Modeling the Argasid Tick (Ornithodoros moubata) Life Cycle
- 420 Downloads
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.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.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.D.A. Apanaskevich, J.H. Oliver Jr., Life cycles and natural history of ticks. Biol. Ticks 1, 59–73 (2014)Google Scholar
- 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
- 15.J.S. Gray, A. Estrada-Peña, L. Vial, Ecology of nidicolous ticks. Biol. Ticks 2, 39–60 (2014)Google Scholar
- 16.W.R. Hess, African swine fever virus, in African Swine Fever Virus (Springer, Berlin, 1971), pp. 1–33Google Scholar
- 18.H. Hoogstraal, A. Aeschlimann, Tick-host specificity. Bull. de la société Entomologique Suisse 55, 5–32 (1982)Google Scholar
- 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.N. Keyfitz, Introduction to the Mathematics of Population (Addison-Wesley, Reading MA, 1968)Google Scholar
- 37.E. Vinuela, African swine fever virus, in Iridoviridae (Springer, Berlin, 1985), pp. 151–170Google Scholar