Optimal interventions in countable jump Markov processes

In this paper an intervention refers to an immediate change of the state of the system; between interventions, the continuous-time jump Markov process is uncontrollable, with ‘natural’ jump intensities. The multicriteria control problem for such a model is considered, and the constrained version is investigated with the help of the Lagrange multipliers technique. All of the theory is illustrated by an example of the optimal control of epidemic with carriers.