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Original Articles

A net reproductive number for periodic matrix models

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Pages 166-188 | Received 23 Nov 2010, Accepted 26 Nov 2010, Published online: 18 Feb 2011

References

  • Ackleh , A. S. and Chiquet , R. 2009 . The global dynamics of a discrete Juvenile–Adult model with continuous and seasonal reproduction . J. Biol. Dynam. , 3 : 101 – 115 .
  • Ackleh , A. S. , Carter , J. , Cole , L. , Nguyen , T. , Monte , J. and Pettit , C. 2010 . Measuring and modeling the seasonal changes of an urban Green Treefrog (Hyla cinerea) population . Ecol. Model. , 221 : 281 – 289 .
  • Bacaër , N. 2009 . Periodic matrix population models: Growth rate, basic reproduction number, and entropy . Bull. Math. Biol. , 71 : 1781 – 1792 .
  • N. Bacaër and E.H.A. Dads, Genealogy with seasonality, the basic reproduction number, and the influenza pandemic, J. Math. Biol. 2010, doi:10.1007/s00285-010-0354-8
  • A. Berman and R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM Classics in Applied Mathematics, SIAM, Philadelphia, 1994
  • Caswell , H. 2001 . Matrix Population Models: Construction, Analysis and Interpretation , 2 , Sunderland , MA : Sinauer Associates .
  • Caswell , H. 2009 . Stage, age and individual stochasticity in demography . Oikos , 118 : 1763 – 1782 .
  • Caswell , H. and Trevisan , M. C. 1994 . Sensitivity analysis of periodic matrix models . Ecology , 75 ( 5 ) : 1299 – 1303 .
  • Cushing , J. M. 1996 . Periodically forced nonlinear systems of difference equations . J. Difference Equations Appl. , 3 : 547 – 561 .
  • Cushing , J. M. An Introduction to Structured Population Dynamics . CBMS-NSF Regional Conference Series in Applied Mathematics . Vol. 71 , Philadelphia : SIAM .
  • Cushing , J. M. 2009 . Matrix Models and Population Dynamics, Mathematical Biology , Edited by: Lewis , Mark A. , Chaplain , Mark A.J. , Keener , James P. and Maini , Philip K. 47 – 150 . Providence , RI : American Mathematical Society . IAS/Park City Mathematics Series
  • Cushing , J. M. and Zhou , Y. 1994 . The net reproductive value and stability in matrix population models . Nat. Resour. Model. , 8 : 297 – 333 .
  • Henson , S. M. 1996 . Existence and stability of nontrivial periodic solutions of periodically forced discrete dynamical systems . J. Difference Equations Appl. , 2 : 315 – 331 .
  • Hunter , C. M. and Caswell , H. 2005 . Selective harvest of sooty shearwater chicks: Effects on population dynamics and sustainability . J. Anim. Ecol. , 74 : 589 – 600 .
  • Klepac , P. and Caswell , H. The stage-structured epidemic: linking disease and demography with a multi-state matrix approach model . Theoret. Ecol. , doi: 10.1007/s12080-010-0079-8
  • Lefkovitch , L. P. 1965 . The study of population growth in organisms grouped by stages . Biometrics , 21 : 1 – 18 .
  • Leslie , P. H. 1945 . On the use of matrices in certain population mathematics . Biometrika , 33 : 183 – 212 .
  • Leslie , P. H. 1948 . Some further notes on the use of matrices in population mathematics . Biometrika , 35 ( 3–4 ) : 213 – 245 .
  • Lewis , E. G. 1942 . On the generation and growth of a population . Sankhya , 6 : 93 – 96 .
  • Li , H. , C.-K. and Schneider , H. 2002 . Applications of Perron–Frobenius theory to population dynamics . J. Math. Biol. , 44 : 450 – 462 .
  • McFadden , C. S. 1991 . A comparative demographic analysis of clonal reproduction in a temperate soft coral . Ecology , 72 ( 5 ) : 1849 – 1866 .
  • Pham , L. , Boudreaux , Karhbet , Price , B. , Ackleh , A. S. , Carter , J. and Pal , N. 2007 . Population estimates of Hyla cinerea (Schneider) (Green Treefrog) in an urban environment . Southeastern Naturalist , 6 : 203 – 216 .