Modeling the Argasid Tick (Ornithodoros moubata) Life Cycle

Part of the Association for Women in Mathematics Series book series (AWMS, volume 14)


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.



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.


  1. 1.
    A. Aeschlimann, T. Freyvogel, Biology and distribution of ticks of medical importance, in Handbook of Clinical toxicology of Animal Venoms and Poisons, ed. by J. Meier, J. White, vol. 236 (CRC Press, Boca Raton, 1995), pp. 177–189Google Scholar
  2. 2.
    S.A. Allan, Ticks (Class Arachnida: Order Acarina), in Parasitic Diseases of Wild Mammals, 2nd edn. ( Iowa State University Press, Ames, 2001), pp. 72–106Google Scholar
  3. 3.
    D.A. Apanaskevich, J.H. Oliver Jr., Life cycles and natural history of ticks. Biol. Ticks 1, 59–73 (2014)Google Scholar
  4. 4.
    M. Arias, J.M. Sánchez-Vizcaíno, A. Morilla, K.-J. Yoon, J.J. Zimmerman, African swine fever, Trends in Emerging Viral Infections of Swine (Iowa State University Press, Ames, 2002), pp. 119–124Google Scholar
  5. 5.
    A. Astigarraga, A. Oleaga-Pérez, R. Pérez-Sánchez, J.A. Baranda, A. Encinas-Grandes, Host immune response evasion strategies in Ornithodoros erraticus and O. moubata and their relationship to the development of an antiargasid vaccine. Parasite Immunol. 19, 401–410 (1997)CrossRefGoogle Scholar
  6. 6.
    S. Blome, C. Gabriel, M. Beer, Pathogenesis of African swine fever in domestic pigs and European wild boar. Virus Res. 173, 122–130 (2013)CrossRefGoogle Scholar
  7. 7.
    J. Boshe, Reproductive ecology of the warthog Phacochoerus aethiopicus and its significance for management in the Eastern Selous Game Reserve, Tanzania. Biol. Conserv. 20, 37–44 (1981)CrossRefGoogle Scholar
  8. 8.
    T. Clutton-Brock, A. Maccoll, P. Chadwick, D. Gaynor, R. Kansky, and J. Skinner, Reproduction and survival of suricates (Suricata suricatta) in the Southern Kalahari. Afr. J. Ecol. 37, 69–80 (1999)CrossRefGoogle Scholar
  9. 9.
    S. Costard, B. Wieland, W. De Glanville, F. Jori, R. Rowlands, W. Vosloo, F. Roger, D.U. Pfeiffer, L.K. Dixon, African swine fever: how can global spread be prevented? Philos. Trans. R. Soc. B Biol. Sci. 364, 2683–2696 (2009)CrossRefGoogle Scholar
  10. 10.
    J.M. Cushing, An Introduction to Structured Population Dynamics (SIAM, Philadelphia, 1998)CrossRefGoogle Scholar
  11. 11.
    S.J. Cutler, A. Abdissa, J.-F. Trape, New concepts for the old challenge of African relapsing fever borreliosis. Clin. Microbiol. Infect. 15, 400–406 (2009)CrossRefGoogle Scholar
  12. 12.
    S. Elaydi, An Introduction to Difference Equations (Springer, Berlin, 2005)zbMATHGoogle Scholar
  13. 13.
    H. Gaff, E. Schaefer, Metapopulation models in tick-borne disease transmission modelling, in Modelling Parasite Transmission and Control (Springer, Berlin, 2010), pp. 51–65CrossRefGoogle Scholar
  14. 14.
    H.D. Gaff, L.J. Gross, Modeling tick-borne disease: a metapopulation model. Bull. Math. Biol. 69, 265–288 (2007)MathSciNetCrossRefGoogle Scholar
  15. 15.
    J.S. Gray, A. Estrada-Peña, L. Vial, Ecology of nidicolous ticks. Biol. Ticks 2, 39–60 (2014)Google Scholar
  16. 16.
    W.R. Hess, African swine fever virus, in African Swine Fever Virus (Springer, Berlin, 1971), pp. 1–33Google Scholar
  17. 17.
    H. Hoogstraal, Argasid and nuttalliellid ticks as parasites and vectors. Adv. Parasitol. 24, 135–238 (1985)CrossRefGoogle Scholar
  18. 18.
    H. Hoogstraal, A. Aeschlimann, Tick-host specificity. Bull. de la société Entomologique Suisse 55, 5–32 (1982)Google Scholar
  19. 19.
