The objective of the thesis is to model the behavior of the reaction between two species of bacteria and antibiotics by building an ordinary differential equation (ODE) system under a list of assumptions. With the ODE, we analyze equilibrium points and the stability of these equilibrium points to forecast the trend of each species of bacteria and antibiotics. We test the validity of the model assumptions. Based on these outcomes, we show that: 1. Both equilibrium points and eigenvalues differ in orders of magnitude. 2. Some figures which were generated using different initial values do not make any sense. 3. There were abnormal values of the variables sensitivity.