Abstract
Hantavirus pulmonary syndrome is an emerging disease of humans that is carried by wild rodents. Humans are usually exposed to the virus through geographically isolated outbreaks. The driving forces behind these outbreaks is poorly understood. Certainly, one key driver of the emergence of these viruses is the virus population dynamics within the rodent population. Two new mathematical models for hantavirus infection in rodents are formulated and studied. The new models include the dynamics of susceptible, exposed, infective, and recovered male and female rodents. The first model is a system of ordinary differential equations while the second model is a system of stochastic differential equations. These new models capture some of the realistic dynamics of the male/female rodent hantavirus interaction: higher seroprevalence in males and variability in seroprevalence levels.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Abramson, G., Kenkre, V.M., 2002. Spatiotemporal patterns in hantavirus infection. Phys. Rev. E 66, 011912, 1–5.
Abramson, G., Kenkre, V.M., Yates, T.L., Parmenter, R.R., 2003. Traveling waves of infection in the hantavirus epidemics. Bull. Math. Biol. 65, 519–534.
Allen, E.J., 1999. Stochastic differential equations and persistence time for two interacting populations. Dyn. Cont. Discrete Impulsive Syst. 5, 271–281.
Allen, L.J.S., Allen, E.J., 2003. A comparison of three different stochastic population models with regard to persistence time. Theor. Pop. Biol. 64, 439–449.
Allen, L.J.S., 2003. An Introduction to Stochastic Processes with Applications to Biology. Prentice Hall: Upper Saddle River, N.J.
Allen, L.J.S., Cormier, P.J., 1996. Environmentally-driven epizootics. Math. Biosci. 131, 51–80.
Allen, L.J.S., Langlais, M., Phillips, C., 2003. The dynamics of two viral infections in a single host population with applications to hantavirus. Math. Biosci. 186, 191–217.
Caswell, H., 2001. Matrix Population Models: Construction, Analysis and Interpretation. 2nd ed. Sinauer Associates, Sunderland, MA.
Bernshtein, A.D., Apekina, N.S., Mikhailova, T.V., Myasnikov Y.A., Khlyap, L.A., Korotkov, Y.S., Gavrilovskaya, I.N., 1999. Dynamics of Puumala hantavirus infection in naturally infected bank voles (Clethrinomys glareolus). Arch. Virol. 144, 2415–2428.
CDC MMWR, 2002. Hantavirus pulmonary syndrome—United States: Updated recommendations for risk reduction, July 26, 2002, 51 (RR09), 1–12.
CDC NCID, 2004. Special Pathogens Branch. El Niño Special Report: Could El Niño cause an outbreak of hantavirus disease in the southwestern United States? Last reviewed June 18, 2004. Retrieved from http://www.cdc.gov/ncidod/diseases/hanta/hps/noframes/elnino.htm
Childs, J.E., Ksiazek, T.G., Spiropoulou, C.F., Krebs, J.W., Morzunov, S., Maupin, G.O., Gage, K.L., Rollin, P.E., Sarisky, J., Enscore, R.E., Frey, J.K., Peters, C.J., Nichol, S.T., 1994. Serologic and genetic identification of Peromyscus maniculatus as the primary rodent reservoir for a new hantavirus in the Southwestern United States. J. Infect. Dis. 169, 1271–1280.
Chu, Y.-K., Owen, R.D., Gonzalez, L., Jonsson, C.B., 2003. The complex ecology of hantavirus in Paraguay. Am. J. Trop. Med. Hyg. 69, 263–268.
Davis, B., Schmidley, D.J., 1994. The Mammals of Texas. Texas Parks and Wildlife Press, Austin, TX.
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, 365–382.
Glass, G.E., Livingston, W., Mills, J.N., Hlady, W.G., Fine, J.B., Biggler, W., Coke, T., Frazier, D., Atherley, S., Rollin, P.E., Ksiazek, T.G., Peters, C.J., Childs, J.E., 1998. Black Creek Canal Virus infection in Sigmodon hispidus in southern Florida. Am. J. Trop. Med. Hyg. 59, 699–703.
