Bulletin of Mathematical Biology

, Volume 72, Issue 3, pp 541–564 | Cite as

Hantavirus Transmission in Sylvan and Peridomestic Environments

Original Article

Abstract

We developed a compartmental model for hantavirus infection in deer mice (Peromyscus maniculatus) with the goal of comparing relative importance of direct and indirect transmission in sylvan and peridomestic environments. A direct transmission occurs when the infection is mediated by the contact of an infected and an uninfected mouse, while an indirect transmission occurs when the infection is mediated by the contact of an uninfected mouse with, for instance, infected soil. Based on population dynamics data and estimates of hantavirus decay in the two types of environments, our model predicts that direct transmission dominates in the sylvan environment, while both pathways are important in peridomestic environments. The model allows us to compute a basic reproduction number R 0, which indicates whether the virus will be endemic or eradicated from the mouse population, in both an autonomous and a time-periodic model. Our analysis can be used to evaluate various eradication strategies.

Keywords

Sin Nombre hantavirus Deer mice Compartmental model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abbott, K.D., Ksiazek, T.G., Mills, J.N., 1999. Long-term hantavirus persistency in rodent populations in central Arizona. Emerg. Infect. Dis. 5, 102–112. CrossRefGoogle Scholar
  2. Abramson, G., Kenkre, V.M., 2002. Spatiotemporal patterns in the hantavirus infection. Phys. Rev. E 66, 011912. CrossRefGoogle Scholar
  3. Abramson, G., Kenkre, V.M., Yates, T.L., Parmenter, R.R., 2003. Travelling waves of infection in the hantavirus epidemics. Bull. Math. Biol. 65, 271–281. CrossRefGoogle Scholar
  4. Allen, L.J.S., Langlais, M., Phillips, C., 2003. The dynamics of two viral infections in a single host population with application to hantavirus. Math. Biosci. 186, 191–217. CrossRefMathSciNetMATHGoogle Scholar
  5. Allen, L.J.S., McCormack, R.K., Jonsson, C.B., 2006. Mathematical models for hantavirus infection in rodents. Bull. Math. Biol. 68, 511–524. CrossRefMathSciNetGoogle Scholar
  6. Armstrong, L.R., Zaki, S.R., Goldoft, M.J., Todd, R.L., Khan, A.S., Khabbaz, R.F., Ksiazek, T.G., Peters, C.J., 1995. Hantavirus pulmonary syndrome associated with entering or cleaning rarely used, rodent-infested structures. J. Infect. Dis. 172, 1166. Google Scholar
  7. Bacaer, N., 2007. Approximation of the basic reproduction number R 0 for vector borne diseases with a periodic vector population. Bull. Math. Biol. 69, 1067–1091. CrossRefMathSciNetMATHGoogle Scholar
  8. Calisher, C.H., Root, J.J., Mills, J.N., Beaty, B.J., 2003. Hantaviruses: etiologic agents of rare, but potentially life-threatening zoonotic diseases. J. Am. Vet. Med. Assoc. 222, 163–166. CrossRefGoogle Scholar
  9. 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. CrossRefGoogle Scholar
  10. CDC MMWR, 2002. Hantavirus pulmonary syndrome—United States: updated recommendations for risk reduction. Center Dis. Control Morb. Mort. Weekly Rep. 51, 1–12. Google Scholar
  11. Centers for Disease Control and Prevention, 2007. Case information: hantavirus pulmonary syndrome case count and descriptive statistics as of March 2007. National Center for Infectious Diseases, Special Pathogens Branch Google Scholar
  12. Childs, J.E., Ksiazek, T.G., Spiropoulou, C.F., Krebs, J.W., Morzunov, S., Maupin, G.O., Rollin, P.E., Sarisky, J., Enscore, R.E., 1994. Serologic and genetic identification of Peromyscus maniculatus as the primary rodent reservoir for a new hantavirus in southwestern United States. J. Infect. Dis., 1271–1280. Google Scholar
  13. Diekmann, O., Heesterbeek, J.A.P., Metz, J.A.J., 1990. On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28, 365. CrossRefMathSciNetMATHGoogle Scholar
  14. Douglass, R.J., Semmens, W.J., Matlock-Cooley, S.J., Kuenzi, A.J., 2006. Deer mouse movements in peridomestic and sylvan settings in relation to Sin Nombre virus antibody prevalence. J. Wildlife Dis. 42(4), 813–818. Google Scholar
  15. Douglass, R.J., Wilson, T., Semmens, W.J., Zanto, S.N., Bond, C.W., Van Horn, R.C., Mills, J.N., 2001. Longitudinal studies of Sin Nombre virus in deer mouse dominated ecosystems in Montana. Am. J. Trop. Med. Hyg. 65(1), 33–41. Google Scholar
  16. Glass, G.E., Watson, A.J., LeDuc, J.W., Kelen, G.D., Quinn, T.C., Childs, J.E., 1993. Infection with a rat- borne hantavirus in United States residents is consistently associated with hypertensive renal disease. J. Infect. Dis. 167, 614–619. Google Scholar
  17. Hale, J., Kocak, H., 1991. Dynamics and Bifurcations. Springer, Berlin. MATHGoogle Scholar
