series data by date of infection and an estimate of the generation interval, which is set to follow a lognormal distribution with a mean and standard deviation of 2.90 and 1.64 days (Park et al. 2023), discretized and bounded between 1–12 days.
ELR: To convert the input Electronic Laboratory Reporting (ELR) based time series to an infection date-based time series, EpiNow2 uses a convolved incubation period–a modified Weibull distribution with a mean of 4.24 days (Park et al. 2023)–and a data reporting delay distribution (time from onset to laboratory confirmation)–a lognormal distribution with a mean of 3.1 days and standard deviation of 2.6 days.
Hospitalizations: To convert the input hospital admission date-based time series to an infection date-based time series, EpiNow2 uses a convolved incubation period—a modified Weibull distribution with a mean of 4.24 days (Park et al. 2023)–and an onset to hospitalization delay, which follows a lognormal distribution with a mean of 8.3 days and standard deviation of 11.9 days.
Code repository Modeling methods Model vignette
Ensemble Nowcast
The ensemble nowcast takes the median of all the nowcasts available on a given date and smooths it with a three-day moving average. The methodology aims to be robust to outliers and to avoid kinks in the median nowcast when an input source for the ensemble estimate is unavailable on a certain date. Ensemble confidence interval calculation includes only models with corresponding confidence interval estimates available.
Forecasts
COVID-19 Forecast Hub
covid19forecasthub.org The COVID-19 Forecast Hub is run by the US CDC. The project collects forecast for the weekly new hospitalizations due to COVID-19. Forecasts are weekly, out to four weeks, at the state and national level.
Raw data Code repository
UC Irvine - SIRS
vnminin.github.ioThis model by Vladimir Minin and Damon Bayer at UC Irvine is a SEIR type model stratified by Omicron vs non-Omicron infection with hospitalization compartments. The model is calibrated to California hospital data from the California open data portal using data on COVID variant prevalence from GISAID."
Raw data Code repository
ARIMA-based Model
R forecast PackageModel forecasts are the result of utilizing the forecast package's automatic ARIMA forecasting model. Note that the form of the model may vary between counties and over subsequent published forecasts.
Modeling methods
Holt’s Model
R forecast PackageThe Holt's linear trend method extends simple exponential smoothing to allow the forecasting of data with a trend (Holt 2004).
Damped Holt’s Model
R forecast PackageThe Damped Holt's model is an exponential smoothing model designed to damp erratic trends (Gardner & Mckenzie 1985).
NNETAR Model
R forecast PackageThe neural network autoregression (NNETAR) model is a system of feed-forward neural networks with a single hidden layer and lagged inputs.
Harmonic Regression
R forecast Package A dynamic harmonic regression model captures a seasonal pattern using Fourier terms with short-term time series dynamics handled by an ARIMA error (Young et al. 1999).
TBATS
R forecast Package The acronym “TBATS” stands for: trigonometric seasonality; Box-Cox transformation; ARIMA errors; trend; and seasonal components. TBATS is an exponential smoothing model designed to forecast data with complex seasonal patterns (De Livera et al. 2011).
CDPH EpiNow2 - Hospitalizations
EpiNow2 uses a renewal equation-based model to estimate the time-varying reproduction number (R-effective) based on time series data by date of infection and an estimate of the generation interval, which is set to a lognormal distribution with a mean and standard deviation of 2.90 and 1.64 days (Park et al. 2023), discretized and bounded between 1–12 days. To convert the input hospital admission date-based time series to an infection date-based time series, EpiNow2 uses a convolved incubation period—a modified Weibull distribution with a mean of 4.24 days (Park et al. 2023)–and an onset to hospitalization delay, which follows a lognormal distribution with a mean of 8.3 days and standard deviation of 11.9 days.
Code repository
Modeling methods
Model vignette
CDPH Human Judgement Forecast
This forecast is compiled from individual judgment forecasts from members of the CDPH modeling team. A probability distribution spline is fitted for each submission (in form of quantile predictions), and the median ensemble is calculated from all the forecasts in each epiweek for the final forecast.
Ensemble Forecast
The ensemble forecast takes the median of all the forecasts available on a given date and fits a smoothed spline to the trend. The methodology aims to be robust to outliers, and to avoid artifacts (i.e. abrupt kinks) when the median forecast switches from one source to another.
