Bounds on endemic disease levels, risks and basic reproductive numbers in heterogenous models for HIV/AIDS amongst injecting drug users

Journal of Biological Systems

Volumn 5, Issue 2, 1997, Pages 151-180

  Greenhalgh, David ^a  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Basic reproductive number; Heterogeneity; HIV AIDS; Intravenous drug use; Simulation

Indexed keywords

HUMAN IMMUNODEFICIENCY VIRUS;

EID: 0000237402     PISSN: 02183390     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218339097000126     Document Type: Article

References (21)

1. Allard R., A mathematical model to describe the risk of infection from sharing injection equipment, J. AIDS 3 (1990) pp. 1010-1016.
2. Blower S. M., Hartel D., Dowlatabi H., Anderson R. M. and May, R. M., Drugs, sex and HIV: a mathematical model for New York City, Phil. Trans. Roy. Soc. Lond. Series B 321 (1991) pp. 171-187.
3. Caulkins J. P. and Kaplan E. H., AIDS impact on the number of intravenous drug users, Interfaces 21 (1991) pp. 50-63.
4. o in models for infectious disease in heterogenous populations. J. Math. Biol. 28 (1990) pp. 365-382.
5. Goldberg D. J., Frischer M., Hay G., Green S. T., Taylor A. and McKeganey N., Probability of HIV transmission amongst injecting drug-users in Glasgow. Unpublished manuscript (1996).
6. Greenhalgh D., Effects of heterogeneity on the spread of HIV/AIDS amongst injecting drug users in shooting galleries, Math. Biosci. 136 (1996) pp. 141-186.
7. Kaplan E. H., Needles that kill: Modeling human immunodeficiency virus transmission via shared drug injection equipment in shooting galleries, Reviews of Infectious Diseases, 11 (1989) pp. 289-298.
8. Kaplan, E. H., Probability models of needle exchange, Operations Research 43 (1995) pp. 558-569.
9. Kaplan, E. H. and Heimer R., A circulation theory of needle exchange, AIDS 8 (1994) pp. 567-574.
10. Kaplan E. H. and O'Keefe E., Let the needles do the talking! Evaluating the New Haven needle exchange, Interfaces 23 (1993) pp. 7-26.
11. Longini I. M., Clark W. S., Byers R. H., Ward J. W., Darrow W. W., Lemp G. F. and Hethcote H. W., Statistical analysis of the stages of HIV infection using a Markov model, Statistics in Medicine 8 (1989) pp. 831-843.
12. Nold A., Heterogeneity in disease transmission modelling, Math. Biosci. 52 (1980) pp. 227-240.
13. Peterson D., Willard K., Altmann M., Gatewood L. and Davidson G., Monte-Carlo Simulation of HIV infection in an intravenous drug user community, J. AIDS 3 (1990) pp. 1086-1095.
14. Power R., Hartnoll R. and Davidaud E., Drug injecting, AIDS and risk behaviour: potential for change and intervention strategies, Br. J. Addiction 83 (1988) p. 649.
15. Schaefer H. H., Some spectral properties of positive linear operators, Pacific J. Math. 10 (1960) pp. 1009-1019.
16. Schaefer H. H., Banach Lattices and Positive Operators (Springer-Verlag, 1974).
17. Sheehan M., Oppenheimer E. and Taylor C., Who comes for treatment: drug misusers at three London agencies, Br. J. Addiction 82 (1988) pp. 311-320.
18. Siegel J. E., Weinstein M. C. and Fienberg H. V., Bleach programs for preventing AIDS amongst IV drug users: Modelling the impact of HIV prevalence, Amer. J. Public Health 81 (1991) pp. 1273-1279.
19. Stimson G. V., Alldritt L. J., Dolan K. A., Donoghoe M. C. and Lart R. A., Injecting equipment exchange schemes: final report. Monitoring Research Group, Sociology Dept., Goldsmith's College, New Cross, London, England, 1988.
20. Varga R. S., Matrix Iterative Analysis (Prentice-Hall, New Jersey, 1962).
21. Wolk J., Wodak A., Morlet A., Guinan J. J. and Gold J., HIV-related risk-taking behaviour, knowledge and serostatus of intravenous drug users in Sydney, Med. J. Australia 152 (1990) pp. 453-458.