  18. Kalio, E., Klingstrom, J., Gustafsson, E., Manni, T., Vaheri, A., Henttonen, H., Vapalahti, O., Lundkvist, A., 2006. Prolonged survival of Puumala hantavirus outside the host: evidence for indirect transmission via the environment. J. Gen. Virol. 87, 2127–2134. CrossRefGoogle Scholar
  19. Kenkre, V.M., Giuggioli, L., Abramson, G., Camelo-Neto, G., 2007. Theory of hantavirus infection spread incorporating localized adult and itinerant juvenile mice. Eur. Phys. J. 55, 461–470. Google Scholar
  20. Khan, A.S., et al., 1996. Hantavirus pulmonary syndrome: the first 100 US cases. J. Infect. Dis. 173, 1297–1303. Google Scholar
  21. King, J.A., 1968. Biology of Peromyscus (Rodentia), 1st edn. The American Society of Mammalogists, Stillwater. Google Scholar
  22. King, J.A., 1983. Seasonal dispersal in a semi-natural population of Peromyscus maniculatus. Can. J. Zool. 61(12), 11. CrossRefGoogle Scholar
  23. Krebs, C.J., 1966. Demographic changes in fluctuating populations of Microtus californicus. Ecol. Monogr. 36, 239–273. CrossRefGoogle Scholar
  24. Kuenzi, A.J., Douglass, R.J., White, D. Jr., Bond, C.W., Mills, J.N., 2001a. Antibody to Sin Nombre virus in rodents associated with peridomestic habitats in west central Montana. Am. J. Trop. Med. Hyg. 64, 137–146. Google Scholar
  25. Kuenzi, A.J., Douglass, R.J. Jr., White, D., Bond, C.W., Mills, J.N., 2001b. Antibody to Sin Nombre virus in rodents associated with peridomestic habitats in west central Montana. Am. J. Trop. Med. Hyg. 64, 137–146. Google Scholar
  26. 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. Wildlife Dis. 41, 473–481. Google Scholar
  27. Kuenzi, A.J., Morrison, M.L., Swann, D.E., Hardy, P.C., Downard, G.T., 1999. A longitudinal study of Sin Nombre virus prevalence in rodents in southwestern Arizona. Emerg. Infect. Dis. 5, 113–117. CrossRefGoogle Scholar
  28. Kuenzi, A.J., Zumbrun, M.M., Hughes, K., 2005. Ear tags versus passive integrated transponder (pit) tags for effectively marking deer mice. Int. J. Sci. 11, 66–70. Google Scholar
  29. Lee, P.W., Amyx, H.L., Yanagihara, R., Gajdusek, D.C., Goldgaber, D., Gibbs, C.J. Jr., 1985. Partial characterization of Prospect Hill virus isolated from meadow voles in the United States. J. Infect. Dis. 152, 826–829. Google Scholar
  30. 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
  31. Nichol, S.T., Spiropoulou, C.F., Morzunov, S., Rollin, P.E., Ksiazek, T.G., Feldmann, H., Sanchez, A., Childs, J., Zaki, S., Peters, C.J., 1993. Genetic identification of a hantavirus associated with an outbreak of acute respiratory illness. Science 262, 914–917. CrossRefGoogle Scholar
  32. Padula, P., Figueroa, R., Navarrete, M., Pizarro, E., Cadiz, R., Bellomo, C., Jofre, C., Zaror, L., Rodriguez, E., Murua, R., 2004. Transmission study of Andes hantavirus infection in wild sigmodontine rodents. J. Virol., 11972–11979. Google Scholar
  33. Sauvage, F., Langlais, M., Yoccoz, N.G., Pontier, D., 2003. Modeling hantavirus in fluctuating populations of bank voles: the role of indirect transmission on virus persistence. J. Anim. Ecol. 72, 1–13. CrossRefGoogle Scholar
  34. Schmaljohn, C., Huggins, J., Calisher, C.H., 1999. Laboratory and field safety. In Lee, H.W., Calisher, C.H., Schmaljohn, C. (Eds.), Manual of Hemorrhagic Fever with Renal Syndrome and Hantavirus Pulmonary Syndrome, pp. 192–198. WHO Collaborating Center for Virus Reference and Research (Hantaviruses), Asian Institute for Life Sciences, Seoul, Korea. Google Scholar
  35. Shechmeister, I.L., 1991. Sterilization by ultraviolet irradiation. In: Block, S.S. (Ed.), Disinfection, Sterilization, and Preservation, p. 553. Lea and Febiger, Philadelphia Google Scholar
  36. Tsai, T.F., 1987. Hemorrhagic fever with renal syndrome: mode of transmission to humans. Lab. Anim. Sci. 37, 430. Google Scholar
  37. van den Driessche, P., Watmough, J., 2002. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 10, 29–48. Google Scholar
  38. Wolf, C., 2004. A mathematical model for the propagation of a hantavirus in structured populations. Discrete Contin. Dyn. Syst. B 4(4), 1065–1089. CrossRefMATHGoogle Scholar
  39. Wolf, C., Langlais, M., Sauvage, F., Pontier, D., 2006. A multi-patch epidemic model with periodic demography, direct and indirect transmission and variable maturation rate. Math. Popul. Stud. 13(3), 153–177. CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Society for Mathematical Biology 2009

Authors and Affiliations

  1. 1.Department of Mathematical SciencesMontana State UniversityBozemanUSA
  2. 2.Department of EpidemiologyUniversity of WashingtonSeattleUSA
  3. 3.Department of BiologyMontana Tech of the University of MontanaButteUSA

Personalised recommendations