Monotone approximation for a nonlinear size and class age structured epidemic model

Nonlinear Analysis: Real World Applications

Volumn 8, Issue 3, 2007, Pages 834-852

  Banks, H T ^a   Bokil, V A ^a   Hu, Shuhua ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Comparison principle; Monotone approximations; Size and class age structured models; Well posedness

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL MODELS; PROBLEM SOLVING;

COMPARISON PRINCIPLE; MONOTONE APPROXIMATIONS; SIZE AND CLASS AGE STRUCTURED EPIDEMIC MODEL; WELL-POSEDNESS;

NONLINEAR SYSTEMS;

EID: 33846185492     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2006.03.008     Document Type: Article

References (18)

1. Ackleh A.S., Cole C., Deng K., and Tran H. Existence-uniqueness and monotone approximation for an erythropoiesis age-structured model. J. Math. Anal. Appl. 289 (2004) 530-544
2. Ackleh A.S., and Deng K. A monotone approximation for the nonautonomous size-structured population model. Quart. Appl. Math. 57 (1999) 261-267
3. Ackleh A.S., and Deng K. Monotone method for nonlinear nonlocal hyperbolic problems, Fifth Mississippi State Conference on Differential Equations and Computational Simulations. Electron. J. Differential Equations Conference 10 (2003) 11-22
4. Ackleh A.S., and Deng K. On a first order hyperbolic coagulation model. Math. Meth. Appl. Sci. 26 (2003) 703-715
5. Adimy M., and Pujo-Menjouet L. A mathematical model describing cellular division with a proliferating phase duration depending on the maturity of cells. Electron. J. Differential Equations 2003 (2003) 1-14
6. H.T. Banks, V.A. Bokil, S. Hu, F.C.T. Allnutt, R. Bullis, A.K. Dhar, C.L. Browdy, Shrimp biomass and viral infection for production of biological countermeasures, CRSC-TR05-45, NCSU, December, 2005; Math. Biosci. and Eng., to appear.
7. 1-approximation for size-structured population models. Semigroup Forum 38 (1989) 141-155
8. H.T. Banks, F. Kappel, C. Wang, Weak solutions and differentiability for size-structured population models, in: Control and Estimation of Distributed Parameter Systems International Series of Numerical Mathematics, vol. 100, 1991, pp. 35-50.
9. H.T. Banks, F. Kappel, C. Wang, A semigroup formulation of a nonlinear size-structured distributed rate population model, in: Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomenon, International Series of Numerical Mathematics, vol. 118, 1994, pp. 1-18.
10. J. Dyson, R. Villella-Bressan, G.F. Webb, An age and maturity structured model of cell population dynamics, in: M. Horn, G. Simonnett, G.F. Webb (Eds.), Mathematical Models in Medical and Health Sciences, Innov. Appl. Math. Vanderbilt University Press, Nashville, TN, 1998, pp. 99-116.
11. Dyson J., Villella-Bressan R., and Webb G.F. A nonlinear age and maturity structured model of population dynamics I. Basic theory. J. Math. Anal. Appl. 242 (2000) 93-104
12. Gyllenberg M., and Webb G.F. Age-size structure in populations with quiescence. Math. Biol. 86 (1987) 67-95
13. Hoppensteadt F. An age dependent epidemic model. J. Franklin Inst. 297 (1974) 325-333
14. Howard K.E. A size and maturity structured model of cell dwarfism exhibiting chaotic behavior. Internat. J. Bifur. Chaos Appl. Sci. Eng. 13 (2003) 3001-3013
15. Schenzle D. An age structured model for pre and post-vaccination measles transmission. IMA J. Math. Appl. Med. Biol. 1 (1984) 169-191
16. Sinestrari E., and Webb G.F. Nonlinear hyperbolic systems with nonlocal boundary conditions. J. Math. Anal. Appl. 121 (1987) 449-464
17. Sinko J.W., and Streifer W. A new model for age-size structure of a population. Ecology 48 (1967) 910-918
18. P. Waltman, Deterministic threshold models in the theory of epidemics, Lecture Notes in Biomathematics, Springer, Berlin, 1974.