Orange County, CA COVID-19 Situation Report Jull 11 - Aug 15
Last updated: 2020-09-12
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Knit directory: uci_covid_modeling/
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Orange County, CA COVID-19 Situation Report, Jul 11 - Aug 15
The goal of this report is to inform interested parties about dynamics of SARS-CoV-2 spread in Orange County, CA and to predict epidemic trajectories. Methodological details are provided below and in the accompanying manuscript.
Summary (statements are made assuming 95% credibility levels)
- The number of reported cases (15,000 in this period, shown as black bars in the top-middle plot above) underestimates the actual number of infections by a factor that ranges between 1.6 and 11. This means that we estimate that the total number of infections occurred between July 11, 2020 and August 15, 2020 is between 23,000 and 160,000.
- Prevalence (number of infectious individuals at any time point) is declining, but is projected to stay in tens of thousands in September.
- Deaths are also underreported, but not significantly so (black bars are a little below blue bands in the topleft plot above). Somewhere between 0.2% and 1% of all infections (not cases!) result in death.
- Basic reproductive number (\(R_0\)), defined as the average number of secondary infections one infectious individual produces in a completely susceptible population, is inside the interval (0.43, 0.78).
- Effective reproductive number (\(R_e\)), defined as its basic counterpart above, but allowing for some fraction of the population to be removed (recovered or deceased), as of August 15, 2020 is inside the interval (0.41, 0.72). We want to keep \(R_e < 1\) in order to control virus transmission.
Abbreviated technical details (optional)
Our approach is based on fitting a mechanistic model of SARS-CoV-2 spread to multiple sources of surveillance data. More flashed out method description is in the manuscript.
Model inputs
Our method takes three time series as input: daily new tests, case counts, and deaths. However, we find daily resolution to be too noisy due to delay in testing reports, weekend effect, etc. So we aggregated/binned the three types of counts in 3 day intervals. These aggregated time series are shown below.
Model structure
We assume that all individuals in Orange County, CA can be split into 6 compartments: S = susceptible individuals, E = infected, but not yet infectious individuals, \(\text{I}_\text{e}\) = individuals at early stages of infection, \(\text{I}_\text{p}\) = individuals at progressed stages of infection (assumed 20% less infectious than individuals at the early infection stage), R = recovered individuals, D = individuals who died due to COVID-19. Possible progressions of an individual through the above compartments are depicted in the diagram below.
| Version | Author | Date |
|---|---|---|
| 4ca76fb | igoldsteinh | 2020-08-27 |
Mathematically, we assume that dynamics of the proportions of individuals in each compartment follow a set of ordinary differential equations corresponding to the above diagram. These equations are controlled by the following parameters:
- Basic reproductive number (\(R_0\))
- mean duration of the latent period
- mean duration of the early infection period
- mean duration of the progressed infection period
- probability of transitioning from progressed infection to death, rather than to recovery (i.e., IFR)
We fit this model to data by assuming that case counts are noisy realizations of the actual number of individuals progressing from \(\text{I}_\text{e}\) compartment to \(\text{I}_\text{p}\) compartment. Similarly we assume that observed deaths are noisy realizations of the actual number of individuals progressing from \(\text{I}_\text{p}\) compartment to \(\text{D}\) compartment. A priori, we assume that death counts are significantly less noisy than case counts. We use a Bayesian estimation framework, which means that all estimated quantities receive credible intervals (e.g., 80% or 95% credible intervals). Width of these credible intervals encode the amount of uncertainty that we have in the estimated quantities.
Appendix
Sensitivity to Prior for \(R_0\)
We examine how sensitive our conclusions about \(R_0\) are to our prior assumptions by repeating estimation of all model parameters under different priors for this parameter. The priors are listed in the titles of the figures. Although the prior distribution of \(R_0\) does have some effect on its posterior (as it should), the our results and conclusions are not too sensitive to a particular specification of this prior.
Sensitivity to prior for fraction initially infected
We examine how sensitive our conclusions about \(R_0\) are to our prior assumptions by repeating estimation of all model parameters under different priors for the parameter controlling how many people are infected initially. This prior changes depending on the time period, so we adjust by changing the prior mean to be twice as large or one half as large as the default prior.
Last updated on 2020-09-12.
R version 4.0.0 (2020-04-24)
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