Skip to main content

Advertisement

SpringerLink
Log in

Modeling Tick-Borne Disease: A Metapopulation Model

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

Recent increases in reported outbreaks of tick-borne diseases have led to increased interest in understanding and controlling epidemics involving these transmission vectors. Mathematical disease models typically assume constant population size and spatial homogeneity. For tick-borne diseases, these assumptions are not always valid. The disease model presented here incorporates non-constant population sizes and spatial heterogeneity utilizing a system of differential equations that may be applied to a variety of spatial patches. We present analytical results for the one patch version and find parameter restrictions under which the populations and infected densities reach equilibrium. We then numerically explore disease dynamics when parameters are allowed to vary spatially and temporally and consider the effectiveness of various tick-control strategies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Anderson, B.E., Sims, K.G., Olson, J.G., Childs, J.E., Piesman, J.F., Happ, C.M., Maupin, G.O., Johnson, B.J.B., 1993. Amblyomma americanum: a potential vector of human ehrlichiosis. Am J. Trop. Med. Hyg. 49, 239–244.

    Google Scholar 

  • Anderson, B.E., Sumner, J.W., Dawson, J.E., Tzianabos, T., Greene, C.R., Olson, J.G., Fishbein, D.B., Olsen-Rasmussen, M., Holloway, B.P., George, E.H., Azad, A.F., 1992. Detection of the etiologic agent of human ehrlichiosis by polymerase chain reaction. J. Clin. Microbiol. 30, 775–780.

    Google Scholar 

  • Awerbuch, T.E., Sandberg, S., 1995. Trends and oscillations in tick population dynamics. J. Theor. Biol. 175, 511–516.

    Article  Google Scholar 

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

    Google Scholar 

  • Brauer, F., Nohel, J.A., 1969. The Qualitative Theory of Ordinary Differential Equations. W. A. Benjamin, Inc., New York.

    Google Scholar 

  • CDC, 1997. Demographic differences in notifiable infectious disease morbidity. MMWR 46, 637–641.

    Google Scholar 

  • Davidson, W.R., Siefken, D.A., Creekmore, L.H., 1994a. Influence of annual and biennial prescribed burning during March on the abundance of Amblyomma americanum (Acari: Ixodidae) in central Georgia. J. Med. Entomol. 31, 72–81.

    Google Scholar 

  • Davidson, W.R., Siefken, D.A., Creekmore, L.H., 1994b. Seasonal and annual abundance of Amblyomma americanum (Acari: Ixodidae) in central Georgia. J. Med. Entomol. 31, 67–71.

    Google Scholar 

  • Dawson, J.E., Childs, J.E., Biggie, K.L., Moore, C., Stallknecht, D., Shaddock, J., Bouseman, J., Hofmeister, E., Olson, J.G., 1994. White-tailed deer as a potential reservoir of Ehrlichia spp. J. Wildl. Dis. 30, 162–168.

    Google Scholar 

  • Des Vignes, F., Levin, M.L., Fish, D., 1999. Comparative vector competence of dermacentor variabilis and ixodes scapularis (acari: Ixodidae) for the agent of human granulocytic ehrlichiosis. J. Med. Entomol. 36, 182–185.

    Google Scholar 

  • Ewing, S.A., Dawson, J.E., Kocan, A.A., Barker, R.W., Warner, C.K., Panciera, R.J., Fox, J.C., Kocan, K.M., Blouin, E.F., 1995. Experimental transmission of Ehrlichia chaffeensis (Rickettsiales: Ehrlichieae) among white-tailed deer by Amblyomma americanum (Acari: Ixodidae). J. Med. Entomol. 32, 368–374.

    Google Scholar 

  • Fitzgibbon, W.E., Parrott, M.E., Webb, G.F., 1996. A diffusive epidemic model for a host-vector system. In: Martelli, M., Cooke, K., Cumberbatch, E., Tang, B., Thieme, H. (Eds.), Differential Equations and Applications to Biology and Industry. World Scientific Press, Singapore, pp. 401–408.

    Google Scholar 

  • Gerhardt, R.R., Lohmeyer, K.H., Marsland, E.J., Paulsen, D.J., 1998. Seasonal abundance of the free-living stages of the lone star tick (Ambloymma americanum) in Cumberland County, Tennessee. J. Tenn. Acad. Sci. 73, 100–103.

    Google Scholar 

  • Ghosh, M., Pugliese, A., 2004. Seasonal population dynamics of ticks, and its influence on infection transmission: A semi-discrete approach. Bull. Math. Biol. 66, 1659–1684.

    Article  MathSciNet  Google Scholar 

  • Haile, D.G., Mount, G.A., 1987. Computer simulation of population dynamics of the lone star tick, Amblyomma americanum (Acari: Ixodidae). J. Med. Entomol. 24, 356–369.

    Google Scholar 

  • Lockhart, J.M., Davidson, W.R., Dawson, J.E., Stallknecht, D.E., 1995. Temporal association of Amblyomma americanum with the presence of Ehrlichia chaffeensis reactive antibodies in white-tailed deer. J. Wildl. Dis. 31, 119–124.

    Google Scholar 

  • Lockhart, J.M., Davidson, W.R., Stallknecht, D.E., Dawson, J.E., 1996. Site-specific geographic association between Amblyomma americanum (Acari: Ixodidae) infestations and Ehrlichia chaffeensis-reactive (Rickettsiales: Ehrlichieae) antibodies in white-tailed deer. J. Med. Entomol. 33, 153–158.

    Google Scholar 

  • Lockhart, J.M., Davidson, W.R., Stallknecht, D.E., Dawson, J.E., Howerth, E.W., 1997. Isolation of Ehrlichia chaffeensis from wild white-tailed deer (Odocoileus virginianus) confirms their role as natural reservoir hosts. J. Clin. Microbiol. 35, 1681–1686.

