Core recruitment effects in SIS models with constant total populations

Mathematical Biosciences

Volumn 160, Issue 2, 1999, Pages 109-158

  Kribs Zaleta, Christopher M ^a  

^a UNIVERSITY OF TEXAS AT ARLINGTON   (United States)

Author keywords

Core; Heterosexual transmission; Internal demographics; Limit cycle; Recruitment; SIS model

Indexed keywords

ARTICLE; HETEROSEXUALITY; MATHEMATICAL MODEL; POPULATION DYNAMICS; PREDICTION; SEXUAL TRANSMISSION; SEXUALLY TRANSMITTED DISEASE;

FEMALE; HETEROSEXUALITY; HUMANS; MALE; MODELS, BIOLOGICAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; PLASMA; PREVALENCE; RISK FACTORS; SEXUAL BEHAVIOR; SEXUALLY TRANSMITTED DISEASES;

EID: 0032783870     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0025-5564(99)00031-0     Document Type: Article

References (24)

1. H.W. Hethcote, J.A. Yorke, Gonorrhea Transmission Dynamics and Control, Lecture Notes in Biomathematics 56, Springer, New York, 1984.
2. W. Huang, K.L. Cooke, C. Castillo-Chavez, Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission, SIAM J. Appl. Math. 52 (1992) 835.
3. F. Brauer, S.P. Blythe, C. Castillo-Chavez, Demographic recruitment in sexually transmitted disease models, in: M. Witten (Ed.), Computational Medicine, Public Health and Biotechnology: Building a Man in the Machine, World Scientific, Singapore, 1995, p. 1438.
4. K.P. Hadeler, C. Castillo-Chavez, A core group model for disease transmission, Math. Biosci. 128 (1995) 41.
5. H.R. Thieme, C. Castillo-Chavez, How may infection-age-dependent infectivity affect the dynamics of HIV/AIDS?, SIAM J. Appl. Math. 53 (1993) 1447.
6. K.R. Heiderich, W. Huang, C. Castillo-Chavez, Nonlocal response in a simple epidemiological model, Mathematical Sciences Institute Technical Report 94-29, Cornell University, Ithaca, NY, 1994.
7. S.P. Blythe, F. Brauer, C. Castillo-Chavez, J.X. Velasco-Hernández, Models for sexually transmitted diseases with recruitment, in: O. Arino, D. Axelrod, M. Kimmel, M. Langlais (Eds.), Mathematical population dynamics: Analyses of heterogeneity, Wuerz Publishing, Winnipeg, Canada, 1995, p. 197.
8. F. Brauer, C. Castillo-Chavez, J.X. Velasco-Hernández, Recruitment effects in heterosexually transmitted disease models, Int. J. Appl. Sci. Comput. 3 (1996) 78.
9. F. Brauer, C. Castillo-Chavez, J.X. Velasco-Hernández, Recruitment into a core group and its effect on the spread of a sexually-transmitted disease, Biometrics Unit Technical Report BU-1320-M, Cornell University, Ithaca, NY, 1996.
10. J.X. Velasco-Hernández, F. Brauer, C. Castillo-Chavez, Effects of treatment and prevalence-dependent recruitment on the dynamics of a fatal disease, IMA J. Math. Appl. Med. Biol. 13 (1996) 175.
11. K.P. Hadeler, P. van den Driessche, Backward bifurcation in epidemic control, Math. Biosci. 146 (1997) 15.
12. C. Castillo-Chavez, W. Huang, J. Li, On the existence of stable pairing distributions, J. Math. Biol. 34 (1996) 413.
13. S.F. Hsu Schmitz, Some theories, estimation methods and applications of marriage functions and two-sex mixing functions in demography and epidemiology, Doctoral Dissertation, Cornell University, Ithaca, NY, 1994.
14. K. Dietz, K.P. Hadeler, Epidemiological models for sexually transmitted diseases, J. Math. Biol. 26 (1988) 1.
15. R. Waldstätter, Pair formation in sexually transmitted diseases, in: C. Castillo-Chavez (Ed.), Mathematical and Statistical Approaches to AIDS epidemiology, Lecture Notes in Biomathematics 83, Springer, New York, 1989, p. 260.
16. C. Castillo-Chavez, W. Huang, J. Li, The effects of females' susceptibility on the coexistence of multiple pathogen strains of sexually transmitted diseases, J. Math. Biol. 35 (1997) 503.
17. C.M. Kribs-Zaleta, Structured models for heterosexual disease transmission, Math. Biosci. 160 (1990) 83.
18. C.M. Kribs-Zaleta, Toward quantifying the spectrum of recovery functions, Dyn. Contin. Discrete Impuls. Syst., in press.
19. C. Castillo-Chavez, K.L. Cooke, W. Huang, J. Li, On the role of long incubation periods in the dynamics of AIDS. Part II: Multiple-group models, in: C. Castillo-Chavez (Ed.), Mathematical and statistical approaches to AIDS epidemiology, Lecture Notes in Biomathematics 83, Springer, New York, 1989, p. 200.
20. F. Brauer, A class of Volterra integral equations arising in delayed-recruitment population models, Natural Resource Modeling 2 (1987) 259.
21. S.P. Blythe, C. Castillo-Chavez, The one-sex mixing problem: a choice of solutions? Cornell University Biometrics Unit Technical Report BU-1075-M, Cornell University, Ithaca, NY, 1990.
22. R.K. Miller, Nonlinear Volterra Integral Equations, Benjamin, New York, 1971.
23. C.M. Kribs, Core recruitment effects in modeling a sexually transmitted disease, Doctoral Dissertation, University of Wisconsin, Madison, WI, 1997.
24. J. Dushoff, W. Huang, C. Castillo-Chavez, Backwards bifurcations and catastrophe in simple models of fatal diseases, J. Math. Biol. 36 (1998) 227.