An Efficient Geometric Search Algorithm of Pandemic Boundary Detection

Abstract

We consider a scenario where the pandemic infection rate is inversely proportional to the power of the distance between the infected region and the non-infected region. In our study, we analyze the case where the exponent of the distance is 2, which is in accordance with Reilly’s law of retail gravitation. One can test for infection but such tests are costly so one seeks to determine the region of infection while performing few tests. Our goal is to find a boundary region of minimal size that contains all infected areas. We discuss efficient algorithms and provide the asymptotic bound of the testing cost and simulation results for this problem.