A model for an SI disease in an age - Structured population

Discrete and Continuous Dynamical Systems - Series B

Volumn 2, Issue 2, 2002, Pages 257-264

  Brauer, Fred ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Age structured populations; Epidemic models

Indexed keywords

EID: 0042762712     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2002.2.257     Document Type: Article

References (9)

1. S. Bochner, On the integral equations of renewal theory, Ann. Math. Stat. 12 (1941), 243-267.
2. F. Brauer, Infectious disease models with chronological age structure and epidemiological age structure, Mathematical Approaches for Emerging and Re-emerging Diseases, Part 2: Models, Methods, and Theory, (C. Castillo-Chavez, with S. Blower, D. Kirschner, P. van den Driessche, A.-A. Yakubu, eds.), Springer-Verlag 2001, 231-243.
3. S. Busenberg, K.L. Cooke, and M. Ianelli, Endemic thresholds and stability in a class of age-structured epidemics, SIAM J. Appl. Math. 48 (1988), 1379-1395.
4. S. Busenberg, M. Ianelli, and H.R. Thieme, Global behavior of an age-structured epidemic model, SIAM J. Math. Anal. 22 (1991), 1065-1080.
5. C. Castillo-Chavez and H.R. Thieme, Asymptotically autonomous epidemic models, Mathematical Population Dynamics: Analysis of Heterogeneity, I. Theory of Epidemics (O. Arino, D. Axebrod, M. Kimmel, M. Langlais, eds.), Wuerz, Winnipeg (1995), 33-50., Wuerz 1995, 33-50.
6. K. Dietz, Transmission and control of arbovirus disease, Epidemiology (D. Ludwig and K.L. Cooke, eds.), SIAM 1975, 104-121.
7. J.J. Levin and D.F. Shea, On the asymptotic behaviour of the bounded solutions of some integral equations, I, II, III, J. Math. Anal. and Appl. 37 (1972), 42-82, 288-326, 537-575.
8. S.O. Londen, On the asymptotic behavior of the bounded solutions of a nonlinear Volterra equation, SIAM J. Math. Anal. 5 (1974), 849-875.
9. J.A. Nohel, Some problems in nonlinear Volterra equations, Bull. Amer. Math. Soc. 68 (1962), 323-329.