Predicting Whom to Test is More Important Than More Tests - Modeling the Impact of Testing on the Spread of COVID-19 Virus By True Positive Rate Estimation

Paul F Rodriguez

The SEIR infectious disease spread model was implemented in the R package EpiDynamics (Baquero & Marques, 2015) , using methods from Keeling & Matt (2008) . I modified the model so that the change in number of persons infected, dI/dt, is decreased by [-1 * TP rate * I] and the recovered pool (R) is increased by the same amount, which implies detected cases are immediately removed from the susceptible pool (S). The TP rate was given by the curve in Figure 1 with 4 parameters; TP-infpt, is the TP rate inflection point, t1='time-to-start' is the time during which few tests were done as the epidemic started, t2='time-to-ramp-up' is the time at which maximum daily tests were given, and P for population size. For example, South Korea did not start with 15000 tests but took some days to get organized and ramp up. Based upon reports, tests increased rapidly and steadily after February 10 th up to March 28th (South Korea CDC). Use a starting time around mid-January, I set t1=20, t2=68. The other parameters are set as described in Table 1 . Note that beta was varied to model and test different effects of TP rates, and mu was set to 0 to ignore birth/death rates. I ran the model for TP-infpt = 0.1 to 0.5, beta= 0.22 to 0.42 (R0~beta*7, or R0~1.5 to 3.0, where 1/7 is recovery rate, and beta is the contact rate). The contour plot in Figure 2 shows the maximum values reached in simulations (up to t = 120). The goal of the simulations is not to precisely match reported number of infected persons, which likely do not reflect true values, but to match the general time of peaking in the growth curve to within an order of magnitude. The growth plot in Figure 2 shows an example where the TP-infpt and beta parameters match the empirical growth curve for South Korea (e.g. www.worldodemeters.info). For South Korea, the peak value of infected cases was about 7300, and peak days were about 45-60 days (early to mid-March). The effective TP rate can have a big impact on whether growth is suppressed or increases because it essentially counteracts R0, the reproduction number (i.e. transmission rate). However, when R0 is very high (i.e. beta > 0.40) the impact of TP rate is relatively smaller, which is why Figure 2 has non-linear contour lines in that region. Even so, as the example growth plot shows, the TP rate can make a big difference over time. I also ran the model to compare to New York state. Based on reported testing numbers (COVID Table 2 . Simulation parameters for New York state simulation. Notice the testing phase time points are higher but steeper than South Korea.