Advanced Search
Article Contents
Article Contents

Preliminary analysis of an agent-based model for a tick-borne disease

Abstract Related Papers Cited by
  • 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.
    Mathematics Subject Classification: Primary: 92B08; Secondary: 90B15.


    \begin{equation} \\ \end{equation}
  • [1]

    Centers for Disease Control and Prevention, Summary of Notifiable Diseases - United States, 2006, MMWR, 55 (2008), 1-94.


    D. E. Sonenshine and T. N. Mather, "Ecological Dynamics of Tick-Borne Zoonoses," Oxford University Press, 1994.


    H. Gaff and L. J. Gross, Analysis of a tick-borne disease model with varying population sizes in various habitats, Bulletin of Mathematical Biology, 69 (2007), 265-288.doi: 10.1007/s11538-006-9125-5.


    H. Gaff and E. Schaefer, Metapopulation models in tick-borne disease transmission modelling, In "Modelling parasitic Disease Transmission: Biology to Control," eds. Michael, E. & Spear, R. Landes Bioscience, Eurekah: Austin, TX, USA, 2008.


    H. Gaff, L. Gross and E. Schaefer, Results from a mathematical model for human monocytic ehrlichiosis, Proceedings of the 5th Conference on Rickettsiae and Rickettsial diseases, Supplement to Clinical Microbiology and Infection, 15 (2008), 1-2.


    D. G. Haile and G. A. Mount, Computer simulation of population dynamics of the lone star tick, Amblyomma americanum (Acari: Ixodidae), Journal of Medical Entomology, 24 (1987), 356-369.


    G. A. Mount and D. G. Haile, Computer simulation of population dynamics of the American dog tick (Acari: Ixodidae), Journal of Medical Entomology, 26 (1989), 60-76.


    G. A. Mount, D. G. Haile, R. B. Davey and L. M. Cooksey, Computer simulation of boophilus cattle tick (Acari: Ixodidae) population dynamics, Journal of Medical Entomology, 28 (1991), 223-240.


    G. A. Mount, D. G. Haile, D. R. Barnard and E. Daniels, New version of LSTSIM for computer simulation of Amblyomma americanum (Acari: Ixodidae) population dynamics, Journal of Medical Entomology, 30 (1993), 843-857.


    G. A. Mount, D. G. Haile and E. Daniels, Simulation of blacklegged tick (Acari: Ixodidae) population dynamics and transmission of Borrelia burgdorferi, Journal of Medical Entomology, 34 (1997), 461-484.


    G. A. Mount, D. G. Haile and E. Daniels, Simulation of management strategies for the blacklegged tick (Acari: Ixodidae) and the Lyme disease spirochete, Borrelia burgdorferi, Journal of Medical Entomology, 90 (1997), 672-683.


    S. Sandberg, T. E. Awerbuch and A. Spielman, A comprehensive multiple matrix model representing the life cycle of the tick that transmits the age of Lyme disease, Journal of Theoretical Biology, 157 (1992), 203-220.doi: 10.1016/S0022-5193(05)80621-6.


    T. E. Awerbuch and S. Sandberg, Trends and oscillations in tick population dynamics, Journal of Theoretical Biology, 175 (1995), 511-516.doi: 10.1006/jtbi.1995.0158.


    S. Randolph, Epidemiological uses of a population model for the tick Rhipicephalus appendiculatus, Tropical Medicine and International Health, 4 (1999), A34-A42.doi: 10.1046/j.1365-3156.1999.00449.x.


    J. E. Bunnell, S. D. Price, A. Das, T. M. Shields and G. E. Glass, Geographic Information Systems and Spatial Analysis of Adult Ixodes scapularis (Acari: Ixodidae) in the Middle Atlantic Region of the U.S.A., Journal of Medical Entomology, 40 (2003), 570-576.doi: 10.1603/0022-2585-40.4.570.


    A. Das, S. R. Lele, G. E. Glass, T. Shields and J. Petz, Modelling a discrete spatial response using generalized linear mixed models: Application to Lyme disease vectors, International Journal of Geographical Information Science, 16 (2002), 151-166.doi: 10.1080/13658810110099134.


    G. E. Glass, B. S. Schwartz, J. M. Morgan, D. T. Johnson, P. M. Noy and E. Israel, Environmental risk factors for Lyme disease identified with geographic information systems, American Journal of Public Health, 85 (1995), 944-948.doi: 10.2105/AJPH.85.7.944.


    W. E. Fitzgibbon, M. E. Parrott and G. F. Webb, A diffusive epidemic model for a host-vector system, In "Differential Equations and Applications to Biology and Industry," M. Martelli, K. Cooke, E. Cumberbatch, B. Tang, and H. Thieme, (Eds.), World Scientific Press, Singapore, 1996.


    J. Radcliffe and L. Rass, The spatial spread and final size of models for the deterministic host-vector epidemic, Mathematical Biosciences, 70 (1984), 123-146.doi: 10.1016/0025-5564(84)90094-4.


