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Seasonality and Outbreaks in West Nile Virus Infection

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Abstract

In this paper we analyze the impact of seasonal variations on the dynamics of West Nile Virus infection. We are interested in the generation of new epidemic peaks starting from an endemic state. In many cases, the oscillations generated by seasonality in the dynamics of the infection are too small to be observable. The interplay of this seasonality with the epidemic oscillations can generate new outbreaks starting from the endemic state through a mechanism of parametric resonance. Using experimental data we present specific cases where this phenomenon is numerically observed.

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References

  • Aron, J.L., Schwartz, I.B., 1984. Seasonality and period-doubling bifurcations in an epidemic model. J. Theor. Biol. 110, 665–679.

    Article  MathSciNet  Google Scholar 

  • Bacaer, N., 2007. Approximation of the basic reproductive number R 0 for vector-borne diseases with a periodic vector population. Bull. Math. Biol. 69, 1067–1091.

    Article  MATH  MathSciNet  Google Scholar 

  • Bacaer, N., Guernaoi, S., 2006. The epidemic threshold of vector-borne diseases with seasonality. J. Math. Biol. 53, 421–436.

    Article  MATH  MathSciNet  Google Scholar 

  • Campbell, L.G., Martin, A.A., Lanciotti, R.S., Gubler, D.J., 2002. West Nile Virus. Lancet Infect. Dis. 2, 519–529.

    Article  Google Scholar 

  • Center for Disease Control and Prevention (CDC), 1999. Update: West Nile-like viral encephalitis, New York, 1999. Morb. Mort. Wkly. Rep. 48, 890–892.

    Google Scholar 

  • Center for Disease Control and Prevention (CDC), 2005. www.westnilemaps.usgs.gov/.

  • Coddington, E.A., Levinson, N., 1984. Theory of Ordinary Differential Equations. Krieger Publishing, Florida.

    Google Scholar 

  • Coutinho, F.A.B., Bourattini, M.N., Lopez, L.F., Massad, E., 2005. An approximate threshold condition for non-autonomous system: An application to a vector-borne infection. Math. Comput. Simul. 70, 149–158.

    Article  MATH  Google Scholar 

  • Coutinho, F.A.B., Bourattini, M.N., Lopez, L.F., Massad, E., 2006. Threshold condition for a non-autonomous epidemic system describing the population dynamics of dengue. Bull. Math. Biol. 68, 2263–2282.

    Article  MathSciNet  Google Scholar 

  • Cruz-Pacheco, G., Esteva, L., Montan̄o-Hirose, J.A., Vargas, C., 2005. Modelling the dynamics of West Nile Virus. Bull. Math. Biol. 67, 1157–1172.

    Article  MathSciNet  Google Scholar 

  • Dietz, K., 1976. The incidence of infectious diseases under the influence of seasonal fluctuations. Lect. Notes Biomath. 11, 1–15.

    Google Scholar 

  • Edman, J.D., Taylor, D.J., 1974. Host-feeding patterns of Florida mosquitoes. III. Culex (Culex) and Culex (Neoculex). J. Med. Entomol. 11, 95–104.

    Google Scholar 

  • Foppa, I.M., Spielman, A., 2007. Does reservoir host mortality enhance transmission of West Nile virus? Theor. Biol. Med. Model. 4, 17. doi:10.1186/1742-4682-4-17.

    Article  Google Scholar 

  • Gatton, M.L., Kelly-Hope, L.A., Kay, B.H., Ryan, P.A., 2004. Spatial-temporal analysis of Ross River virus disease patterns in Queensland, Australia. Am. J. Trop. Med. Hyg. 71(5), 629–635.

    Google Scholar 

  • Grassly, N.C., Fraser, Ch., 2006. Seasonal infectious disease epidemiology. Proc. R. Soc. B 273, 2541–2550.

    Article  Google Scholar 

  • Grossman, Z., 1980. Oscillatory phenomena in a model of infectious diseases. Theor. Popul. Biol. 18, 204–243.