    Google Scholar 

  • LoGiudice, K., Ostfeld, R.S., Schmidt, K.A., Keesing, F., 2003. The ecology of infectious disease: Effects of host diversity and community composition on lyme disease risk. Proc. Natl. Acad. Sci. 100, 567–571.

    Article  Google Scholar 

  • Maeda, K., Markowitz, N., Hawley, R.C., Ristic, M., Cox, D., McDade, J.E., 1987. Human infections with Ehrlichia canis, a leukocyctic ricksettsia. New Engl. J. Med. 316, 853–836.

    Article  Google Scholar 

  • Marsland, E.J., 1997. Tick control and monitoring of tick transmitted diseases in Eastern Tennessee. Master’s thesis, University of Tennessee.

  • McQuiston, J.H., Paddock, C.D., Holman, R.C., Childs, J.E., 1999. The human ehrlichioses in the united states. Emerg. Infect. Dis. 5, 635–642.

    Article  Google Scholar 

  • Mount, G.A., Haile, D.G., 1989. Computer simulation of population dynamics of the american dog tick (Acari: Ixodidea). J. Med. Entomol. 26, 60–76.

    Google Scholar 

  • Mount, G.A., Haile, D.G., Barnard, D.R., Daniels, E., 1993. New version of LSTSIM for computer simulation of Amblyomma americanum (Acari: Ixodidae) population dynamics. J. Med. Entomol. 30, 843–857.

    Google Scholar 

  • Mount, G.A., Haile, D.G., Daniels, E., 1997a. Simulation of blacklegged tick (Acari: Ixodidea) population dynamics and transmission of borrelia burgdorferi. J. Med. Entomol. 34, 461–484.

    Google Scholar 

  • Mount, G.A., Haile, D.G., Daniels, E., 1997b. Simulation of management strategies for the blacklegged tick (Acari: Ixodidea) and the Lyme disease spirochete, borrelia burgdorferi. J. Med. Entomol. 90, 672–683.

    Google Scholar 

  • Mount, G.A., Haile, D.G., Davey, R.B., Cooksey, L.M., 1991. Computer simulation of boophilus cattle tick (Acari: Ixodidea) population dynamics. J. Med. Entomol. 28, 223–240.

    Google Scholar 

  • Paddock, C.D., Childs, J.E., 2003. Ehrlichia chaffeensis: A prototypical emerging pathogen. Clin. Microbiol. Rev. 16, 37–64.

    Article  Google Scholar 

  • Pound, J.M., Miller, J.A., George, J.E., Oehler, D.D., Harmel, D.E., 1996. Systemic treatment of white-tailed deer with Ivermectin-medicated bait to control free-living populations of lone star ticks (Acari: Ixodidae). J. Med. Entomol. 33, 385–394.

    Google Scholar 

  • Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T., 1988. Numerical Recipes in C. Cambridge University Press, Cambridge.

    MATH  Google Scholar 

  • Radcliffe, J., Rass, L., 1984. The spatial spread and final size of models for the deterministic host-vector epidemic. Math. Biosci. 70, 123–146.

    Article  MATH  MathSciNet  Google Scholar 

  • Radcliffe, J., Rass, L., 1985. The rate of spread of infection in models for the deterministic host-vector epidemic. Math. Biosci. 74, 257–273.

    Article  MATH  MathSciNet  Google Scholar 

  • Randolph, S., 1999. Epidemiological uses of a population model for the tick Rhipicephalus appendiculatus. Trop. Med. Int. Health 4, A34–A42.

    Article  Google Scholar 

  • Richter, D., Spielman, A., Komar, N., Matuschka, F.-R., 2000. Competence of american robins as reservoir hosts for lyme disease spirochetes. Emerg. Infect. Dis. 6, 133–138.

    Article  Google Scholar 

  • Sandberg, S., Awerbuch, T.E., Spielman, A., 1992. A comprehensive multiple matrix model representing the life cycle of the tick that transmits the age of Lyme disease. J. Theor. Biol. 157, 203–220.

    Article  Google Scholar 

  • Schulze, T.L., Jordan, R.A., Hung, R.W., 2001. Effects of selected meteorological factors on diurnal questing of ixodes scapularis and amblyomma americanum (acari: Ixodidade). J. Med. Entomol. 38, 318–324.

    Article  Google Scholar 

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

    Google Scholar 

  • Standaert, S.M., Dawson, J.E., Schaffner, W., Childs, J.E., Biggie, K.L., Singleton, J., Gerhardt, R.R., Knight, M.L., Hutcheson, R.J., 1995. Ehrlichiosis in a golf-oriented retirement community. N. Engl. J. Med. 333, 420–425.

    Article  Google Scholar 

  • University of Rhode Island Tick Research Laboratory, 2003. Ehrlichiosis. Http://www.riaes.org/resources/ticklab/ehrlich.html (Accessed 6 August 2003).

Download references

Author information

Authors and Affiliations

  1. Department of Epidemiology and Preventive Medicine, School of Medicine, University of Maryland, 660 West Redwood Street, Howard Hall, Room 140D, Baltimore, MD, 21201, USA

    Holly D. Gaff

  2. University of Tennessee, Knoxville, TN, USA

    Louis J. Gross

Authors
  1. Holly D. Gaff
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Louis J. Gross
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Holly D. Gaff.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gaff, H.D., Gross, L.J. Modeling Tick-Borne Disease: A Metapopulation Model. Bull. Math. Biol. 69, 265–288 (2007). https://doi.org/10.1007/s11538-006-9125-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-006-9125-5

Keywords

Search

Navigation