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Mathematical Biosciences and Engineering

2012, Volume 9, Issue 3: 487-526. doi: 10.3934/mbe.2012.9.487
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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
  • 2.
    Department of Mathematics and Statistics, East Tennessee State University, Johnson City, TN 37614-70663
  • 3.
    Department of Mathematics, Boston College, Chestnut Hill, MA 02467-3806
  • 4.
    Department of Mathematics, State University of New York at Geneseo, Geneseo, NY 14454
  • 5.
    Department of Mathematics, Bryn Mawr College, Bryn Mawr, PA 19010-2899
  • Received: 01 November 2011 Accepted: 29 June 2018 Published: 01 July 2012

  • MSC : 60J27, 60J22, 92D25.

  • 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[J]. Mathematical Biosciences and Engineering, 2012, 9(3): 487-526. doi: 10.3934/mbe.2012.9.487

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  • 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.


    Dear Editorial Board Members,

    It is my pleasure to share with you the year-end report for AIMS Environmental Science. The journal continues to improve its quality as indicated by steady increases in the number of manuscripts received and the number of articles published over the past three years (Figure 1). We have received 69 submissions with 28 published online. The most downloaded and cited papers are listed in Tables 1 and 2. The top read article received more than 11390 downloads.

    Figure 1.  Manuscript statistics.
    DownLoad: Full-Size Img PowerPoint
    Table 1.  The top 10 articles with most pdf download: (By December 31th 2019).
    Title Usages
    Quantifying the local-scale ecosystem services provided by urban treed streetscapes in Bolzano, Italy 11390
    Feasibility study of a solar photovoltaic water pumping system for rural Ethiopia 2021
    Biophilic architecture: a review of the rationale and outcomes 2016
    Low temperature selective catalytic reduction of NOx with NH3 over Mn-based catalyst: A review 1834
    Remote sensing of agricultural drought monitoring: A state of art review 1808
    Challenges and opportunities in municipal solid waste management in Mozambique: a review in the light of nexus thinking 1643
    Nitrate pollution of groundwater by pit latrines in developing countries 1524
    Assessment of repeated harvests on mercury and arsenic phytoextraction in a multi-contaminated industrial soil 1506
    Urban agriculture in the transition to low carbon cities through urban greening 1463
    A state-and-transition simulation modeling approach for estimating the historical range of variability 1438
     | Show Table
    DownLoad: CSV
    Table 2.  The top 10 articles with most cited: (By December 31th 2019).
    Title Number
    Biophilic architecture: a review of the rationale and outcomes 21
    Traffic-related air pollution and brain development 19
    Enhancing water flux of thin-film nanocomposite (TFN) membrane by incorporation of bimodal silica nanoparticles 15
    Quantifying the local-scale ecosystem services provided by urban treed streetscapes in Bolzano, Italy 14
    Nitrate pollution of groundwater by pit latrines in developing countries 13
    The mechanism of kaolin clay flocculation by a cation-independent bioflocculant produced by Chryseobacterium daeguense W6 12
    An integrated approach to modeling changes in land use, land cover, and disturbance and their impact on ecosystem carbon dynamics: a case study in the Sierra Nevada Mountains of California 11
    Climate change and land management impact rangeland condition and sage-grouse habitat in southeastern Oregon 11
    Catalytic hydrothermal liquefaction (HTL) of biomass for bio-crude production using Ni/HZSM-5 catalysts 11
    Influence of everyday activities and presence of people in common indoor environments on exposure to airborne fungi 10
     | Show Table
    DownLoad: CSV

    I would like to thank all the board members for serving on the Editorial Board and their dedication and contribution to the journal, especially to the editors for two special issues: Impacts of Microplastics in the Urban Environment Conference and Green built environment. The goal in 2020 is to solicit more manuscripts and increase paper citations. We will try our best to reduce the processing time and supply with a better experience for publication. To recognize the contribution of the Editorial Board members and authors during the years, we will continue to offer that (1) for authors invited, the article processing charge (APC) is automatically waived; (2) each editorial board member is entitled for some waivers. I am looking forward to continuing working with you to make the AIMS Environmental Science a sustainable and impactful journal. Please don’t hesitate to send me e-mails if you have new ideas and suggestions to help us to achieve this goal.

    Yifeng Wang, Ph.D.

    Editor in Chief, AIMS Environmental Science

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  • © 2012 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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