How Host Population Dynamics Translate into Time-Lagged Prevalence: An Investigation of Sin Nombre Virus in Deer Mice

  • Frederick R. Adler
  • Jessica M. C. Pearce-Duvet
  • M. Denise Dearing
Original Article


Human cases of hantavirus pulmonary syndrome caused by Sin Nombre virus are the endpoint of complex ecological cascade from weather conditions, population dynamics of deer mice, to prevalence of SNV in deer mice. Using population trajectories from the literature and mathematical modeling, we analyze the time lag between deer mouse population peaks and peaks in SNV antibody prevalence in deer mice. Because the virus is not transmitted vertically, rapid population growth can lead initially to reduced prevalence, but the resulting higher population size may later increase contact rates and generate increased prevalence. Incorporating these factors, the predicted time lag ranges from 0 to 18 months, and takes on larger values when host population size varies with a longer period or higher amplitude, when mean prevalence is low and when transmission is frequency-dependent. Population size variation due to variation in birth rates rather than death rates also increases the lag. Predicting future human outbreaks of hantavirus pulmonary syndrome may require taking these effects into account.


Hantavirus Sin Nombre virus Time lags 


  1. Abbott, K.D., Ksiazek, T.G., Mills, J.N., 1999. Long-term hantavirus persistence in rodent populations in central Arizona. Emerg. Infect. Dis. 5, 102–112. Google Scholar
  2. Abramson, G., Kenkre, V.M., 2002. Spatiotemporal patterns in the hantavirus infection. Phys. Rev. E 66, 011912. CrossRefGoogle Scholar
  3. Allen, L.J.S., McCormack, R.K., Johnson, C.B., 2006. Mathematical models for hantavirus infection in rodents. Bull. Math. Biol. 68, 511–524. CrossRefMathSciNetGoogle Scholar
  4. Anderson, R., May, R., 1992. Infectious Diseases of Humans. Oxford University Press, Oxford. Google Scholar
  5. Barlow, N.D., 2000. Non-linear transmission and simple models for bovine tuberculosis. J. Animal Ecol. 69, 703–713. CrossRefGoogle Scholar
  6. Begon, M., Feore, S.M., Brown, K., Chantrey, J., Jones, T., Bennett, M., 1998. Population and transmission dynamics of cowpox in bank voles: testing fundamental assumptions. Ecol. Lett. 1, 82–86. CrossRefGoogle Scholar
  7. Biggs, J.R., Bennett, K.D., Mullen, M.A., Haarmann, T.K., Salisbury, M., Robinson, R.J., Keller, D., Torrez-Martinez, N., Hjelle, B., 2000. Relationship of ecological variables to Sin Nombre virus antibody seroprevalence in populations of deer mice. J. Mammal. 81, 676–682. CrossRefGoogle Scholar
  8. Boone, J.D., Otteson, E.W., McGwire, K.C., Villard, P., Rowe, J.E., Jeor, S.C.S., 1998. Ecology and demographics of hantavirus infections in rodent populations in the Walker River Basin of Nevada and California. Am. J. Trop. Med. Hyg. 59, 445–451. Google Scholar
  9. Botten, J., Mirowsky, K., Ye, C.Y., Gottlieb, K., Saavedra, M., Ponce, L., Hjelle, B., 2002. Shedding and intracage transmission of Sin Nombre hantavirus in the deer mouse (Peromyscus maniculatus) model. J. Virol. 76, 7587–7594. CrossRefGoogle Scholar
  10. Brown, J.H., Ernest, S.K.M., 2002. Rain and rodents: complex dynamics of desert consumers. Bioscience 52, 979–987. CrossRefGoogle Scholar
  11. Buceta, J., Escudero, C., de la Rubia, F.J., Lindenberg, K., 2004. Outbreaks of hantavirus induced by seasonality. Phys. Rev. E 69, 021906. CrossRefGoogle Scholar
  12. Caley, P., Ramsey, D., 2001. Estimating disease transmission in wildlife, with emphasis on leptospirosis and bovine tuberculosis in possums, and effects of fertility control. J. Appl. Ecol. 38, 1362–1370. CrossRefGoogle Scholar
  13. Calisher, C.H., Sweeney, W., Mills, J.N., Beaty, B.J., 1999. Natural history of Sin Nombre virus in western Colorado. Emerg. Infect. Dis. 5, 126–134. Google Scholar
