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Mathematical Biosciences and Engineering

2011, Volume 8, Issue 2: 463-473. doi: 10.3934/mbe.2011.8.463
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Preliminary analysis of an agent-based model for a tick-borne disease

  • 1.
    Department of Biological Sciences, Old Dominion University, Norfolk, VA 23529
  • Received: 01 March 2010 Accepted: 29 June 2018 Published: 01 April 2011

  • MSC : Primary: 92B08; Secondary: 90B15.

  • Ticks have a unique life history including a distinct set of life stages and a single blood meal per life stage. This makes tick-host interactions more complex from a mathematical perspective. In addition, any model of these interactions must involve a significant degree of stochasticity on the individual tick level. In an attempt to quantify these relationships, I have developed an individual-based model of the interactions between ticks and their hosts as well as the transmission of tick-borne disease between the two populations. The results from this model are compared with those from previously published differential equation based population models. The findings show that the agent-based model produces significantly lower prevalence of disease in both the ticks and their hosts than what is predicted by a similar differential equation model.

    Citation: Holly Gaff. Preliminary analysis of an agent-based model for a tick-borne disease[J]. Mathematical Biosciences and Engineering, 2011, 8(2): 463-473. doi: 10.3934/mbe.2011.8.463

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    [1] Holly Gaff, Robyn Nadolny . Identifying requirements for the invasion of a tick species and tick-borne pathogen through TICKSIM. Mathematical Biosciences and Engineering, 2013, 10(3): 625-635. doi: 10.3934/mbe.2013.10.625
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  • Ticks have a unique life history including a distinct set of life stages and a single blood meal per life stage. This makes tick-host interactions more complex from a mathematical perspective. In addition, any model of these interactions must involve a significant degree of stochasticity on the individual tick level. In an attempt to quantify these relationships, I have developed an individual-based model of the interactions between ticks and their hosts as well as the transmission of tick-borne disease between the two populations. The results from this model are compared with those from previously published differential equation based population models. The findings show that the agent-based model produces significantly lower prevalence of disease in both the ticks and their hosts than what is predicted by a similar differential equation model.


  • This article has been cited by:

    1. Anne E. Yust, Davida S. Smyth, 2020, Chapter 5, 978-3-030-33644-8, 217, 10.1007/978-3-030-33645-5_5
    2. Identifying requirements for the invasion of a tick species and tick-borne pathogen through TICKSIM, 2013, 10, 1551-0018, 625, 10.3934/mbe.2013.10.625
    3. Shelby M. Scott, Casey E. Middleton, Erin N. Bodine, 2019, 40, 9780444641526, 3, 10.1016/bs.host.2018.10.001
    4. Antoinette Ludwig, Howard S. Ginsberg, Graham J. Hickling, Nicholas H. Ogden, A Dynamic Population Model to Investigate Effects of Climate and Climate-Independent Factors on the Lifecycle ofAmblyomma americanum(Acari: Ixodidae), 2016, 53, 0022-2585, 99, 10.1093/jme/tjv150
    5. Kamuela E. Yong, Anuj Mubayi, Christopher M. Kribs, Agent-based mathematical modeling as a tool for estimating Trypanosoma cruzi vector–host contact rates, 2015, 151, 0001706X, 21, 10.1016/j.actatropica.2015.06.025
    6. Milliward Maliyoni, Faraimunashe Chirove, Holly D. Gaff, Keshlan S. Govinder, A stochastic epidemic model for the dynamics of two pathogens in a single tick population, 2019, 127, 00405809, 75, 10.1016/j.tpb.2019.04.004
    7. David Gammack, Elsa Schaefer, Holly Gaff, 2013, 9780124157804, 105, 10.1016/B978-0-12-415780-4.00004-1
    8. R. Nadolny, H. Gaff, Modelling the Effects of Habitat and Hosts on Tick Invasions, 2018, 5, 23737867, 10.30707/LiB5.1Nadolny
    9. Milliward Maliyoni, Faraimunashe Chirove, Holly D. Gaff, Keshlan S. Govinder, A Stochastic Tick-Borne Disease Model: Exploring the Probability of Pathogen Persistence, 2017, 79, 0092-8240, 1999, 10.1007/s11538-017-0317-y
    10. Olivier M. Zannou, Achille S. Ouedraogo, Abel S. Biguezoton, Emmanuel Abatih, Marco Coral-Almeida, Souaïbou Farougou, Kouassi Patrick Yao, Laetitia Lempereur, Claude Saegerman, Models for Studying the Distribution of Ticks and Tick-Borne Diseases in Animals: A Systematic Review and a Meta-Analysis with a Focus on Africa, 2021, 10, 2076-0817, 893, 10.3390/pathogens10070893
    11. Xue Zhang, Jianhong Wu, A coupled algebraic-delay differential system modeling tick-host interactive behavioural dynamics and multi-stability, 2023, 86, 0303-6812, 10.1007/s00285-023-01879-8
    12. Alexis L. White, Holly D. Gaff, 2021, Chapter 4, 978-3-030-84595-7, 31, 10.1007/978-3-030-84596-4_4
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  • © 2011 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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