    J.E. Keirans, L.A. Durden, Invasion: exotic ticks (Acari: Argasidae, Ixodidae) imported into the United States. a review and new records. J. Med. Entomol. 38, 850–861 (2001)Google Scholar
  20. 20.
    N. Keyfitz, Introduction to the Mathematics of Population (Addison-Wesley, Reading MA, 1968)Google Scholar
  21. 21.
    R. Kon, Y. Iwasa, Single-class orbits in nonlinear Leslie matrix models for semelparous populations. J. Math. Biol. 55, 781–802 (2007)MathSciNetCrossRefGoogle Scholar
  22. 22.
    J. Kruger, B. Reilly, I. Whyte, Application of distance sampling to estimate population densities of large herbivores in Kruger National Park. Wildl. Res. 35, 371–376 (2008)CrossRefGoogle Scholar
  23. 23.
    E.C. Loomis, Life histories of ticks under laboratory conditions (Acarina: Ixodidae and Argasidae). J. Parasitol. 47, 91–99 (1961)CrossRefGoogle Scholar
  24. 24.
    B. Lubisi, R. Dwarka, D. Meenowa, R. Jaumally, An investigation into the first outbreak of African swine fever in the Republic of Mauritius. Transbound. Emerg. Dis. 56, 178–188 (2009)CrossRefGoogle Scholar
  25. 25.
    C.K. Mango, R. Galun, Suitability of laboratory hosts for rearing of Ornithodoros moubata ticks (Acari: Argasidae). J. Med. Entomol. 14, 305–308 (1977)CrossRefGoogle Scholar
  26. 26.
    C.K. Mango, R. Galun, Ornithodoros moubata: breeding in vitro. Exp. Parasitol. 42, 282–288 (1977)CrossRefGoogle Scholar
  27. 27.
    S. Marino, I.B. Hogue, C.J. Ray, D.E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology. J. Theor. Biol. 254, 178–196 (2008)MathSciNetCrossRefGoogle Scholar
  28. 28.
    N. Meshkat, C. E.-Z. Kuo, J. DiStefano III, On finding and using identifiable parameter combinations in nonlinear dynamic systems biology models and COMBOS: a novel web implementation. PloS One 9, e110261 (2014)CrossRefGoogle Scholar
  29. 29.
    M.-L. Penrith, W. Vosloo, F. Jori, A.D. Bastos, African swine fever virus eradication in Africa. Virus Res. 173, 228–246 (2013)CrossRefGoogle Scholar
  30. 30.
    W. Plowright, J. Parker, M. Peirce, African swine fever virus in ticks (Ornithodoros moubata, Murray) collected from animal burrows in Tanzania. Nature 221, 1071–1073 (1969)CrossRefGoogle Scholar
  31. 31.
    J.M. Sánchez-Vizcaíno, L. Mur, B. Martínez-López, African swine fever: an epidemiological update. Transbound. Emerg. Dis. 59, 27–35 (2012)CrossRefGoogle Scholar
  32. 32.
    C. Schradin, N. Pillay, Demography of the striped mouse (Rhabdomys pumilio) in the succulent karoo. Mamm. Biology-Zeitschrift für Säugetierkunde 70, 84–92 (2005)CrossRefGoogle Scholar
  33. 33.
    C. Schradin, N. Pillay, Intraspecific variation in the spatial and social organization of the African striped mouse. J. Mammal. 86, 99–107 (2005)CrossRefGoogle Scholar
  34. 34.
    H.R. Thieme, Mathematics in Population Biology (Princeton University Press, Princeton, 2003)zbMATHGoogle Scholar
  35. 35.
    T. Vergne, A. Gogin, D. Pfeiffer, Statistical exploration of local transmission routes for African swine fever in pigs in the Russian federation, 2007–2014. Transbound. Emerg. Dis. 64, 504–512 (2017)CrossRefGoogle Scholar
  36. 36.
    L. Vial, Biological and ecological characteristics of soft ticks (Ixodida: Argasidae) and their impact for predicting tick and associated disease distribution. Parasite 16, 191–202 (2009)CrossRefGoogle Scholar
  37. 37.
    E. Vinuela, African swine fever virus, in Iridoviridae (Springer, Berlin, 1985), pp. 151–170Google Scholar

Copyright information

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

Authors and Affiliations

  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

Personalised recommendations