Abstract
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).
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.
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.
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.
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.
Kuske, R., Gordillo, L. F., & Greenwood, P. (2007). Sustained oscillations via coherence resonance in SIR. J. Theor. Biol., 245, 459–469.
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.
Nåsell, I. (2011). Extinction and quasi-stationarity in the stochastic logistic SIS model. Lecture notes in mathematics: Vol. 2022. New York: Springer.
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.
Nåsell, I. (2012b) Recurrence conditions for childhood infections. J. Theor. Biol., 313, 212–216.
Nåsell, I. (2012c) Diffusion approximations of some SIRS models. www.math.kth.se/~ingemar/SIRS/SIRS.html.
Pollett, P. K. (2001). Diffusion approximations for ecological models. In Proc. int. congr. modelling and simulation.
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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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DOI: https://doi.org/10.1007/s11538-013-9882-x