Global behaviour in age structured S.I.S. models with seasonal periodicities and vertical transmission

Journal of Mathematical Analysis and Applications

Volumn 213, Issue 2, 1997, Pages 511-533

  Langlais, Michel ^a   Busenberg, Stavros ^b  

^a UNIVERSITÉ BORDEAUX 1   (France)

^b HARVEY MUDD COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; DISEASES; EPIDEMIOLOGY; THEOREM PROVING;

DEMOGRAPHIC PARAMETERS; EPIDEMIC PARAMETERS; VERTICAL TRANSMISSION;

MATHEMATICAL MODELS;

EID: 0031572067     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1997.5554     Document Type: Article

References (22)

1. 1. J. Aron and I. Schwartz, Seasonality and period-doubling bifurcations in an epidemic model, J. Theoret. Biol. 110 (1984), 665-679.
2. 2. S. Busenberg and K. Cooke, Periodic solutions of a periodic non-linear delay differential equation, SIAM J. Appl. Math. 35 (1978), 704-721.
3. 3. S. Busenberg and K. Cooke, Vertically transmitted diseases, models and dynamics, in "Biomathematics," Vol. 23, Springer-Verlag, New York/Berlin, 1993.
4. 4. S. Busenberg, K. Cooke, and M. Iannelli, Endemic thresholds and stability in a class of age-structured epidemics, SIAM J. Appl. Math. 48 (1988), 1379-1395.
5. 5. S. Busenberg, and M. Iannelli, Separable models in age-dependent population dynamics, J. Math. Biol. 22 (1985), 145-173.
6. 6. S. Busenberg, M. Iannelli, and H. Thieme, Global behavior of an age-structured SIS model, SIAM J. Math. Anal. 22 (1991), 1065-1080.
7. 7. S. Busenberg, M. Iannelli, and H. Thieme, Dynamics of an age structured epidemic model, in, "Dynamical Systems" (S.-T. Liao, Y.-Q. Ye, and T.-R. Ding, Eds.), pp. 1-19, World Scientific, Singapore, 1993.
8. 8. S. Busenberg and M. Langlais, Global behaviour in age structured SIS models with seasonal periodicities, in "Differential Equations and Applications to Biology and to Industry," pp. 281-288, World Scientific, Singapore, 1996.
9. 9. K. Dietz, The incidence of infections diseases under the influence of seasonal variations, in "Lecture Notes in Biomathematics," Vol. 11, Springer-Verlag, Berlin/Heidelberg/New York, 1976.
10. 10. Z. Grossman, Oscillatory phenomena in a model of infections diseases, Theoret. Population Biol. 18 (1980), 204-243.
11. 11. M. E. Gurtin, A system of equations for age dependent population diffusion, J. Theoret. Biol. 40 (1973), 389-392.
12. 12. M. Iannelli, F. Milner, and A. Pugliese, Analytical and numerical results for the age-structured SIS epidemic model with mixed intra-intercohort transmission, SIAM J. Math. Anal. 23 (1992), 662-688.
13. 13. M. A. Krasnosel'skii, "Positive Solutions of Operator Equations," Noordhoff, Groningen, 1964.
14. 14. M. Kubo and M. Langlais, Periodic solutions for a population dynamics problem with age dependence and spatial structure, J. Math. Biol. 29 (1991), 363-378.
15. 15. K. Kunish, W. Schappacher, and G. F. Webb, Non linear age dependent population dynamics with random diffusion, Comput. Math. Appl. 11 (1985), 155-173.
16. 16. M. Langlais, A non linear problem in age dependent population diffusion, J. Math. Biol. 26 (1988), 319-346.
17. 17. M. Langlais, Large time behavior in a non-linear age-dependent population dynamics problem with diffusion, SIAM J. Math. Anal. 16 (1985), 510-529.
18. 18. M. Langlais, A mathematical analysis of the SIS intra-cohort model with age-structured, in "Mathematical Population Dynamics," Vol. 1, pp. 103-117, Wuerz Publishing Ltd., Winnipeg, Canada, 1995.
19. 19. H. Smith, Subharmonics bifurcation in an S-I-R epidemic model, J. Math. Biol. 17 (1983), 163-177.
20. 20. H. Smith, Multiple subharmonics for a periodic epidemic model, J. Math. Biol. 17 (1983), 179-190.
21. 21. K. E. Swick, Periodic solutions of a non-linear age-dependent model of a single species population dynamics, SIAM J. Math. Anal. 11 (1980), 901-910.
22. 22. G. Webb, Theory of non-linear age-dependent population dynamics, in "Pure and Applied Mathematics," Vol. 89, Dekker, New York, 1985.