Managing the emergence of antibiotic resistance through optimal control
The emergence of infectious pathogens resistant to antibiotics in a faster pace than the discovery of new antibiotics is nowadays a challenge for the treatment of infectious diseases. We have modelled the interaction between an infection, possibly caused by several strains of bacteria, and the treatment using a number of different antibiotics. In our model, the antibiotics remove part of the susceptible infection but, at the same time, act as an evolutionary pressure that fosters the emergence of resistant strains. We consider the treatment as the feedback control input of the system and set a optimal control problem. Using optimal control, dynamical system tools and numerical simulations we determine the parameter region such that the infection is controllable on a finite-time horizon and the best treatment strategy.