# Modeling the Argasid Tick (Ornithodoros moubata) Life Cycle

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.

## References

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)
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)
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)
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)
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)
10. 10.
J.M. Cushing, An Introduction to Structured Population Dynamics (SIAM, Philadelphia, 1998)
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)
12. 12.
S. Elaydi, An Introduction to Difference Equations (Springer, Berlin, 2005)
13. 13.
H. Gaff, E. Schaefer, Metapopulation models in tick-borne disease transmission modelling, in Modelling Parasite Transmission and Control (Springer, Berlin, 2010), pp. 51–65
14. 14.
H.D. Gaff, L.J. Gross, Modeling tick-borne disease: a metapopulation model. Bull. Math. Biol. 69, 265–288 (2007)
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)
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.
21. 21.
R. Kon, Y. Iwasa, Single-class orbits in nonlinear Leslie matrix models for semelparous populations. J. Math. Biol. 55, 781–802 (2007)
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)
23. 23.
E.C. Loomis, Life histories of ticks under laboratory conditions (Acarina: Ixodidae and Argasidae). J. Parasitol. 47, 91–99 (1961)
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)
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)
26. 26.
C.K. Mango, R. Galun, Ornithodoros moubata: breeding in vitro. Exp. Parasitol. 42, 282–288 (1977)
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)
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)
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)
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)
31. 31.
J.M. Sánchez-Vizcaíno, L. Mur, B. Martínez-López, African swine fever: an epidemiological update. Transbound. Emerg. Dis. 59, 27–35 (2012)
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)
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)
34. 34.
H.R. Thieme, Mathematics in Population Biology (Princeton University Press, Princeton, 2003)
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)
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)
37. 37.
E. Vinuela, African swine fever virus, in Iridoviridae (Springer, Berlin, 1985), pp. 151–170Google Scholar

© 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