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Modeling the Argasid Tick (Ornithodoros moubata) Life Cycle

  • Sara M. Clifton
  • Courtney L. Davis
  • Samantha Erwin
  • Gabriela Hamerlinck
  • Amy Veprauskas
  • Yangyang Wang
  • Wenjing Zhang
  • Holly Gaff
Chapter
Part of the Association for Women in Mathematics Series book series (AWMS, volume 14)

Abstract

The first mathematical models for an argasid tick are developed to explore the dynamics and identify knowledge gaps of these poorly studied ticks. These models focus on Ornithodoros moubata, an important tick species throughout Africa and Europe. Ornithodoros moubata is a known vector for African swine fever (ASF), a catastrophically fatal disease for domesticated pigs in Africa and Europe. In the absence of any previous models for soft-bodied ticks, we propose two mathematical models of the life cycle of O. moubata. One is a continuous-time differential equation model that simplifies the tick life cycle to two stages, and the second is a discrete-time difference equation model that uses four stages. Both models use two host types: small hosts and large hosts, and both models find that either host type alone could support the tick population and that the final tick density is a function of host density. While both models predict similar tick equilibrium values, we observe significant differences in the time to equilibrium. The results demonstrate the likely establishment of these ticks if introduced into a new area even if there is only one type of host. These models provide the basis for developing future models that include disease states to explore infection dynamics and possible management of ASF.

Notes

Acknowledgements

The work described in this chapter was initiated during the Association for Women in Mathematics collaborative workshop Women Advancing Mathematical Biology hosted by the Mathematical Biosciences Institute (MBI) at Ohio State University in April 2017. Funding for the workshop was provided by MBI, NSF ADVANCE “Career Advancement for Women Through Research-Focused Networks” (NSF-HRD 1500481), Society for Mathematical Biology, and Microsoft Research.

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Copyright information

© The Author(s) and the Association for Women in Mathematics 2018

Authors and Affiliations

  • Sara M. Clifton
    • 1
  • Courtney L. Davis
    • 2
  • Samantha Erwin
    • 3
  • Gabriela Hamerlinck
    • 4
  • Amy Veprauskas
    • 5
  • Yangyang Wang
    • 6
  • Wenjing Zhang
    • 7
  • Holly Gaff
    • 8
  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Natural Science DivisionPepperdine UniversityMalibuUSA
  3. 3.Department of Population Health and PathobiologyCollege of Veterinary Medicine, North Carolina State UniversityRaleighUSA
  4. 4.BioQUEST Curriculum Consortium, Inc.MadisonUSA
  5. 5.Mathematics DepartmentUniversity of Louisiana at LafayetteLafayetteUSA
  6. 6.Mathematical Biosciences InstituteOhio State UniversityColumbusUSA
  7. 7.Department of Mathematics and StatisticsTexas Tech UniversityLubbockUSA
  8. 8.Department of Biological SciencesOld Dominion UniversityNorfolkUSA

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