An optimal control problem applied to plasmid-mediated antibiotic resistance.

We formulate a system of ordinary differential equations to model the contribution of antibiotic treatment and immune system to combat bacterial infections. We obtained threshold conditions that determine when the bacteria can be eliminated, which are consistent with biological phenomena. In order to minimize the bacterial population, we formulated an optimal control problem considering the action of both antibiotic and immune system. The optimal control is obtained applying the Pontryagin's Principle. The results show the relevance of the synergism between the antibiotic treatment and the immune system response. [ABSTRACT FROM AUTHOR]