The project A-CH4 of M. von Kleist, C. Hartmann and M. Weber is concerned with optimal control of a stochastic dynamical system governed by a chemical master equation, which is modeling the evolution of microbial strains which are resistant to different drugs. The dual martingale methods recently developed in [HSZ16] for the optimal control of hydroelectric storage and production systems are to be adapted to the dynamical systems treated in the project A-CH4.