    J. Radcliffe and L. Rass, The rate of spread of infection in models for the deterministic host-vector epidemic, Mathematical Biosciences, 74 (1985), 257-273.doi: 10.1016/0025-5564(85)90059-8.


    A. R. Giardina, K. A. Schmidt, E. M. Schauber and R. S. Ostfeld, Modeling the role of songbirds and rodents in the ecology of Lyme disease, Canadian Journal of Zoology, 78 (2000), 2184-2197.doi: 10.1139/cjz-78-12-2184.


    K. LoGiudice, R. S. Ostfeld, K. A. Schmidt and F. Keesing, The ecology of infectious disease: Effects of host diversity and community composition on Lyme disease risk, Proceedings of the National Academies of Science, USA, 100 (2003), 567-571.


    M. Ghosh and A. Pugliese, Seasonal population dynamics of ticks, and its influence on infection transmission: A semi- discrete approach, Bulletin of Mathematical Biology, 66 (2004), 1659-1684.doi: 10.1016/j.bulm.2004.03.007.


    W. Ding, Optimal Control on Hybrid ODE Systems with Application to a Tick Disease Model, Mathematical Biosciences and Engineering, 4 (2007), 633-659.


    D. L. DeAngelis and L. J. Gross, "Individual-based Models and Approaches in Ecology: Populations, Communities and Ecosystems," Taylor and Francis, 1992.


    D. L. DeAngelis, L. J. Gross, W. F. Wolff, D. M. Fleming, M. P. Nott and E. J. Comiskey, Individual-based models on the landscape: Applications to the Everglades, in "Landscape Ecology: A Top-Down Approach," J. Sanderson and L. D. Harris (eds.), Lewis Publishers, Boca Raton, FL, 2000.


    S. Eubank, H. Guclu, V. S. A. Kumar, M. V. Marathe, A. Srinivasan, Z. Toroczkai and N. Wang, Modelling disease outbreaks in realistic urban social networks, Nature, 429 (2004), 180-184.doi: 10.1038/nature02541.


    A. G. Barbour, "Lyme Disease: The Cause, the Cure, the Controversy," John Hopkins University Press, Baltimore, Maryland, 1996.


    F. Des Vignes, M. L. Levin and D. Fish, Comparative vector competence of Dermacentor variabilis and Ixodes scapularis (Acari: Ixodidae) for the agent of human granulocytic ehrlichiosis, Journal of Medical Entomology, 36 (1999), 182-185.


    Dania Richter, Andrew Spielman, Nicholas Komar and Franz-Rainer Matuschka, Competence of American robins as reservoir hosts for Lyme disease spirochetes, Emerging Infectious Diseases, 6 (2000), 133-138.doi: 10.3201/eid0602.000205.


    V. Grimm, U. Berger, F. Bastiansen, S. Eliassen, V. Ginot, J. Giske, J. Goss-Custard, T. Grand, S. K. Heinz, G. Huse, A. Huth, J. U. Jepsen, C. Jørgensen, W. M. Mooij, B. Müller, G. Peer, C. Piou, S. F. Railsback, A. M. Robbins, M. M. Robbins, E. Rossmanith, N. Rüger, E. Strand, S. Souissi, R. A. Stillman, R. Vabø, U. Visser and D. L. DeAngelis, A standard protocol for describing individual-based and agent-based models, Ecological Modelling 198 (2006), 115-26.doi: 10.1016/j.ecolmodel.2006.04.023.


    A. L. Bauer, C. A. A. Beauchemin and A. S. Perelson, Agent-based modeling of host-pathogen systems: The successes and the challenges, Information Sciences, 179 (2009), 1379-1389.doi: 10.1016/j.ins.2008.11.012.


    V. Grimm and S. F. Railsbeck, "Individual-based Modeling and Ecology," Princeton University Press, 2005.


    J. M. Lockhart, W. R. Davidson, J. E. Dawson and D. E. Stallknecht, Temporal association of Amblyomma americanum with the presence of Ehrlichia chaffeensis reactive antibodies in white-tailed deer, Journal of Wildlife Diseases, 31 (1995), 119-124.


    J. E. Dawson, J. E. Childs, K. L. Biggie, C. Moore, D. Stallknecht, J. Shaddock, J. Bouseman, E. Hofmeister and J. G. Olson, White-tailed deer as a potential reservoir of Ehrlichia spp., Journal of Wildlife Diseases, 30 (1994), 162-168.


    B. E. Anderson, K. G. Sims, J. G. Olson, J. E. Childs, J. F. Piesman, C. M. Happ, G. O. Maupin and B. J. B. Johnson, Amblyomma americanum: A potential vector of human ehrlichiosis, American Journal of Tropical Medicine and Hygiene, 49 (1993), 239-244.

  • 加载中

Article Metrics

HTML views() PDF downloads(56) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint