Continuous-time age-structured models in population dynamics and epidemiology

Lecture Notes in Mathematics

Volumn 1945, Issue , 2008, Pages 205-227

  Li, Jia ^a   Brauer, Fred ^b  

^a University of Alabama in Huntsville ^*  (United States)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 42249113631     PISSN: 00758434     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-78911-6_9     Document Type: Article

References (43)

1. R. M. Anderson and R. M. May, Infectious Diseases of Humans, Dynamics and Control, Oxford University Press, Oxford, 1991.
2. S. P. Blythe and C. Castillo-Chavez, Like-with-like preference and sexual mixing models, Math. Biosci., 96 (1989), 221-238.
3. S. P. Blythe, C. Castillo-Chavez, J. S. Palmer and M. Cheng, Toward a unified theory of sexual mixing and pair formation, Math. Biosci., 107 (1991), 379-405.
4. F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer, Berlin Heidelberg New York, 2001.
5. S. Busenberg and C. Castillo-Chavez, Interaction, pair formation and force of infection terms in sexually transmitted diseases, in: C. Castillo-Chavez, (ed.), Mathematical and Statistical Approaches to AIDS Epidemiology, Lecture Notes in Biomathematics, Vol. 83, Springer, Berlin Heidelberg New York, (1989), 289-300.
6. S. Busenberg and C. Castillo-Chavez, A general solution of the problem of mixing of subpopulations and its application to risk- and age-structured epidemic models for the spread of AIDS, IMA J. Math. Appl. Med. Biol., 8 (1991), 1-29.
7. C. Castillo-Chavez and S. P. Blythe, Mixing Framework for Social/Sexual Behavior, in: C. Castillo-Chavez, (ed.), Mathematical and Statistical Approaches to AIDS Epidemiology, Lecture Notes in Biomathematics, Vol. 83, Springer, Berlin Heidelberg New York, (1989), 275-288.
8. R. F. Costantino and R. A. Desharnais, Population Dynamics and the 'Tribolium' Model: Genetics and Demography, Mono. Theor. Appl. Gen., 3 (1991), Springer, Berlin Heidelberg New York.
9. J. M. Cushing, Existence and stability of equilibria in age-structured population dynamics, J. Math. Biol., 20 (1984), 259-276.
10. J.M. Cushing, Equilibria in structured populations, J. Math. Biol., 23 (1985), 15-39.
11. J. M. Cushing, An Introduction to Structured Population Dynamics, SIAM, Philadelphia, 1998.
12. J. M. Cushing and Jia Li, Juvenile versus adult competition, J. Math. Biol., 29 (1991), 457-473.
13. O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and computation of the basic reproduction ratio Ao in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382.
14. O. Diekmann, K. Dietz and J.A.P. Heesterbeek, The basic reproduction ratio for sexually transmitted diseases, Part 1: Theoretical considerations, Math. Biosci., 107 (1991), 325-339.
15. O. Diekmann and J. A. P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases, Wiley, New York, 2000.
16. W. S. Gurney and R. M. Nisbet, Ecological Dynamics, Oxford University Press, Oxford, 1998.
17. M. E. Gurtin and R. C. MacCamy, Non-linear age-dependent population dynamics, Archive for Rational Mechanics and Analysis, 54 (1985), 281-300.
18. K. P. Hadeler, R. Waldstatter and A. Worz-Busekros, Models for pair-formation in bisexual populations, J. Math. Biol., 26 (1988), 635-649.
19. K. P. Hadeler and J. Müller, Vaccination in age structured populations I: The reproductive number, in: V. Isham and G. Medley, (eds.), Models for Infectious Human Diseases: Their Structure and Relation to Data, Cambridge University Press, Combridge, (1995), 90-101.
20. A. Hastings, Age-dependent predation is not a simple process, I. Continuous models, Theor. Popul. Biol., 23 (1983), 347-362.
21. J. A. P. Heesterbeek, Ao, Thesis, Centre for Mathematics and Computer Science, Amsterdam, (1991).
22. H. W. Hethcote, An age-structured model for pertussis transmission, Math. Biosci., 145 (1997), 89-136.
23. H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev, 42 (2000), 599-653.
24. J. M. Hyman, Jia Li and E. A. Stanley, Threshold conditions for the spread of the HIV infection in age-structured populations of homosexual men, J. Theor. Biol., 166 (1994), 9-31.
25. J. M. Hyman and Jia Li, An intuitive formulation for the reproductive number for the spread of diseases in heterogeneous populations, Math. Biosci., 167 (2000), 65-86.
26. M. Iannelli, Mathematical Theory of Age-Structured Population Dynamics, Appl. Math. Monogr. C.N.R., 7 (1995).
27. H. Inaba, Threshold and stability for an age-structured epidemic model, J. Math. Biol., 28 (1990), 411-434.
28. J. A. Jacquez, C. P. Simon, and J. Koopman, The reproductive number in deterministic models of contagious diseases, Comm. Theor. Biol., 2 (1991), 159-209.
29. K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Springer, Berlin Heidelberg New York, 1999.
30. T. Kostova and Jia Li, Oscillations and stability due to juvenile versus adult competition, Int. J. Comput. Math. Appl., 32 (1996), 57-70.
31. T. Kostova,, Jia Li and M. Friedman, Two models for competition between age classes, Math. Biosci., 157 (1999), 65-89.
32. Jia Li and T. G. Hallam, Survival in continuous structured population models, J. Math. Biol., 26 (1988), 421-433.
33. Jia Li, Threshold conditions in age-structured AIDS models with biased mixing, CNLS Newsletter, Los Alamos National Laboratory, 58 (1990), 1-10.
34. A. G. McKendrick, Applications of mathematics to medical problems, Proc. Edinb. Math. Soc. 44 (1926), 98-130.
35. R. M. Nisbet and L. Onyiah, Population dynamic consequences of competition within and between age classes. J. Math. Bio., 32 (1994), 329-344.
36. T.R. Park, Age-Dependence in Epidemic Models of Vector-Borne Infections, Ph.D. Dissertation, University of Alabama in Huntsville, 2004.
37. R. Ross, The Prevention of Malaria, Murray, London, 1909.
38. H. R. Thieme, Mathematics in Population Biology, Princeton University Press, Princeton, 2003.
39. W. O. Tschumy, Competition between juveniles and adults in age-structured populations, Theor. Popul. Biol., 21 (1982), 255-268.
40. D. W. Tudor, An age-dependent epidemic model with application to measles, Math. Biosci., 73 (1985), 131-147.
41. P. Waltman, Deterministic Threshold Models in the Theory of Epidemics, Lect. Notes Biomath., 1 (1974), Springer, Berlin Heidelberg New York.
42. G. F. Webb, Theory of Age Dependent Population Dynamics, Marcel Dekker, New York, 1985.
43. W. H. Wernsdorfer, The importance of malaria in the world, in: Kreier, J. P. (ed.), Malaria, Epidemology, Chemotherapy, Morphology, and Metabolism, Vol. 1, Academic, New York, 1980.