Qualitative properties of a population dynamics system describing pregnancy

Mathematical Models and Methods in Applied Sciences

Volumn 15, Issue 4, 2005, Pages 507-554

  Fragnelli, G ^a   Martinez, P ^b   Vancostenoble, J ^b  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

Author keywords

Asymptotic behavior; Population dynamics; Qualitative properties

Indexed keywords

EID: 17144393012     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202505000455     Document Type: Article

References (27)

1. S. Aniţa, Analysis and control of age-dependent population dynamics, in Mathematical Modelling: Theory and Applications, Vol. 11 (Kluwer, 2000).
2. W. Arendt, C. J. K. Batty, M. Hieber and F. Neubrander, Vector-valued Laplace Transforms and Cauchy Problems, Monographs in Mathematics, Vol. 96 (Birkhäuser, 2001).
3. S. Brendle and R. Nagel, Partial functional differential equations with nonautonomous past, Disc. Cont. Dyn. Syst. 8 (2002) 953-966.
4. J.-M. Buchot and J.-P. Raymond, A linearized model for boundary layer equations, Int. Ser. Numer. Math. 139 (2001) 31-42.
5. E. A. Carl, Population control in arctic ground squirrels, Ecology 52 (1971) 395-413.
6. O. Diekmann, M. Gyllenberg, J. A. J. Metz and H. R. Thieme, On the formulation and analysis of general deterministic structured population models. I. Linear theory, J. Math. Biol. 36 (1998) 349-388.
7. O. Diekmann, M. Gyllenberg, H. Huang, M. Kirkilionis, J. A. J. Metz and H. R. Thieme, On the formulation and analysis of general deterministic structured population models. II. Nonlinear theory, J. Math. Biol. 43 (2001) 157-189.
8. O. Diekmann, M. Gyllenberg and H. R. Thieme, Perturbing evolutionary systems by step responses and cumulative outputs, Diff. Integral Eqs. 8 (1995) 1205-1244.
9. G. Doetsch, Einführung in Theorie und Andwendung der Laplace-Transormation, Mathematische Reihe (Birkhäuser, 1958).
10. K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics (Springer-Verlag, 1999).
11. G. Fragnelli, Delay equations with nonautonomous past, PhD. Thesis, Mathematischen Fakultät der Eberhard-Karls-Universität Tübingen, 2002.
12. p-spaces, Diff. Int. Eqns. 16 (2003) 327-348.
13. p-spaces, Abst. Appl. Anal. 8 (2003) 933-951.
14. G. Fragnelli, P. Martinez and J. Vancostenoble, Qualitative properties of a population dynamics system describing pregnancy, Preprint Laboratoire M.I.P. Université Paul Sabatier, Toulouse III (2003).
15. G. Fragnelli and L. Tonetto, A population equation with diffusion, J. Math. Anal. Appl., to appear.
16. W. S. C. Gurney and R. M. Nisbet, The regulation of inhomogeneous populations, J. Theor. Biol. 52 (1975) 441-457.
17. I. Lasiecka and R. Triggiani, Exact boundary controllability of a first order, non-linear hyperbolic equation with non-local integral terms arising in epidemic modeling, in Direct and Inverse Problems of Mathematical Physics (Newark, DE, 1997), Int. Soc. Anal. Appl. Comput. 5 (Kluwer, 2000), pp. 363-398.
18. P. Marcati and M. A. Pozio, Global asymptotic stability for a vector disease model with spatial spread, J. Math. Biol. 9 (1980) 179-187.
19. J. A. J. Metz and O. Diekmann, The dynamics of physiologically structured populations, papers from the colloquium held in Amsterdam, 1983, Lecture Notes in Biomathematics Vol. 68 (Springer-Verlag, 1986).
20. G. Nickel and A. Rhandi, Positivity and stability of delay equations with nonautonomous past, Tübinger Berichte (2002) 253-267.
21. S. Mischler, B. Perthame and L. Ryzhik, Stability in a nonlinear population maturation model, Math. Models Meth. Appl. Sci. 12 (2002) 1751-1772.
22. S. Piazzera, An age-dependent population equation with delayed-birth process, Math. Meth. Appl. Sci., to appear.
23. M. A. Pozio, Behavior of solutions for some abstract functional differential equations and application to predator-prey dynamics, Nonlinear Anal. Theory, Meth. Appl. 4 (1980) 917-938.
24. M. A. Pozio, Some conditions for global asymptotic stability of equilibria of integro-differential equations, J. Math. Anal. Appl. 95 (1983) 501-527.
25. J. G. Skellam, Random dispersal in theoretical populations, Biomet. 38 (1951) 196-218.
26. G. F. Webb, Theory of Nonlinear Age-Dependent Population Dynamics, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 89 (Marcel Dekker, 1985).
27. J. Wu, Theory and Applications of Partial Functional Differential Equations (Springer-Verlag, 1996).