Modeling quarantine during epidemics by mass-testing with drones

Leonid Sedov; Alexander Krasnochub; valentin polishchuk

Since the parameters of SIR (and hence SIQR) vary widely depending on the country, anti-epidemic measures, quality of the available data and other factors, we do not confine ourselves to specific values for the parameters. Instead, we present SIQR curves for a whole range of the parameters. Specifically, we started from the open-source GeoGebra applet [S20] which computes SIR curves S, I, R for any values of the parameters a and b set by the user; the parameters are set simply by moving a and b sliders, so the curves change interactively as the parameters are modified (the applet assumes that the total population size is 1, i.e., it shows the fractions of population in the S, I and R compartments). We changed the sliders to represent the recovery time and the effective reproduction number R0 (the number of people infected by one infected person): a and b are then calculated as b=1/T, a=R0*b = R0/T; we choose T and R0 as the user-input parameters because they are the ones estimates for which are easier to find reported (sources with various estimates bound, but we do not restrict ourselves to any particular one since we give the full flexibility with the parameters choice). To extend SIR to our SIQR, we add the slider for the inter-testing interval D, calculate c=1/D and change the SIR differential equations to the SIQR equations above. We also depict the curve CI showing the total (cumulative) number of people infected; that is, CI(t) is the number of people that have been infected by the time t (since the transition to infected happens only from the susceptible, CI is simply the total population minus S). Figure 3 shows screenshots of our SIQR applet --it can be seen how the curve flattens with D=8 (the applet is interactive, and we invite the reader to play online with our sliders for the different parameters at http://tiny.cc/SIQR). Figure 1 for the number of different-capacity drones needed to reach D=8) Figure 4 shows real data (pink crosses) for confirmed COVID-19 cases in Sweden starting from 100 cases on March 06 2020 [ECDE] (see [GWWK+20] for detailed COVID-19 history in Sweden). The basic SIR model (Q=0) fits the data with a modest (for the novel coronavirus) value of R0=2.27, which is reasonable given the general hygiene and cultural distancing in Sweden. Because not all the population was tested, we do not know the true number of infected people. Instead of trying to estimate this true number (which would introduce yet another parameter), we fit our pink curve into the confirmed cases; in this sense R0 represents here the number of new confirmed cases per one confirmed case Our SIQR model suggests that regular mass-testing with the interval D=30 (which roughly amounts to randomly testing ~3.3% of the population every day) would flatten the curve quite significantly We again invite the reader to play with our interactive GeoGebra applet http://tiny.cc/SIQR_Swe to see the effects of the testing frequency, as well as the changes in the parameters R0 and T.