  We consider the problem of controlling a mutated diffusion process with an
unknown mutation time. The problem is formulated as the quickest intervention
problem with the mutation modeled by a change-point, which is a generalization
of the quickest change-point detection (QCD). Our goal is to intervene in the
mutated process as soon as possible while maintaining a low intervention cost
with optimally chosen intervention actions. This model and the proposed
algorithms can be applied to pandemic prevention (such as Covid-19) or
misinformation containment. We formulate the problem as a partially observed
Markov decision process (POMDP) and convert it to an MDP through the belief
state of the change-point. We first propose a grid approximation approach to
calculate the optimal intervention policy, whose computational complexity could
be very high when the number of grids is large. In order to reduce the
computational complexity, we further propose a low-complexity threshold-based
policy through the analysis of the first-order approximation of the value
functions in the ``local intervention'' regime. Simulation results show the
low-complexity algorithm has a similar performance as the grid approximation
and both perform much better than the QCD-based algorithms.
