Competitive exclusion in gonorrhea models and other sexually transmitted diseases

SIAM Journal on Applied Mathematics

Volumn 56, Issue 2, 1996, Pages 494-508

  Castillo Chavez, Carlos ^a   Huang, Wenzhang ^a   Li, Jia ^b  

^a Department of Obstetrics Gynecology   (United States)

^b UNIVERSITY OF ALABAMA IN HUNTSVILLE   (United States)

Author keywords

Coevolution; Coexistence; Dynamical systems; Sexually transmitted diseases

Indexed keywords

ASYMPTOTIC STABILITY; DIFFERENTIAL EQUATIONS; DISEASES; DYNAMICS; HEALTH RISKS;

COEVOLUTION; COEXISTENCE; GONORRHEA MODELS; PATHOGENS; SEXUALLY TRANSMITTED DISEASES; STRAIN VIRULENCE; TRANSMISSION DYNAMICS;

MATHEMATICAL MODELS;

EID: 0030128038     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S003613999325419X     Document Type: Article

References (38)

1. R. M. ANDERSON AND R. M. MAY (1982), Co-evolution of host and parasites, Parasitology, 85, pp. 411-426.
2. _ (1991), Infectious Diseases of Humans, Oxford Science Publications, Oxford, UK.
3. K. BECK (1984), Co-evolution. Mathematical aspects of host-parasite interactions, J. Math. Biol., 19, pp. 63-77.
4. H. J. BREMERMANN AND J. PICKERING (1983), A game-theoretical model of parasite virulence, J. Theoret. Biol., 100, pp. 411-426.
5. H. J. BREMERMANN AND H. R. THIEME (1989), A competitive exclusion principle for pathogen virulence, J. Math. Biol., 27, pp. 179-190.
6. S. BUSENBERG AND C. CASTILLO-CHAVEZ (1989), Interaction, pair formation, and force of infection terms in sexually transmitted diseases, Lecture Notes in Biomath. 19, Springer-Verlag, New York, pp. 63-77.
7. _ (1991), A general solution of the problem of mixing of subpopulations, and, its application to risk- and age-structured epidemic models, IMA J. Math. Appl. Med. Biol., 8, pp. 1-29.
8. G. J. BUTLER, S. B. HSU, AND P. WALTMAN (1983), Coexistence of competing predators in a chemostat, J. Math. Biol., 17, pp. 133-151.
9. C. CASTILLO-CHAVEZ, ED. (1989), Mathematical and Statistical Approaches to AIDS Epidemiology, Lecture Notes in Biomath. 83, Springer-Verlag, New York.
10. C. CASTILLO-CHAVEZ, H. W. HETHCOTE, V. ANDREASEN, S. A. LEVIN, AND W.-M. LIU (1988), Cross-immunity in the dynamics of homogeneous and heterogeneous populations, in Mathematical Ecology, T. G. Hallam, L. G. Gross, and S. A. Levin, eds., World Scientific Publishing Co., Singapore, pp. 303-316.
11. _ (1989), Epidemiological models with age structure, proportionate mixing, and cross-immunity, J. Math. Biol., 27, pp. 233-258.
12. C. CASTILLO-CHAVEZ, K. COOKE, W. HUANG, AND S. A. LEVIN (1989a), Results on the dynamics for models for the sexual transmission of the human immunodeficiency virus, Appl. Math. Lett., 2, pp. 327-331.
13. C. CASTILLO-CHAVEZ AND H. R. THIEME (1995), Asymptotically autonomous epidemic models, in Mathematical Population Dynamics: Analysis of Heterogeneity, O. Arino, D. E. Axelrod, and M. Kimmel, eds., pp. 33-50.
14. C. CASTILLO-CHAVEZ AND S. BUSENBERG (1990), On the solution of the two-sex mixing problem, in Proceedings of the International Conference on Differential Equations and Applications to Biology and Population Dynamics, Lecture Notes in Biomathematics 92, S. Busenberg and M. Martelli, eds., Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, Hong Kong, Barcelona, Budapest, pp. 80-98.
