Modeling quarantine during epidemics by mass-testing with drones

Leonid Sedov; Alexander Krasnochub; valentin polishchuk

In the output we seek a route for each drone (see Figure 2 for an example), with the indication of how many people the drone serves in each square along its route (in some squares this number may be 0 meaning that the drone just passes over the square); the total number of people served by the route between successive returns to the hospital should not exceed the drone capacity C. Note that a square may be served by several drones; e.g., if the number of people living in a square is 2C or more, the square will have to be visited at least two times (or possibly more, if one of the times the drone is not used in the square to its full capacity). We suggest that in practice the drone repeats the route twice: first to distribute the tests and then to collect them --the interval between the distribution and collection does not influence our results since we compute a single route for every drone and duplicate it, thus simply doubling the length of the routes and consequently the number of drones needed to maintain certain testing frequency (if the interval is long, people may store their specimen in the fridge [WHO20]). The time a drone spends in each square it serves (i.e., in each square where its route serves >0 people) is set to 15min: this includes the time to possibly distribute the tests to (or collect the tests from) several cottages in the square; it also includes the time to change drone batteries at the base (hospital, lab) when needed. The route for each drone consists of several tours, where each tour is a closed loop that starts and ends at the hospital and the number of people served on each tour is at most C (any such tour may be executed by a drone without returning to the base as long as the battery capacity is not a constraining factor: for a drone with our maximum considered capacity C=1000 this would hold in a reasonable city scenario because 1000 people may be typically reached on a tour of length 10-20km, which is below the range of a non-toy drone; in a rural scenario, however, where visiting 1000 people may require longer tours, the battery may become the limiting factor and the maximum tour length constraint will have to be added when computing the tours). Minimizing the total length of such tours, needed to cover all people in the area, is known as the Capacitated Vehicle Routing Problem (C-VRP). We used Google's OR-Tools [PF] to solve the C-VRP, i.e., to find the tours that collectively serve all people in the area . CC-BY 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.