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The Influence of Immunity Loss on Persistence and Recurrence of Endemic Infections

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Conditions for persistence of endemic infections with immunity loss are derived and shown to agree with conditions for recurrence recently established by Chaffee and Kuske (Bull. Math. Biol. 73(11):2552–2574, 2011).

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References

  • Bartlett, M. S. (1956). Deterministic and stochastic models for recurrent epidemics. In Proceedings of the third Berkeley symposium on mathematical statistics and probability (Vol. 4, pp. 81–109). Berkeley: University of California Press.

    Google Scholar 

  • Chaffee, J., & Kuske, R. (2011). The effect of loss of immunity on noise-induced sustained oscillations in epidemics. Bull. Math. Biol., 73(11), 2552–2574.

    Article  MathSciNet  Google Scholar 

  • Clancy, D., & Mendy, S. T. (2010). The effect of waning immunity on long-term behaviour of stochastic models for the spread of infections. J. Math. Biol., 61, 527–544.

    Article  MathSciNet  MATH  Google Scholar 

  • Doering, C. R., Sargsyan, K. V., & Sander, L. M. (2005). Extinction times for birth-death processes: exact results, continuum asymptotics, and the failure of the Fokker–Planck approximation. Multiscale Model. Simul., 3(2), 283–299.

    Article  MathSciNet  MATH  Google Scholar 

  • Kuske, R., Gordillo, L. F., & Greenwood, P. (2007). Sustained oscillations via coherence resonance in SIR. J. Theor. Biol., 245, 459–469.

    Article  MathSciNet  Google Scholar 

  • Mendy, S. T. (2009). Quasi-stationarity of stochastic models for the spread of infectious diseases. Ph.D. thesis, University of Liverpool.

  • Nåsell, I. (2002). Stochastic models of some endemic infections. Math. Biosci., 179, 1–19.

    Article  MathSciNet  Google Scholar 

  • Nåsell, I. (2011). Extinction and quasi-stationarity in the stochastic logistic SIS model. Lecture notes in mathematics: Vol. 2022. New York: Springer.

    Google Scholar 

  • Nåsell, I. (2012a) Extinction and quasi-stationarity in the stochastic logistic SIS model: a Maple module and corrections. www.math.kth.se/~ingemar/SIS/SIS.html.

    Google Scholar 

  • Nåsell, I. (2012b) Recurrence conditions for childhood infections. J. Theor. Biol., 313, 212–216.

    Google Scholar 

  • Nåsell, I. (2012c) Diffusion approximations of some SIRS models. www.math.kth.se/~ingemar/SIRS/SIRS.html.

    Google Scholar 

  • Pollett, P. K. (2001). Diffusion approximations for ecological models. In Proc. int. congr. modelling and simulation.

    Google Scholar 

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Correspondence to Ingemar Nåsell.

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Nåsell, I. The Influence of Immunity Loss on Persistence and Recurrence of Endemic Infections. Bull Math Biol 75, 2079–2092 (2013). https://doi.org/10.1007/s11538-013-9882-x

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