Mathematical modeling on bacterial resistance to multiple antibiotics caused by spontaneous mutations

• We model the interaction between sensitive and resistant bacteria to multiple antibiotics.
• We consider the most basic mechanisms of acquisition of bacterial resistance to antibiotics.
• Conditions that determine outcome of bacterial elimination or progression are established.

We formulate a mathematical model that describes the population dynamics of bacteria exposed to multiple antibiotics simultaneously, assuming that acquisition of resistance is through mutations due to antibiotic exposure. Qualitative analysis reveals the existence of a free-bacteria equilibrium, resistant-bacteria equilibrium and an endemic equilibrium where both bacteria coexist.