
Mathematical Biosciences and Engineering, 2019, 16(5): 47584776. doi: 10.3934/mbe.2019239.
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Threshold dynamics of a timedelayed hantavirus infection model in periodic environments
School of Science, Xi’an Polytechnic University, Xi’an, Shaanxi 710048, P.R. China
Received: , Accepted: , Published:
Special Issues: Transmission dynamics in infectious diseases
Keywords: Hantavirus; seasonality; time delay; uniform persistence; basic reproduction number
Citation: Junli Liu. Threshold dynamics of a timedelayed hantavirus infection model in periodic environments. Mathematical Biosciences and Engineering, 2019, 16(5): 47584776. doi: 10.3934/mbe.2019239
References:
 1. J. A. Reinoso and F. J. de la Rubia, Stagedependent model for Hantavirus infection: The effect of the initial infectionfree period, Phys. Rev. E, 87 (2013), 042706.
 2. C. H. Calisher, W. Sweeney, J. N. Mills, et al., Natural history of Sin Nombre virus in western Colorado, Emerg. Infect. Dis., 5 (1999), 126–134.
 3. J. N. Mills, T. G. Ksiazek, C. J. Peters, et al., Longterm studies of hantavirus reservoir populations in the southwestern United States: a synthesis, Emerg. Infect. Dis., 5 (1999), 135–142.
 4. J. N. Mills, T. G. Ksiazek, B. A. Ellis, et al., 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 (1997), 273–284.
 5. G. E. Glass, W. Livingston, J. N. Mills, et al., Black Creek Canal Virus infection in Sigmodon hispidus in southern Florida, Am. J. Trop. Med. Hyg., 59 (1998), 699–703.
 6. G. Abramson and V. M. Kenkre, Spatiotemporal patterns in the Hantavirus infection, Phys. Rev. E, 66 (2002), 011912.
 7. G. Abramson, V. M. Kenkre, T. L. Yates, et al., Traveling Waves of Infection in the Hantavirus Epidemics, Bull. Math. Biol., 65 (2003), 519–534.
 8. L. J. S. Allen, M. Langlais and C. J. Phillips, The dynamics of two viral infections in a single host population with applications to hantavirus, Math. Biosci., 186 (2003), 191–217.
 9. V. M. Kenkre, L. Giuggioli, G. Abramson, et al., Theory of hantavirus infection spread incorporating localized adult and itinerant juvenile mice, Eur. Phys. J. B, 55 (2007), 461–470.
 10. T. Gedeon, C. Bodelón and A. Kuenzi, Hantavirus Transmission in Sylvan and Peridomestic Environments, Bull. Math. Biol., 72 (2010), 541–564.
 11. F. Sauvage, M. Langlais, N. G. Yoccoz, et al., Modelling hantavirus in fluctuating populations of bank voles: the role of indirect transmission on virus persistence, Journal of Animal Ecology, 72 (2003), 1–13.
 12. C. Wolf, A mathematical model for the propagation of a hantavirus in structured populations, Discrete Contin. Dyn. Syst. Ser. B, 4 (2004), 1065–1089.
 13. C. Wolf, M. Langlais, F. Sauvage, et al., A multipatch epidemic model with periodic demography, direct and indirect transmission and variable maturation rate, Math. Popul. Stud., 13 (2006), 153–177.
 14. J. A. Reinoso and F. J. de la Rubia, Spatial spread of the Hantavirus infection, Phys. Rev. E, 91 (2015), 032703.
 15. J. Buceta, C. Escudero, F. J. de la Rubia, et al., Outbreaks of Hantavirus induced by seasonality, Phys. Rev. E, 69 (2004), 021906.
 16. L. J. S. Allen, R. K. McCormack and C. B. Jonsson, Mathematical models for hantavirus Infection in rodents, Bull. Math. Biol., 68 (2006), 511–524.
 17. R. Bürger, G. Chowell, E. Gavilán, et al., Numerical solution of a spatiotemporal genderstructured model for hantavirus infection in rodents, Math. Biosci. Eng., 15 (2018), 95–123.
 18. R. Ostfeld and F. Keesing, Pulsed resources and community dynamics of consumers in terrestrial ecosystems, Trends in Ecology and Evolution, 15 (2000), 232–237.
 19. K. D. Abbott, T. G. Ksiazek and J. N. Mills, Longterm hantavirus persistency in rodent populations in central Arizona, Emerg. Infect. Dis., 5 (1999), 102–112.
 20. A. J. Kuenzi, M. L. Morrison, D. E. Swann, et al., A longitudinal study of Sin Nombre virus prevalence in rodents in southwestern Arizona, Emerg. Infect. Dis., 5 (1999), 113–117.
 21. J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer, New York, 1993.
 22. H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems,Math. Surveys Monogr. 41, AMS, Providence, RI, 1995.
 23. X.Q. Zhao, Basic reproduction ratios for periodic compartmental models with time delay, J. Dyn. Diff. Equat., 29 (2017), 67–82.
 24. W. Walter,On strongly monotone flows, Ann. Polon. Math., 66 (1997), 269–274.
 25. P. Magal and X.Q. Zhao, Global attractors and steady states for uniformly persistent dynamical systems, SIAM. J. Math. Anal., 37 (2005), 251–275.
 26. X. Liang and X.Q. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Comm. Pure Appl. Math., 60 (2007), 1–40.
 27. X. Wang and X.Q. Zhao, Dynamics of a timedelayed Lyme disease model with seasonality, SIAM J. Appl. Dyn. Syst., 16 (2017), 853–881.
 28. X.Q. Zhao, Dynamical Systems in Population Biology, SpringerVerlag, New York, 2003.
 29. Y. Yuan and X.Q. Zhao, Global stability for nonmonotone delay equations (with application to a model of blood cell production), J. Differ. Equations, 252 (2012), 2189–2209.
 30. D. Posny and J. Wang, Computing the basic reproductive numbers for epidemiological models in nonhomogeneous environments, Appl. Math. Comput., 242 (2014), 473–490.
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