  14. Calisher, C.H., Mills, J.N., Sweeney, W.P., Choate, J.R., Sharp, D.E., Canestorp, K.M., Beaty, B.J., 2001. Do unusual site-specific population dynamics of rodent reservoirs provide clues to the natural history of hantaviruses? J. Wild. Dis. 37, 280–288. Google Scholar
  15. Calisher, C.H., Root, J.J., Mills, J.N., Rowe, J.E., Reeder, S.A., Jentes, E.S., Wagoner, K., Beaty, B.J., 2005. Epizootiology of Sin Nombre and El Moro Canyon hantavirus, southeastern Colorado, 1995–2000. J. Wild. Dis. 41, 1–11. Google Scholar
  16. Davis, S., Begon, M., De Bruyn, L., Ageyev, V.S., Klassovskiy, N.L., Pole, S.B., Viljugrein, H., Stenseth, N.C., Leirs, H., 2004. Predictive thresholds for plague in Kazakhstan. Science 304, 736–738. CrossRefGoogle Scholar
  17. Davis, S., Calvet, E., Leirs, H., 2005. Fluctuating rodent populations and risk to humans from rodent-borne zoonoses. Vector-Borne Zoonotic Dis. 5, 305–314. CrossRefGoogle Scholar
  18. Douglass, R.J., Wilson, T., Semmens, W.J., Zanto, S.N., Bond, C.W., Horn, R.C.V., Mills, J.N., 2001. Longitudinal studies of Sin Nombre virus in deer mouse-dominated ecosystems of Montana. Am. J. Trop. Med. Hyg. 65, 33–41. Google Scholar
  19. Engelthaler, D.M., Mosley, D.G., Cheek, J.E., Levy, C.E., Komatsu, K.K., Ettestad, P., Davis, T., Tanda, D.T., Miller, L., Frampton, J.W., Porter, R., Bryan, R.T., 1999. Climatic and environmental patterns associated with hantavirus pulmonary syndrome, Four Corners region, United States. Emerg. Infect. Dis. 5, 87–94. Google Scholar
  20. Enscore, R.E., Biggerstaff, B.J., Brown, T.L., Fulgham, R.F., Reynolds, P.J., Engelthaler, D.M., Levy, C.E., Parmenter, R.R., Montenieri, J.A., Cheek, J.E., Grinnell, R.K., Ettestad, P.J., Gage, K.L., 2002. Modeling relationships between climate and the frequency of human plague cases in the southwestern United States, 1960–1997. Am. J. Trop. Med. Hyg. 66, 186–196. Google Scholar
  21. Escutenaire, S., Chalon, P., Verhagen, R., Heyman, P., Thomas, I., Karelle-Bui, L., Avsic-Zupanc, T., Lundkvist, A., Plyusnin, A., Pastoret, P.P., 2000. Spatial and temporal dynamics of Puumala hantavirus infection in red bank vole (Clethrionomys glareolus) populations in Belgium. Virus Res. 67, 91–107. CrossRefGoogle Scholar
  22. Fairbairn, D.J., 1977. The spring decline in deer mice: death or dispersal. Can. J. Zool. 55, 84–92. Google Scholar
  23. Glass, G.E., Cheek, J.E., Patz, J.A., Shields, T.M., Doyle, T.J., Thoroughman, D.A., Hunt, D.K., Enscore, R.E., Gage, K.L., Irland, C., Peters, C.J., Bryan, R., 2000. Using remotely sensed data to identify areas at risk for hantavirus pulmonary syndrome. Emerg. Infect. Dis. 6, 238–247. Google Scholar
  24. Graham, T.B., Chomel, B.B., 1997. Population dynamics of the deer mouse (Peromyscus maniculatus) and Sin Nombre Virus, California Channel Islands. Emerg. Infect. Dis. 3, 367–370. Google Scholar
  25. Helle, B., Yates, T., (2001) Modeling hantavirus maintenance and transmission in rodent communities. In: Schmaljohn, C.S., Nichol, S.T. (Eds.), Hantaviruses, pp. 77–90. Springer, Berlin. Google Scholar
  26. Hjelle, B., Glass, G.E., 2000. Outbreak of hantavirus infection in the Four Corners region of the United States in the wake of the 1997–1998 El Nino-southern oscillation. J. Infect. Dis. 181, 1569–1573. CrossRefGoogle Scholar
  27. Keesing, F., Holt, R.D., Ostfeld, R.S., 2006. Effects of species diversity on disease risk. Ecol. Lett. 9, 485–498. CrossRefGoogle Scholar
  28. Kolivras, K.N., Comrie, A.C., 2004. Climate and infectious disease in the southwestern United States. Prog. Phys. Geogr. 28, 387–398. CrossRefGoogle Scholar
  29. Kuenzi, A.J., Douglass, R.J., Bond, C.W., Calisher, C.H., Mills, J.N., 2005. Long-term dynamics of Sin Nombre viral RNA and antibody in deer mice in Montana. J. Wildl. Dis. 41, 473–481. Google Scholar
  30. McCallum, H., Barlow, N.D., Hone, J., 2001. How should pathogen transmission be modelled? Trends Ecol. Evol. 16, 295–300. CrossRefGoogle Scholar
