Optimal vaccination strategies - For whom?

Mathematical Biosciences

Volumn 139, Issue 2, 1997, Pages 133-154

  Müller, Johannes ^a  

^a UNIVERSITY OF TÜBINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; INFECTION PREVENTION; MATHEMATICAL ANALYSIS; STATISTICAL ANALYSIS; THEORY; VACCINATION;

COMMUNICABLE DISEASE CONTROL; EPIDEMIOLOGIC METHODS; HUMANS; IMMUNIZATION PROGRAMS; MATHEMATICS; MODELS, STATISTICAL; PROBABILITY; VACCINATION;

EID: 0031568283     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0025-5564(96)00140-X     Document Type: Article

References (20)

1. 1 D. Greenhalgh, Some results on optimal control applied to epidemics. Math. Biosci. 88:125-158 (1988).
2. 2 K. H. Wickwire, Mathematical models for the control of pests and infectious diseases: a survey. Theor. Popul. Biol. 11:128-238 (1977).
3. 3 K. P. Hadeler and J. Müller, Vaccination in age-structured populations II: optimal vaccination strategies. In Models for Infectious Human Diseases: Their Structure and Relation to Data, V. Isham and G. Medley, Eds., Cambridge Univ. Press, 1996, pp. 90-101.
4. 4 H. W. Hethcote and J. W. van Ark, Epidemiological models for heterogeneous populations: proportional mixing, parameter estimation, and immunization programs. Math. Biosci. 84:85-118 (1987).
5. 5 J. Müller, Optimal vaccination patterns in age structured populations. Dissertation, Fakultät für Mathematik, Tübingen, Germany, 1994.
6. 6 K. Dietz, Heutige Impfstrategien. Internist 33:575-580 (1992).
7. 7 d'Alembert, Opuscules Mathématique, Vol. 2. Paris, 1761.
8. 8 P. M. Fine and J. A. Clarkson, Individual versus public priorities in the determination of optimal vaccination policies. Am. J. Epidemiol. 124:1012-1020 (1986).
9. 9 H. W. Hethcote, A thousand and one epidemic models. Lect. Notes Biomath. 100:504-515 (1994).
10. 10 S. N. Busenberg and K. P. Hadeler, Demography and epidemics. Math. Biosci. 101:63-74 (1990).
11. 11 D. Greenhalgh, Vaccination in density-dependent epidemic models. Bull. Math. Biol. 54:733-758 (1992).
12. 12 K. P. Hadeler and J. Müller, Vaccination in age-structured populations I: the reproduction number. In Models for Infectious Human Diseases: Their Structure and Relation to Data, V. Isham and G. Medley, Eds., Cambridge Univ. Press, 1996, pp. 102-114.
13. 13 K. P. Hadeler and J. Müller, The effect of vaccination on sexually transmitted disease in heterosexual population. In Proc. Third Int. Conf. on Mathematical Population Dynamics, Pau (France), O. Arino, D. Axelrod, and M. Kimmel, Eds., Wuert Publishing Ltd., Winnipeg, 1993, pp. 251-278.
14. 14 A. Pugliese, Population models for disease with no recovery. J. Math. Biol. 28:65-82 (1990).
15. 15 V. Capasso and G. Serio, A generalization of the Kermack-McKendrick deterministic epidemic model. Math. Biosci. 42:43-61 (1978).
16. 16 W. R. Derrick and P. van den Driessche, A disease transmission model in a nonconstant population. J. Math. Biol. 31:495-512 (1993).
17. 17 H. W. Hethcote and P. van den Driessche, Some epidemiological models with nonlinear incidence. J. Math. Biol. 29:271-287 (1991).
18. 18 W. M. Liu, S. A. Levin, and Y. Iwasa, Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models. J. Math. Biol. 23:187-204 (1986).
19. 19 B. Schönfisch, Cellular automata and differential equation models for epidemics. Preprint (1997).
20. 20 J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer-Verlag, 1983.