Approximate Testing in Uncertain Epidemic Processes

Diagnostic tests have proven to be a critical tool in controlling the progression of a virus. In this paper, we formulate the testing of a homogeneous population as an optimal control problem. The population state, given by the distribution of agents' viral states in a compartmental model, is assumed to be unknown. Information regarding the population state is provided via noisy tests, which are allocated from a stockpile whose size is updated via a stochastic process. The objective of the control problem is to allocate tests so as to minimize uncertainty of the underlying population state over a finite horizon. As such, the control problem is cast as a POMDP with a negative entropy reward function. We study various heuristic policies and investigate conditions under which each heuristic performs best.