Prediction of the susceptible and resistant bacteria with antibiotic therapy

The use of antibiotics has made bacterial infection no longer a lethal threat to humans, but the ensuing problem of bacterial resistance has become a new medical challenge. In the paper, an ordinary differential model of the susceptible and resistant bacteria with the antibiotics therapy is presented. We first demonstrate the existence and stability of a coexistence equilibrium of susceptible and resistant bacteria when antibiotics are continuously injected. Subsequently, we give some conclusions when antibiotics are impulsively injected. Besides, the sensitivity index is usually used to assess the importance of each parameter responsible for changes in the bacterial population size and the bacterial population composition. Finally, we present some discussion of the above theoretical results.