# American Institute of Mathematical Sciences

2012, 9(3): 487-526. doi: 10.3934/mbe.2012.9.487

## A comparison of computational efficiencies of stochastic algorithms in terms of two infection models

 1 Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695-8212, United States, United States 2 Department of Mathematics and Statistics, East Tennessee State University, Johnson City, TN 37614-70663, United States, United States 3 Department of Mathematics, Boston College, Chestnut Hill, MA 02467-3806, United States 4 Department of Mathematics, State University of New York at Geneseo, Geneseo, NY 14454, United States 5 Department of Mathematics, Bryn Mawr College, Bryn Mawr, PA 19010-2899, United States

Received  November 2011 Revised  May 2012 Published  July 2012

In this paper, we investigate three particular algorithms: a stochastic simulation algorithm (SSA), and explicit and implicit tau-leaping algorithms. 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 Immunodeficiency Virus (HIV) within host infection model. While the first has a low species count and few transitions, the second is more complex with a comparable number of species involved. The relative efficiency 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 efficiency 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 modification of tau-Leaping methods are preferred.
Citation: H. Thomas Banks, Shuhua Hu, Michele Joyner, Anna Broido, Brandi Canter, Kaitlyn Gayvert, Kathryn Link. A comparison of computational efficiencies of stochastic algorithms in terms of two infection models. Mathematical Biosciences & Engineering, 2012, 9 (3) : 487-526. doi: 10.3934/mbe.2012.9.487
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