Free Access
Math. Model. Nat. Phenom.
Volume 5, Number 3, 2010
Mathematical modeling in the medical sciences
Page(s) 94 - 114
Published online 28 April 2010
  1. W. Arendt, A. Grabosch, G. Greiner, U. Groh, H. P. Lotz, U. Moustakas, R. Nagel, F. Neubrander, U. Schlotterbeck. One-Parameter Semigroups of Positive Operators. Springer-Verlag, Berlin, 1986. [Google Scholar]
  2. R. Borges, À. Calsina, S. Cuadrado. Equilibria of a cyclin structured cell population model. Discrete Contin. Dyn. Syst., Ser. B, 11 (2009), No. 3, 613–627. [CrossRef] [MathSciNet] [Google Scholar]
  3. À. CalsinaJ. Saldaña. Basic theory for a class of models of hierarchically structured population dynamics with distributed states in the recruitment. Math. Models Methods Appl. Sci., 16 (2006), No. 10, 1695–1722. [CrossRef] [MathSciNet] [Google Scholar]
  4. Ph. Clément, H. J. A. M Heijmans, S. Angenent, C. J. van Duijn, B. de Pagter. One-Parameter Semigroups. North–Holland, Amsterdam, 1987. [Google Scholar]
  5. M. J. Costello. Ecology of sea lice parasitic on farmed and wild fish. Trends in Parasitol., 22 (2006), No. 10, 475–483. [CrossRef] [Google Scholar]
  6. J. M. Cushing. An Introduction to Structured Population dynamics. SIAM, Philadelphia, 1998. [Google Scholar]
  7. O. Diekmann, M. Gyllenberg. Abstract delay equations inspired by population dynamics. in “Functional Analysis and Evolution Equations" (Eds. H. Amann, W. Arendt, M. Hieber, F. Neubrander, S. Nicaise, J. von Below). Birkhäuser, 2007, 187–200. [Google Scholar]
  8. O. Diekmann, Ph. GettoM. Gyllenberg. Stability and bifurcation analysis of Volterra functional equations in the light of suns and stars. SIAM J. Math. Anal., 39 (2007), No. 4, 1023–1069. [CrossRef] [MathSciNet] [Google Scholar]
  9. K.-J. Engel, R. Nagel. One-Parameter Semigroups for Linear Evolution Equations. Springer, New York, 2000. [Google Scholar]
  10. J. Z. FarkasT. Hagen. Stability and regularity results for a size-structured population model. J. Math. Anal. Appl., 328 (2007), No. 1, 119–136. [CrossRef] [MathSciNet] [Google Scholar]
  11. J. Z. FarkasT. Hagen. Asymptotic analysis of a size-structured cannibalism model with infinite dimensional environmental feedback. Commun. Pure Appl. Anal., 8 (2009), No. 6, 1825–1839. [CrossRef] [MathSciNet] [Google Scholar]
  12. J. Z. Farkas, T. Hagen. Hierarchical size-structured populations: The linearized semigroup approach. to appear in Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. [Google Scholar]
  13. P. A. HeuchT. A. Mo. A model of salmon louse production in Norway: effects of increasing salmon production and public management measures. Dis. Aquat. Org., 45 (2001), No. 2, 145–152. [CrossRef] [PubMed] [Google Scholar]
  14. M. Iannelli. Mathematical Theory of Age-Structured Population Dynamics. Giardini Editori, Pisa, 1994. [Google Scholar]
  15. T. Kato. Perturbation Theory for Linear Operators. Springer, New York, 1966. [Google Scholar]
  16. Y. Kubokawa, Ergodic theorems for contraction semi-groups, J. Math. Soc. Japan 27 (1975), 184-193. [CrossRef] [MathSciNet] [Google Scholar]
  17. J. A. J. Metz, O. Diekmann. The Dynamics of Physiologically Structured Populations. Springer, Berlin, 1986. [Google Scholar]
  18. A. G. MurrayP. A. Gillibrand. Modelling salmon lice dispersal in Loch Torridon, Scotland. Marine Pollution Bulletin, 53 (2006), No. 1-4, 128–135. [CrossRef] [PubMed] [Google Scholar]
  19. J. Prüß. Stability analysis for equilibria in age-specific population dynamics. Nonlin. Anal. TMA 7 (1983), No. 12, 1291–1313. [CrossRef] [Google Scholar]
  20. C. W. Revie, C. Robbins, G. Gettinby, L. KellyJ. W. Treasurer. A mathematical model of the growth of sea lice, Lepeophtheirus salmonis, populations on farmed Atlantic salmon, Salmo salar L., in Scotland and its use in the assessment of treatment strategies. J. Fish Dis. 28 (2005), 603–613. [CrossRef] [PubMed] [Google Scholar]
  21. C. S. Tucker, R. Norman, A. Shinn, J. Bron, C. SommervilleR. Wootten. A single cohort time delay model of the life-cycle of the salmon louse Lepeophtheirus salmonis on Atlantic salmon Salmo salar. Fish Path. 37 (2002), No. 3-4, 107–118. [Google Scholar]
  22. O. TullyD. T. Nolan. A review of the population biology and host-parasite interactions of the sea louse Lepeophtheirus salmonis (Copepoda: Caligidae). Parasitology, 124 (2002), 165–182. [Google Scholar]
  23. G. F. Webb. Theory of nonlinear age-dependent population dynamics. Marcel Dekker, New York, 1985. [Google Scholar]
  24. K. Yosida. Functional analysis. Springer, Berlin, 1995. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.