15. K. L. COOKE AND J. A. YORKE (1973), Some equations modelling growth processes and gonorrhea epidemics, Math. Biosci., 58, pp. 93-109.
16. 0 in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28, pp. 365-382.
17. K. DIETZ (1979), Epidemiologic interference of virus populations, J. Math. Biol., 8, pp. 291-300.
18. G. DWYER, S. A. LEVIN, AND L. BUTTEL (1990), A simulation model of the population dynamics and evolution of myxomatosis, Ecological Monographs, 60, pp. 423-447.
19. W. P. EWALD (1993), The evolution of virulence, Scientific American, April, pp. 86-93.
20. F. FENNER AND K. MYERS (1978), Myxoma virus and myxomatosis in retrospect: The first quarter century of a new disease, in Viruses and the Environment, J. I. Cooper and F. O. MacCallum, eds., Academic Press, London, pp. 539-570.
21. F. FENNER AND F. N. RATCLIFFE (1965), Myxomatosis, Cambridge University Press, Cambridge.
22. 0, Ph.D. thesis, CWI, Amsterdam, the Netherlands.
23. H. W. HETHCOTE AND J. A. YORKE (1984), Gonorrhea Transmission Dynamics and Control, Lecture Notes in Biomath. 56, Springer-Verlag, New York.
24. W. HUANG, K. COOKE, AND C. CASTILLO-CHAVEZ (1992), Stability and bifurcation for a multiple group model for the dynamics of HIV/AIDS transmission, SIAM J. Appl. Math., 52, pp. 835-854.
25. A. LAJMANOVICH AND J. A. YORKE (1976), A deterministic model for gonorrhea in a nonhomogeneous population, Math. Biosci., 28, pp. 221-236.
26. S. A. LEVIN (1970), Community equilibria and stability, and an extension of the competitive principle exclusion, Amer. Naturalist, 104, pp. 413-423.
27. _ (1983a), Co-evolution, in Population Biology, H. I. Freedman and C. Strobeck, eds., Lecture Notes in Biomath. 52, Springer-Verlag, New York.
28. _ (1983b), Some approaches to the modeling of co-evolutionary interactions, in Co-evolution, M. Nitecki, ed., University of Chicago Press, Chicago, IL.
29. S. A. LEVIN AND D. PIMENTEL (1981), Selection of intermediate rates increase in parasite-host systems, Amer. Naturalist, 117, pp. 308-315.
30. A. J. LOTKA (1923), Contributions to the analysis of malaria epidemiology, Amer. J. Hygiene, 3, Jan. Supplement.
31. R. M. MAY (1975), Stability and complexity in models ecosystems, Princeton University Press, Princeton, NJ.
32. R. M. MAY AND R. M. ANDERSON (1983), Epidemiology and genetics in the co-evolution of parasites and hosts, Philos. Trans. Royal Soc. London, B, 219, pp. 281-313.
33. J. MAYNARD SMITH (1974), Models in ecology, Cambridge University Press, Cambridge, UK.
34. R. ROSS (1911), The Prevention of Malaria, 2nd ed., with Addendum, John Murray, London.
35. H. L. SMITH (1988), Systems of ordinary differential equations which generate an order preserving flow. A survey of results, SIAM Rev., 30, pp. 87-113.
36. H. R. THIEME (1992), Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations, J. Math. Biol., 30, pp. 755-763.
37. H. R. THIEME AND C. CASTILLO-CHAVEZ (1989), On the role of variable infectivity in the dynamics of the human immunodeficiency virus, in Mathematical and Statistical Approaches to AIDS Epidemiology, C. Castillo-Chavez, ed., Lecture Notes in Biomath. 83, Springer-Verlag, New York, pp. 200-217.
38. _ (1993), How may infection-age dependent infectivity affect the dynamics of HIV/AIDS? SIAM J. Appl. Math., 53, pp. 1449-1479.