  31. Mills, J.N., Ksiazek, T.G., Mills, J.N., Ksiazek, T.G., Ellis, B.A., Rollin, P.E., Nichol, S.T., Yates, T.L., Gannon, W.L., Levy, C.E., Engelthaler, D.M., Davis, T., Tanda, D.T., Frampton, J.W., Nichols, C.R., Peters, C.J., Childs, J.E., 1997. Patterns of association with host and habitat: antibody reactive with Sin Nombre virus in small mammals in the major biotic communities of the southwestern United States. Am. J. Trop. Med. Hyg. 56, 273–284. Google Scholar
  32. Mills, J.N., Ksiazek, T.G., Peters, C.J., Childs, J.E., 1999. Long-term studies of hantavirus reservoir populations in the southwestern United States: a synthesis. Emerg. Infect. Dis. 5, 135–142. CrossRefGoogle Scholar
  33. Olsson, G.E., White, N., Ahlm, C., Elgh, F., Verlemyr, A.C., Juto, P., Palo, R.T., 2002. Demographic factors associated with hantavirus infection in bank voles (Clethrionomys glareolus). Emerg. Infect. Dis. 8, 924–929. Google Scholar
  34. Olsson, G.E., Ahim, C., Elgh, F., Verlemyr, A.C., White, N., Juto, P., Palo, R.T., 2003. Hantavirus antibody occurrence in bank voles (Clethrionomys glareolus) during a vole population cycle. J. Wild. Dis. 39, 299–305. Google Scholar
  35. Petticrew, B., Sadleir, R., 1974. The ecology of the deer mouse Peromyscus maniculatus in a coastal coniferous forest: population dynamics. Can. J. Zool. 52, 107–118. CrossRefGoogle Scholar
  36. R Development Core Team, 2005. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. Google Scholar
  37. Ramsey, D., Spencer, N., Caley, P., Efford, M., Hansen, K., Lam, M., Cooper, D., 2002. The effects of reducing population density on contact rates between brushtail possums: implications for transmission of bovine tuberculosis. J. Appl. Ecol. 39, 806–818. CrossRefGoogle Scholar
  38. Root, J.J., Calisher, C.H., Beaty, B.J., 1999. Relationships of deer mouse movement, vegetative structure, and prevalence of infection with Sin Nombre Virus. J. Wildl. Dis. 35, 311–316. Google Scholar
  39. Root, J.J., Black, W.I.V., Calisher, C.H., Wilson, K.R., Mackie, R.S., Schountz, T., Mills, J.N., Beaty, B.J., 2003. Analyses of gene flow among populations of deer mice (Peromyscus maniculatus) at sites near hantavirus pulmonary syndrome case-patient residences. J. Wildl. Dis. 39, 287–298. Google Scholar
  40. Sanchez, A.J., Abbott, K.D., Nichol, S.T., 2001. Genetic identification and characterization of limestone canyon virus, a unique Peromyscus-borne hantavirus. Virol. 286, 345–353. CrossRefGoogle Scholar
  41. Sauvage, F., Langlais, M., Pontier, D., 2007. Predicting the emergence of human hantavirus disease using a combination of viral dynamics and rodent demographic patterns. Epidemiol. Infect. 135, 46–56. CrossRefGoogle Scholar
  42. Sauvage, F., Langlais, M., Yoccoz, N.G., Pontier, D., 2003. Modelling hantavirus in fluctuating populations of bank voles: the role of indirect transmission on virus persistence. J. Animal Ecol. 72, 1–13. CrossRefGoogle Scholar
  43. Schmaljohn, C., Hjelle, B., 1997. Hantaviruses: a global disease problem. Emerg. Infect. Dis. 3, 95–104. CrossRefGoogle Scholar
  44. Wolff, J.O., 1985. The effects of density, food, and interspecific interference on home range size in Peromyscus leucopus and Peromyscus maniculatus. Can. J. Zool. 63, 2657–2662. CrossRefGoogle Scholar
  45. Yates, T.L., Mills, J.N., Parmenter, C.A., Ksiazek, T.G., Parmenter, R.R., Castle, J.R.V., Calisher, C.H., Nichol, S.T., Abbott, K.D., Young, J.C., Morrison, M.L., Beaty, B.J., Dunnum, J.L., Baker, R.J., Salazar-Bravo, J., Peters, C.J., 2002. The ecology and evolutionary history of an emergent disease: hantavirus pulmonary syndrome. Bioscience 52, 989–998. CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2007

Authors and Affiliations

  • Frederick R. Adler
    • 1
  • Jessica M. C. Pearce-Duvet
    • 2
  • M. Denise Dearing
    • 2
  1. 1.Department of Mathematics and Department of Biology, 155 South 1400 EastUniversity of UtahSalt Lake CityUSA
  2. 2.Department of Biology, 257 South 1400 EastUniversity of UtahSalt Lake CityUSA

Personalised recommendations