In reichlab/covidEnsembles: What the Package Does (One Line, Title Case)

\def\logit{\text{logit}}

knitr::opts_chunk$set(echo = FALSE, message=FALSE, cache=TRUE)

library(tidyverse)

Some Exploratory Plots

covid <- read_csv('../../../data-raw/jhu-incident.csv')
pops <- read_csv('../../../data-raw/location_traits.csv')
covid <- covid %>%
  dplyr::left_join(
    pops %>%
      select(
        location_abbreviation=postalCode,
        pop=totalpop
      ))

ggplot(
  data = covid,
  mapping = aes(x = week, y = value, group=location)) +
  geom_line() +
  facet_wrap( ~ location_abbreviation, scales = 'free_y') +
  ggtitle('incident deaths, vertical scale per location')

ggplot(
  data = covid,
  mapping = aes(x = week, y = value, group=location)) +
  geom_line() +
  facet_wrap( ~ location_abbreviation) +
  ggtitle('incident deaths, same vertical scale')

ggplot(
  data = covid,
  mapping = aes(x = week, y = value/pop, group=location)) +
  geom_line() +
  facet_wrap( ~ location_abbreviation) +
  ggtitle('incident deaths/population, same vertical scale')

Observations:

• We have integer counts of deaths
• scaling by population is helpful.

Models

SIRD fit separately by state

Notation:

• $N$ = population for location
• $y(t)$ = count of deaths for location at time $t$
• $s(t)$ = proportion of population susceptible at time $t$
• $i(t)$ = proportion of population infected at time $t$
• $r(t)$ = proportion of population recovered at time $t$
• $d(t)$ = proportion of population dead at time $t$

Model:

\begin{align} y(t) &\sim \text{Negative Binomial}\left({d(t) - d(t-1)}N, \phi\right) \ \frac{d}{dt} s(t) &= - \beta s(t) i(t) \ \frac{d}{dt} i(t) &= \beta s(t) i(t) - \gamma i(t) - \mu i(t) \ \frac{d}{dt} r(t) &= \gamma i(t) \ \frac{d}{dt} d(t) &= \mu i(t) \ \end{align}

Priors:

\begin{align} d(0) &= 0.0 \ \tilde{s}(0) &\sim \text{Normal}(\nu_s, \sigma^2_s) \ \nu_s &\sim \text{Normal}(7.0, 2.0) \ \sigma_s &\sim \text{Gamma}(1, 1) \ \tilde{i}(0) &\sim \text{Normal}(\nu_s, \sigma^2_s) \ \nu_i &\sim \text{Normal}(0.0, 2.0) \ \sigma_i &\sim \text{Gamma}(1, 1) \ \tilde{r}(0) &= 0.0 \ \begin{bmatrix}s(0) \ i(0) \ r(0) \end{bmatrix} &= \text{softmax}\left( \begin{bmatrix}\tilde{s}(0) \ \tilde{i}(0) \ \tilde{r}(0) \end{bmatrix} \right) \ \log(\beta) &\sim \text{Normal}(\nu_{\beta}, \sigma^2_{\beta}) \ \nu_{\beta} &\sim \text{Normal}(0.33, 2) \ \sigma_{\beta} &\sim \text{Gamma}(1, 1) \ \log(\gamma) &\sim \text{Normal}(\nu_{\gamma}, \sigma^2_{\gamma}) \ \nu_{\gamma} &\sim \text{Normal}(-0.7, 2) \ \sigma_{\gamma} &\sim \text{Gamma}(1, 1) \ \log(\mu) &\sim \text{Normal}(\nu_{\mu}, \sigma^2_{\mu}) \ \nu_{\mu} &\sim \text{Normal}(-7.5, 2) \ \sigma_{\mu} &\sim \text{Gamma}(1, 1) \ \log(\phi) &\sim \text{Normal}(\nu_{\phi}, \sigma^2_{\phi}) \ \nu_{\phi} &\sim \text{Normal}(1, 2) \ \sigma_{\phi} &\sim \text{Gamma}(1, 1) \ \end{align}

reichlab/covidEnsembles documentation built on Jan. 31, 2024, 7:21 p.m.