In this paper, we investigate three particular algorithms: A sto- chastic simulation algorithm (SSA), and explicit and implicit tau-leaping al- gorithms. To compare these methods, we used them to analyze two infection models: A Vancomycin-resistant enterococcus (VRE) infection model at the population level, and a Human Immunode ciency Virus (HIV) within host in- fection model. While the rst has a low species count and few transitions, the second is more complex with a comparable number of species involved. The relative effciency of each algorithm is determined based on computational time and degree of precision required. The numerical results suggest that all three algorithms have the similar computational effciency for the simpler VRE model, and the SSA is the best choice due to its simplicity and accuracy. In addition, we have found that with the larger and more complex HIV model, implementation and modication of tau-Leaping methods are preferred.