Testing and tracing
To incorporate testing and tracing mechanistically, we have expanded the basic model in order to be able to
- continue to make use of case reporting data (positive test confirmations per day) without having the results confounded by variation in testing intensity (by incorporating both positive and negative tests into our calibration);
- facilitate analysis of scenarios involving changes in testing intensity and contact tracing.
Our basic approach is to add an additional set of compartments to our model, expanding each compartment into the following sub-compartments:
- untested (
_u extension) People with negative test results move back into this category since they can be tested again if there are new reasons for the test.
- tested, awaiting report, sample is negative (
_n extension) either because the tested individual was uninfected, or because of a lack of test sensitivity. We can assign compartment-specific probabilities of a positive test (low for \(S\) [currently set as 0], high for \(I\) compartments [currently set as 1], and possibly lower for non-symptomatic/early stages than for later stages).
- tested, awaiting report, sample is positive (
_p extensions) either because the tested individual was infected, or because of a lack of test specificity.
- tested positive (
_t extension) Individuals who have a positive test will not be tested again, and may change their behaviour (isolate), depending on degree of compliance to public health advice.
In addition to these compartments, we also add accumulator compartments for negative and positive test reports. The appropriate accumulator is incremented at an appropriate time.
- If test results are indexed to the time of sampling then the accumulators are incremented during the
_u to _n and _u to _p transitions
- If test results are indexed to the time of reporting then the accumulators are incremented during the
_n to _u and _p to _t transitions
We can then recover the daily numbers of negative and positive tests recorded by differencing the cumulative totals (and add observation error if desired).
## Loading required package: shape
Individuals can also move between epidemiological compartments while awaiting test results, e.g. from “presymptomatic, awaiting positive test results” (Ip_p) to “mild infection, awaiting positive test results” (Im_p). This does not change their testing status, except that when untested, severely symptomatic individuals are hospitalized for COVID, we assume they are tested immediately (i.e. `
In order to reflect the range of possible testing strategies, we assign a testing weight to each compartment in the model that specifies what fraction of the current testing intensity is allocated to that compartment. We take the current testing intensity \(T\) (overall per capita tests/day) as a model input. Then, given testing weights \(w_i\), the *per capita} rate at which individuals in epidemiological compartment \(i\) move from _u to _n or _p (awaiting test results) is \[\begin{equation}
\frac{T w_i}{\sum_j w_j P_j} \,,
\end{equation}\] where \(P_j\) is the proportion of the population in compartment \(i\). The weights depend on the testing strategy and population state in complicated ways; if only confirmatory testing is being done (no screening or contact tracing or surveillance testing), then the weights will be skewed toward symptomatic compartments – although not entirely, as observed test positivity rarely goes above 20%, and sensitivity is thought to be much higher than this. More contact tracing will increase the weights of non-symptomatically infected people. More random-surveillance testing will make the weights of all the groups more similar.
Including the testing structure increases the number of compartments substantially, and consequently yields a much larger flow matrix
vis_model(testify=TRUE,aspect="fill")
## Warning in rExp(p, return_val = "eigenvector", ...): CHECK: may not be working
## properly for testify?
Explicit testing structure is enabled if the parameter vector/list contains an element testing_intensity which is set >0. (As a side note, if you are using read_params("PHAC_testify.csv") to capture our most recent set of default parameters, and you don’t want an explicit-testing model, you should use update(., testing_intensity=0).) The argument testing_time to the make_ratemat() function determines when testing is counted (“sample” or “report”); this can be passed to run_sim() (or from farther upstream) in the ratemat_args (list) argument; the default is to set counting time to “sample”, with a warning.
