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Articles

Demographic population cycles and ℛ0 in discrete-time epidemic models

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Pages 179-200 | Received 10 Apr 2018, Accepted 10 Oct 2018, Published online: 13 Nov 2018

References

  • L. J. S. Allen, Some discrete-time SI, SIR and SIS epidemic models. Math. Biosc. 124 (1994), pp. 83–105. doi: 10.1016/0025-5564(94)90025-6
  • L. J. S. Allen, P. van den Driessche, The basic reproduction number in some discrete-time epidemic models. J. Diff. Eqns. & Appl. 14(10–11) (2008), pp. 1127–1147. doi: 10.1080/10236190802332308
  • N. Bacaër and E.H. Ait Dads, On the biological interpretation of a definition for the parameter R0 in periodic models, J. Math. Biol. 65 (2012), pp. 601–621. doi: 10.1007/s00285-011-0479-4
  • J.T. Barton, An Introduction to Discrete Mathematical Modeling with Microsoft Office Excel, John Wiley & Sons, Inc, Hoboken, NJ, 2016.
  • F. Brauer, Z. Feng, and C. Castillo-Chavez, Discrete epidemic models, Math. Biosc. Eng. 7(1) (2010), pp. 1–15. doi: 10.3934/mbe.2010.7.1
  • C. Castillo-Chavez and A.-A. Yakubu, Dispersal, disease and life-history evolution, Math. Biosc. 173 (2001), pp. 35–53. doi: 10.1016/S0025-5564(01)00065-7
  • J.M. Cushing and O. Diekmann, The many guises of R0 (a diadactic note), J. Theor. Biol. 404 (2016), pp. 295–302. doi: 10.1016/j.jtbi.2016.06.017
  • J.M. Cushing and Z. Yicang, The net reproductive value and stability in matrix population models, Nat. Resour. Model. 8 (1994), pp. 297–333. doi: 10.1111/j.1939-7445.1994.tb00188.x
  • M. Devold, B. Krossay, V. Aspehaug, and A. Nylund, Use of RT-PCR for diagnosis of infectious salmon anaemia virus (ISAv) in carrier sea trout Salmo trutta after experimental infection, Dis. Aquat. Org. 40 (2000), pp. 9–18. doi: 10.3354/dao040009
  • O. Diekmann, J.A.P. Heesterbeek, and J.A.J. Metz, On the definition and computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, J. Math. Biol. 28 (1990), pp. 365–382. doi: 10.1007/BF00178324
  • S. Elaydi, Discrete Chaos, Chapman & Hall/CRC, Boca Raton, FL, 2000.
  • S. Elaydi and A.-A. Yakubu, Global stability of cycles: Lotka-Volterra competition model with stocking, J. Difference Equ. Appl. 8(6) (2002), pp. 537–549. doi: 10.1080/10236190290027666
  • K. Falk, E. Namork, E. Rimstad, S. Mjaaland, and B.H. Dannevig, Characterization of infectious salmon anemia virus, an orthomyxo-like virus isolated from Atlantic salmon (Sahmo salar L.), J. Virol. 71 (1997), pp. 9016–9023.
  • P.J. Hudson, A.P. Dobson, and D. Newborn, Prevention of population cycles by parasite removal, Science 282(5397) (1998), pp. 2256–2258. doi: 10.1126/science.282.5397.2256
  • F.S.B. Kibenge, O.N. Garate, G.R. Johnson, R. Arriagada, M.J.T. Kibenge, and D. Wadowska, Isolation and identification of infectious salmon anaemia virus (ISAv) from Coho salmon in Chile, Dis. Aquat. Org. 45(1) (2001), pp. 9–18. doi: 10.3354/dao045009
  • M. Krkosek, M.A. Lewis, and J.P. Volpe, Transmission dynamics of parasitic sea lice from farm to wild salmon, Proc. R. Soc. B. 272 (2005), pp. 689–696. doi: 10.1098/rspb.2004.3027
  • D.A. Levy and C.C. Wood, Review of proposed mechanisms for sockeye salmon population cycles in the Fraser river, Bull. Math. Biol. 54(2–3) (1992), pp. 241–261. doi: 10.1007/BF02464832
  • C.-K. Li and H. Schneider, Applications of Perron-Frobenius theory to population dynamics, J. Math. Biol. 44 (2002), pp. 450–462. doi: 10.1007/s002850100132
  • M. Martcheva, An introduction to mathematical epidemiology, Springer Texts in Applied Mathematics 61, Springer, New York, 2015.
  • R.M. May, Simple mathematical models with very complicated dynamics, Nature 261 (1976), pp. 459–467. doi: 10.1038/261459a0
  • E. Milliken and S.S. Pilyugim, A model of infectious salmon anemia virus with viral diffusion between wild and farmed patches, Discrete & Cont. Dyn. Sys. B 21(6) (2016), pp. 1869–1893. doi: 10.3934/dcdsb.2016027
  • W.E. Ricker, Stock and recruitment, J. Fish. Res. Board Can. 11 (1954), pp. 559–623. doi: 10.1139/f54-039
  • A.R.E. Sinclair, D. Chitty, C.I. Stefan, and C.J. Krebs, Mammal population cycles: Evidence for intrinsic differences during snowshoe hare cycles, Can. J. Zool. 81(2) (2003), pp. 216–220. doi: 10.1139/z03-006
  • J.H. Tien and D.J.D. Earn, Multiple transmission pathways and disease dynamics in a water borne pathogen model, Bull. Math. Biol. 72(6) (2010), pp. 1506–1533. doi: 10.1007/s11538-010-9507-6
  • P. van den Driessche, Reproduction numbers of infectious disease models. Infect. Dis. Model. 2 (2017), pp. 1–16.
  • P. van den Driessche and A.-A. Yakubu, Disease extinction versus persistence in discrete-time epidemic models, Bull. Math. Biol. 2018 (In press).
  • S. Vike, S. Nylund, and A. Nylund, ISA virus in Chile. Evidence of vertical transmission, Arch. Virol. 154 (2009), pp. 1–8. doi: 10.1007/s00705-008-0251-2
  • H.I. Wergeland, and R.A. Jakobsen, A salmonid cell line (TO) for production of infectious salmon anaemia virus (ISAv), Dis. Aquat. Org. 44 (2001), pp. 183–190. doi: 10.3354/dao044183
  • A.-A. Yakubu, Introduction to discrete-time epidemic models, DIMACS Series in Discrete Math. Theor. Comput. Sci. 75 (2010), pp. 83–109. doi: 10.1090/dimacs/075/04