    Article  MATH  MathSciNet  Google Scholar 

  • Hay, S.I., Myers, M.F., Burke, D.S., Vaughn, D.W., , 2000. Etiology of interepidemic periods of mosquito-borne disease. Proc. Natl. Acad. Sci. U.S.A. 97, 9335–9339.

    Article  Google Scholar 

  • Hayes, C.G., 1989. West Nile fever. In: Monath, T.P. (Ed.), The Arboviruses: Epidemiology and Ecology, vol. V, pp. 59–88. CRC Press, Florida.

    Google Scholar 

  • He, D., Earn, D.J.D., 2007. Epidemiological effects of seasonal oscillations in birth rates. Theor. Popul. Biol. 72, 274–291.

    Article  MATH  Google Scholar 

  • Hethcote, H.W., Stech, H.W., van den Driessche, P., 1981. Nonlinear oscillations in epidemic models. SIAM J. Appl. Math. 40, 1–9.

    Article  MATH  MathSciNet  Google Scholar 

  • Landau, L.D., Lifschitz, E.M., 1960. Mechanics. Pergamon, Oxford.

    MATH  Google Scholar 

  • London, W.P., Yorke, J.A., 1973. Recurrent outbreaks of measles, chickenpox, and mumps. I. Seasonal variation in contact rates. Am. J. Epidemiol. 98, 453–468.

    Google Scholar 

  • Lord, C.C., Day, F.J., 2001. Simulations studies of St. Louis Encephalitis and West Nile Viruses: The impact of bird mortality. Vector Borne Zoonotic Dis. 1, 317–329.

    Article  Google Scholar 

  • Magnus, W., Winkler, S., 1966. Hill’s Equation. Dover, New York.

    MATH  Google Scholar 

  • Reiter, P., 2000. From Shakespeare to Defoe: Malaria in England in the little ice age. Emerg. Infect. Dis. 6(1), 1–11.

    Google Scholar 

  • Reiter, P., 2001. Climate change and mosquito-borne disease. Environ. Health Perspect. Suppl. 109, 141–161.

    Article  Google Scholar 

  • Schwartz, I.B., 1985. Multiple stable recurrent outbreaks and predictability in seasonally forced nonlinear epidemic models. J. Math. Biol. 21, 347–361.

    Article  MATH  MathSciNet  Google Scholar 

  • Schwartz, I.B., 1992. Small amplitude, long period outbreaks in seasonally driven epidemics. J. Math. Biol. 30, 473–491.

    Article  MATH  MathSciNet  Google Scholar 

  • Stone, L., Olinky, R., Huppert, A., 2007. Seasonal dynamics of recurrent epidemics. Nature 446, 533–536.

    Article  Google Scholar 

  • Vaidyanathan, R., Scott, T.W., 2006. Seasonal variation in susceptibility to West Nile virus infection in Culex pipiens pipiens (L.) (Diptera: Culicidae) from San Joaquin County, California. J. Vector Ecol. 31(2), 423–425.

    Article  Google Scholar 

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Authors and Affiliations

  1. IIMAS, UNAM, Mexico City, 04510, Mexico

    Gustavo Cruz-Pacheco

  2. Departamento de Matemáticas, Facultad de Ciencias, UNAM, Mexico City, 04510, Mexico

    Lourdes Esteva

  3. Departamento de Control Automático, CINVESTAV–IPN, A.P. 14-740, Mexico City, 07000, Mexico

    Cristobal Vargas

Authors
  1. Gustavo Cruz-Pacheco
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  2. Lourdes Esteva
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  3. Cristobal Vargas
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Correspondence to Lourdes Esteva.

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Cruz-Pacheco, G., Esteva, L. & Vargas, C. Seasonality and Outbreaks in West Nile Virus Infection. Bull. Math. Biol. 71, 1378–1393 (2009). https://doi.org/10.1007/s11538-009-9406-x

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  • DOI: https://doi.org/10.1007/s11538-009-9406-x

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