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Stability and periodic solutions for a model of bacterial resistance to antibiotics caused by mutations and plasmids

Abstract:

Bacterial resistance is one of the most prominent public health problems affecting the entire world population. Although some infectious diseases are no longer a problem as they were in the past, the acquisition of bacterial resistance continues to increase. In particular, antibiotics have been losing their effectiveness after decades of misuse and overuse, which has generated an emergency situation. In this work, we formulate and analyse a deterministic model for the population dynamics of susceptible and resistant bacteria to antibiotics, assuming that drug resistance is acquired through mutations and plasmid transmission. Qualitative analysis reveals the existence of a bacteria-free equilibrium, a resistant bacteria equilibrium, an a coexistence equilibrium and a limit cycle arising from Hopf bifurcation. The stability of the equilibria are given in terms of the growth rate of bacteria, the acquisition of resistance, as well as the elimination of bacteria due to the immune system and the action of antibiotics. Numerical simulations corroborate our analytical results, and illustrate the temporal dynamics of the susceptible and resistant bacteria.