Hethcote, H.W., 2000. The mathematics of infectious disease. SIAM Rev. 42, 599–653.
Iannelli, M., Martcheva, M., Milner, F.A., 2005. Gender-Structured Population Modeling Mathematical Methods, Numerics, and Simulations. SIAM Frontiers in Applied Mathematics, Philadelphia, PA.
Kirupaharan, N., Allen, L.J.S., 2004. Coexistence of multiple pathogen strains in stochastic epidemic models with density-dependent mortality. Bull. Math. Biol. 66, 841–864.
Klein, S.L., Bird, B.H., Glass, G.E., 2001. Sex differences in immune responses and viral shedding following Seoul virus infection in Norway rats. Am. J. Trop. Med. Hyg. 65, 57–63.
Kloeden, P.E., Platen, E., 1992. Numerical Solution of Stochastic Differential Equations. Springer-Verlag, New York.
Kloeden, P.E., Platen, E., Schurz, H., 1997. Numerical Solution of SDE through Computer Experiments. Springer-Verlag, Berlin.
Ksiazek, T.G., Nichol, S.T., Mills, J.N., Groves, M.G., Wozniak, A., McAdams, S., Monroe, M.C., Johnson, A.M., Martin, M.L., Peters, C.J., Rollin, P.E., 1997. Isolation, genetic diversity, and geographic distribution of Bayou virus (Bunyaviridae: Hantavirus) Am. J. Trop. Med. Hyg. 57, 445–448.
Langlois, J.P., Fahrig, L., Merriam, G., Artsob, H., 2001. Landscape structure influences continental distribution of hantavirus in deer mice. Landscape Ecol. 16, 255–266.
Lee, H.W., van der Groen, G., 1989. Hemorrhagic fever with renal syndrome. Prog. Med. Virol. 36, 92–102.
McIntyre, N.E., Chu, Y.K., Owen, R.D., Abuzeineh, A., De La Sancha, N., Dick, C.W., Holsomback, T., Nisbet, R.A., Jonsson, C., 2005. A longitudinal study of Bayou virus, hosts, and habitat. Am. J. Trop. Med. Hyg. 73(6), 1043–1049.
Mena-Lorca, J., Hethcote, H.W., 1992. Dynamic models of infectious diseases as regulators of population sizes. J. Math. Biol. 30, 693–716.
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 mammals in the major biotic communities of the southwestern United States. Am. J. Trop. Med. Hyg. 56, 273–284.
Monroe, M.C., Morzunov, S.P., Johnson, A.M., Bowen, M.D., Artsob, H., Yates, T., Peters, C.J., Rollin. P.E., Ksizaek, T.G., Nichol, S.T., 1999. Genetic diversity and distribution of Peromyscus-borne hantaviruses in North America. Emerg. Infect. Dis. 5, 75–86.
Plyusnin, A., Morzunov, S.P., 2001. Virus evolution and genetic diversity of hantaviruses and their rodent hosts. Curr. Top. Microbiol. Immunol. 256, 47–75.
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. Anim. Ecol. 72, 1–13.
Schmaljohn, C., Hjelle, B., 1997. Hantaviruses: A global disease problem. Emerg. Infect. Dis. 3, 95–104.
Song, J.W., Baek, L.J., Gajdusek, D.C., Yanagihara, R., Gavrilovskaya, I., Luft, B.J., Mackow, E.R., Hjelle, B., 1994. Isolation of pathogenic hantavirus from white-footed mouse (Peromyscus leucopus). Lancet 344, 1637.
van den Driessche, P., Watmough, J., 2002. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180, 29–48.
Yahnke, C.J., Meserve, P.L., Ksiazek, T.G., Mills, J.N., 2001. Patterns of infection with Laguna Negra virus in wild populations of Calomys laucha in the central Paraguayan chaco. Am. J. Trop. Med. Hyg. 65, 768–776.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Allen, L.J.S., McCormack, R.K. & Jonsson, C.B. Mathematical Models for Hantavirus Infection in Rodents. Bull. Math. Biol. 68, 511–524 (2006). https://doi.org/10.1007/s11538-005-9034-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11538-005-9034-4