Structured models for heterosexual disease transmission

Mathematical Biosciences

Volumn 160, Issue 1, 1999, Pages 83-108

  Kribs Zaleta, C M ^a  

^a UNIVERSITY OF TEXAS AT ARLINGTON   (United States)

Author keywords

Core; Generalized recovery function; Heterosexual transmission; Internal demographics; Recruitment; SIS model

Indexed keywords

ACQUIRED IMMUNE DEFICIENCY SYNDROME; ARTICLE; DEMOGRAPHY; DISEASE TRANSMISSION; ENDEMIC DISEASE; HETEROSEXUALITY; MATHEMATICAL MODEL; SEXUALLY TRANSMITTED DISEASE;

FEMALE; HETEROSEXUALITY; HUMANS; MALE; MODELS, BIOLOGICAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; SEXUALLY TRANSMITTED DISEASES;

EID: 0032838997     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0025-5564(99)00026-7     Document Type: Article

References (30)

1. H.W. Hethcote, J.A. Yorke, Gonorrhea Transmission Dynamics and Control, Lecture Notes in Biomathematics 56, Springer, New York, 1984.
2. C. Castillo-Chavez, S. Busenberg, On the solution of the two-sex mixing problem, in: S. Busenberg, M. Martelli (Eds.), Proceedings on Differential Equations Models in Biology, Epidemiology and Ecology, Claremont, 1990, Lecture Notes in Biomathematics 92, Springer, New York, 1991, pp. 80-98.
3. C. Castillo-Chavez, S. Busenberg, On the solution of the two-sex mixing problem, in: S. Busenberg, M. Martelli (Eds.), Proceedings on Differential Equations Models in Biology, Epidemiology and Ecology, Claremont, 1990, Lecture Notes in Biomathematics 92, Springer, New York, 1991, pp. 80-98.
4. Busenberg S., Castillo-Chavez C. A general solution of the problem of mixing 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.
5. S.P. Blythe, C. Castillo-Chavez, The one-sex mixing problem: a choice of solutions?, Biometrics Unit Technical Report BU-1075-M, Cornell University, Ithaca, NY, 1990.
6. Castillo-Chavez C., Huang W., Li J. On the existence of stable pairing distributions. J. Math. Biol. 34:1996;413.
7. 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.
8. Dietz K., Hadeler K.P. Epidemiological models for sexually transmitted diseases. J. Math. Biol. 26:1988;1.
9. 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.
10. F. Brauer, Epidemic models in populations of varying size, in: C. Castillo-Chavez, S.A. Levin, C.A. Shoemaker (Eds.), Proceedings on Mathematical Approaches to Problems in Resource Management and Epidemiology, Ithaca, 1987, Lecture Notes in Biomathematics 81, Springer, New York, 1989, p. 109.
11. F. Brauer, Epidemic models in populations of varying size, in: C. Castillo-Chavez, S.A. Levin, C.A. Shoemaker (Eds.), Proceedings on Mathematical Approaches to Problems in Resource Management and Epidemiology, Ithaca, 1987, Lecture Notes in Biomathematics 81, Springer, New York, 1989, p. 109.
12. Brauer F., Castillo-Chavez C., Velasco-Hernández J.X. Recruitment effects in heterosexually transmitted disease models. Int. J. Appl. Sci. Comput. 3:1996;78.
13. Hadeler K.P., Castillo-Chavez C. A core group model for disease transmission. Math. Biosci. 128:1995;41.
14. Huang W., Cooke K.L., Castillo-Chavez C. Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission. SIAM J. Appl. Math. 52:1992;835.
15. 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, Winnipeg, Canada, 1995, p. 197.
16. 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.
17. 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.
18. Velasco-Hernández J.X., Brauer F., Castillo-Chavez C. Effects of treatment and prevalence-dependent recruitment on the dynamics of a fatal disease. IMA J. Math. Appl. Med. Biol. 13:1996;175.
19. Hethcote H.W., Stech H.W., van den Driessche P. Stability analysis for models of diseases without immunity. J. Math. Biol. 13:1981;185.
20. C.M. Kribs-Zaleta, Toward quantifying the spectrum of recovery functions, Dynamics of Continuous, Discrete and Impulsive Systems, in press.
21. Brownlee J. The mathematical theory of random migration and epidemic distribution. Proc. R. Soc. Edinburgh. 3:1907;262.
22. A.G. McKendrick, On certain mathematical aspects of malaria, in: Proc. Imp. Malaria Committee, Bombay, 1912, pp. 54-66.
23. R. Ross, The Prevention of Malaria, 2nd ed., with an addendum on the theory of happenings, John Murray, London, 1911.
24. H.W. Hethcote. A thousand and one epidemic models, in: S.A. Levin (Ed.), Frontiers in Mathematical Biology, Lecture Notes in Biomathematics 100, Springer, New York, 1995, p. 504.
25. R.K. Miller, Nonlinear Volterra Integral Equations, Benjamin, New York, 1971.
26. Lajmanovich A., Yorke J.A. A deterministic model for gonorrhea in a nonhomogeneous population. Math. Biosci. 28:1976;221.
27. G.F. Webb, Theory of Nonlinear Age-Dependent Population Dynamics, Marcel Dekker, New York, 1985.
28. Brauer F., Ma Z. Stability of stage-structured population models. J. Math. Anal. Appl. 126:1987;301.
29. Brauer F. A class of Volterra integral equations arising in delayed-recruitment population models. Natural Resource Modeling. 2:1987;259.
30. C.M. Kribs-Zaleta, Core recruitment effects in SIS models with constant total populations, Math. Biosci 160 (1999) in press.