Mathematical models for hantavirus infection in rodents

Bulletin of Mathematical Biology

Volumn 68, Issue 3, 2006, Pages 511-524

  Allen, Linda J S ^a   McCormack, Robert K ^a   Jonsson, Colleen B ^b  

^a TEXAS TECH UNIVERSITY   (United States)

^b SOUTHERN RESEARCH INSTITUTE   (United States)

Author keywords

Hantavirus; SEIR epidemic model; Stochastic differential equation

Indexed keywords

HANTAVIRUS; RODENTIA;

ALGORITHM; ANIMAL; ARTICLE; BIOLOGICAL MODEL; FEMALE; GROWTH, DEVELOPMENT AND AGING; HANTAVIRUS; ISOLATION AND PURIFICATION; MALE; POPULATION DYNAMICS; RODENT; SEX DIFFERENCE; STATISTICS; VIROLOGY; VIRUS INFECTION;

ALGORITHMS; ANIMALS; FEMALE; HANTAVIRUS; HANTAVIRUS INFECTIONS; MALE; MODELS, BIOLOGICAL; POPULATION DYNAMICS; RODENTIA; SEX FACTORS; STOCHASTIC PROCESSES;

EID: 33746651139     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-005-9034-4     Document Type: Article

References (35)

1. Abramson, G., Kenkre, V.M., 2002. Spatiotemporal patterns in hantavirus infection. Phys. Rev. E 66, 011912, 1-5.
2. 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.
3. Allen, E.J., 1999. Stochastic differential equations and persistence time for two interacting populations. Dyn. Cont. Discrete Impulsive Syst. 5, 271-281.
4. 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.
5. Allen, L.J.S., 2003. An Introduction to Stochastic Processes with Applications to Biology. Prentice Hall: Upper Saddle River, N.J.
6. Allen, L.J.S., Cormier, P.J., 1996. Environmentally-driven epizootics. Math. Biosci. 131, 51-80.
7. 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.
8. Caswell, H., 2001. Matrix Population Models: Construction, Analysis and Interpretation. 2nd ed. Sinauer Associates, Sunderland, MA.
9. 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.
10. CDC MMWR, 2002. Hantavirus pulmonary syndrome - United States: Updated recommendations for risk reduction, July 26, 2002, 51 (RR09), 1-12.
11. 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 www.cdc.gov/ncidod/ diseases/hanta/hps/noframes/elnino.htm
12. 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.
13. 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.
14. Davis, B., Schmidley, D.J., 1994. The Mammals of Texas. Texas Parks and Wildlife Press, Austin, TX.
15. 0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28, 365-382.
16. 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.
17. Hethcote, H.W., 2000. The mathematics of infectious disease. SIAM Rev. 42, 599-653.
18. Iannelli, M., Martcheva, M., Milner, F.A., 2005. Gender-Structured Population Modeling Mathematical Methods, Numerics, and Simulations. SIAM Frontiers in Applied Mathematics, Philadelphia, PA.
19. 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.
20. 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.
21. Kloeden, P.E., Platen, E., 1992. Numerical Solution of Stochastic Differential Equations. Springer-Verlag, New York.
22. Kloeden, P.E., Platen, E., Schurz, H., 1997. Numerical Solution of SDE through Computer Experiments. Springer-Verlag, Berlin.
23. 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.
24. 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.
25. Lee, H.W., van der Groen, G., 1989. Hemorrhagic fever with renal syndrome. Prog. Med. Virol. 36, 92-102.
26. 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.
27. Mena-Lorca, J., Hethcote, H.W., 1992. Dynamic models of infectious diseases as regulators of population sizes. J. Math. Biol. 30, 693-716.
28. 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.
29. 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.
30. Plyusnin, A., Morzunov, S.P., 2001. Virus evolution and genetic diversity of hantaviruses and their rodent hosts. Curr. Top. Microbiol. Immunol. 256, 47-75.
31. 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.
32. Schmaljohn, C., Hjelle, B., 1997. Hantaviruses: A global disease problem. Emerg. Infect. Dis. 3, 95-104.
33. 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.
34. 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.
35. 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.