What should be considered in the treatment of bacterial infections by multi-drug therapies: a mathematical perspective?

Bacterial infections are a global health concern with high levels of mortality and morbidity associated. The resistance of pathogens to drugs is one leading cause of this problem, being common the administration of multiple drugs to improve the therapeutic effects. This review critically explores diverse aspects involved in the treatment of bacterial infections through multi-drug therapies, from a mathematical and within-host perspectives. Five recent models were selected and are reviewed. These models fall into the following question: which drugs to select, the respective dose, the administration period to effectively eradicate the infection in the shortest period of time and with reduced side effects? In this analysis, three groups of variables were considered: pharmacokinetics, pharmacodynamics and disturbance variables. To date, there is no model that fully answers to this issue for a living organism and it is questionable whether this would be possible for any case of infection.