  We study a dynamic infection spread model, inspired by the discrete time SIR
model, where infections are spread via non-isolated infected individuals. While
infection keeps spreading over time, a limited capacity testing is performed at
each time instance as well. In contrast to the classical, static, group testing
problem, the objective in our setup is not to find the minimum number of
required tests to identify the infection status of every individual in the
population, but to control the infection spread by detecting and isolating the
infections over time by using the given, limited number of tests. In order to
analyze the performance of the proposed algorithms, we focus on the mean-sense
analysis of the number of individuals that remain non-infected throughout the
process of controlling the infection. We propose two dynamic algorithms that
both use given limited number of tests to identify and isolate the infections
over time, while the infection spreads. While the first algorithm is a dynamic
randomized individual testing algorithm, in the second algorithm we employ the
group testing approach similar to the original work of Dorfman. By considering
weak versions of our algorithms, we obtain lower bounds for the performance of
our algorithms. Finally, we implement our algorithms and run simulations to
gather numerical results and compare our algorithms and theoretical
approximation results under different sets of system parameters.
