tti

The goal of tti is to facilitate the recursive calculation of infection proportions for the test-trace-isolate process.

Installation

You can install the development version of tti from GitHub with:

devtools::install_github("HopkinsIDD/tti")

Examples

library(tti)

The get_dqc_equilibrium() function will iterate through the detected-quarantine-community vectors until “equilibrium” is met, as specified by the tolerance parameter. For example, here we start with 80% symptomatic in the community and 20% asymptomatic in the community.

dqc<- get_dqc_equilibrium(init= c(Ds=0, Da=0, Qcds=0, Qhds=0,
Qcda=0, Qhda=0, Qq=0, Cs=0.8,
Ca=0.2))
dqc#> Ds Da Qcds Qhds Qcda Qhda #> 0.0768155690 0.0096019461 0.0074079812 0.0296319249 0.0004629988 0.0018519953 #> Qq Cs Ca #> 0.0004504876 0.6913401207 0.1824369763

From this, we can calculate the proportion quarantined using the get_prop_quarantined() function.

get_prop_quarantined(dqc)
#> [1] 0.03980539

We can then calculate the (R_{effective}) under this scenario.

get_r_effective(dqc)
#> [1] 2.361799

The function get_proportions_df() will generate a data frame with four columns:

• t: the time (iteration)
• prop_infected: The proportion infected
• r_effective: The effective R value
• category: The category

For example, to run the recursive function over 10 time points, we would run the following.

d<- get_proportions_df(duration=10)
d#> # A tibble: 90 x 4#> t prop_infected r_effective category#> <dbl> <dbl> <dbl> <chr> #> 1 1 0 2.5 Ds #> 2 1 0 2.5 Da #> 3 1 0 2.5 Qcds #> 4 1 0 2.5 Qhds #> 5 1 0 2.5 Qcda #> 6 1 0 2.5 Qhda #> 7 1 0 2.5 Qq #> 8 1 0.8 2.5 Cs #> 9 1 0.2 2.5 Ca #> 10 2 0.08 2.46 Ds #> # … with 80 more rows

library(ggplot2)
ggplot(d, aes(x=t, y=prop_infected, color=category)) + geom_line() + scale_y_continuous("Proportion of Infected")

We can then calculate the effective (R) after each iteration.

library(dplyr)
r<-d %>%
distinct(t, r_effective)
r#> # A tibble: 10 x 2#> t r_effective#> <dbl> <dbl>#> 1 1 2.5 #> 2 2 2.46#> 3 3 2.36#> 4 4 2.36#> 5 5 2.36#> 6 6 2.36#> 7 7 2.36#> 8 8 2.36#> 9 9 2.36#> 10 10 2.36

ggplot(r, aes(x=t, y=r_effective)) +
geom_line() +
scale_y_continuous("Effective R")

We can also look at the (R_{effective}) over a variety of parameters using the get_r_effective_df() function. This can take parameters as either single number scalars or vectors of parameters to try. For example, if we wanted to look at how (R) is affected by varying t_ds between 1 and 14 and rho_s values of 0.05, 0.25, and 0.5, we would run the following.

d<- get_r_effective_df(t_ds=1:14, rho_s= c(0.05, 0.25, 0.5))
d#> # A tibble: 42 x 18#> r_effective alpha R kappa eta nu t_ds t_da t_qcs t_qca t_qhs t_qha#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int> <dbl> <dbl> <dbl> <dbl> <dbl>#> 1 2.41 0.2 2.5 0.5 0.5 4 1 3 3 3 3 3#> 2 2.42 0.2 2.5 0.5 0.5 4 2 3 3 3 3 3#> 3 2.43 0.2 2.5 0.5 0.5 4 3 3 3 3 3 3#> 4 2.43 0.2 2.5 0.5 0.5 4 4 3 3 3 3 3#> 5 2.43 0.2 2.5 0.5 0.5 4 5 3 3 3 3 3#> 6 2.43 0.2 2.5 0.5 0.5 4 6 3 3 3 3 3#> 7 2.44 0.2 2.5 0.5 0.5 4 7 3 3 3 3 3#> 8 2.44 0.2 2.5 0.5 0.5 4 8 3 3 3 3 3#> 9 2.44 0.2 2.5 0.5 0.5 4 9 3 3 3 3 3#> 10 2.44 0.2 2.5 0.5 0.5 4 10 3 3 3 3 3#> # … with 32 more rows, and 6 more variables: t_q <dbl>, omega_c <dbl>,#> # omega_h <dbl>, omega_q <dbl>, rho_s <dbl>, rho_a <dbl>

This gives us a data frame with 18 columns, the first being the (R_{effective}) and the subsequent columns detailing the parameters. Notice here there are 52 rows, because we had 52 combinations of t_ds and rho_s that we provided.

ggplot(d, aes(x=t_ds, y=r_effective, color=factor(rho_s))) +
geom_line() + scale_y_continuous("Effective R") + scale_x_continuous("Delay (symptomatic case detection and isolation)") + scale_color_discrete("P(detected | symptomatic)")

Base functions

We also include some low-level functions that take any sized compartment vector along with a conformable infection matrix and detection matrix. These are meant for more experienced users familiar with the underlying mathematical model.

infect<-matrix(c(2.5, 0, 0,
0, 1, 0,
0, 0, 2.5), nrow=3, byrow=TRUE)
detect<-matrix(c(0.1, 0.5, 0.4,
0.02, 0.9, 0.08,
0.2, 0, 0.8), nrow=3, byrow=TRUE)
dqc<- get_dqc_equilibrium_base(init= c(0, 0, 1), infect=infect,
detect=detect
)
dqc#> [,1] [,2] [,3]#> [1,] 0.1691082 0.154459 0.6764328

get_r_effective_base(dqc, infect)
#> [1] 2.268311