Fig. 3

Model validation by comparing the result from the original model implemented in R and the extended model implemented in C. The three test cases were designed with different model-parameter values from Table 2 and scenarios. Test case 1 has no growth and death of bacteria. Test case 2 has the growth and death of bacteria. In test case 3, the initial dose of antibiotic is kept as the one in test case 2, but the initial number of bacteria is \(1e^{6}\) instead of \(1e^{4}\) as in test case 2. In (a), the x-axis shows the simulated treatment length in 60 min. The y-axis shows the bacteria population over the treatment length. There are 101 stacked areas representing the bacterial population which has 0 to 100% of bound targets. The percent bound legends are depicted by a range of different colors. Since the external concentration input for the extended model is from the output of the original model, we expect that the two models provide similar outputs. The results show that for all three test cases, model behaviors of the original model and the extended model are similar in terms of the bacterial population and percentage bound target. In both models, the results also demonstrate the effect of model parameters such as death/growth rate, initial antibiotic level, and initial population on the final population. In test case 3, the extended model predicts an initial peak for some subpopulations due to the difference of drug-concentration profiles. I.e., the extended model is supplied with concrete values of drug concentration while the original model calculated the continuous drug concentration values at every time step. The plot (b) shows the killing curve assumed for the models, where \(R_{0}\), \(r_{T}\) are the maximum replication rate and replication threshold, respectively; \(D_{0}\), \(k_{T}\) are the death rate and killing threshold, respectively. In (b), the y-axis is the replication/death rate while the x-axis is the percentage of bound target. The more targets in the bacteria are bound, the slower rate that bacteria replicates with until replication threshold \(k_{T}\). When the percentage of bound target reaches killing threshold \(k_{T}\), the death rate becomes \(D_{0}\)