Hostname: page-component-cb9f654ff-p5m67 Total loading time: 0 Render date: 2025-08-30T13:06:38.127Z Has data issue: false hasContentIssue false
  • English
  • Français

Actuarial review of models for describing and predicting the spread of HIV infection and AIDS

Published online by Cambridge University Press:  20 April 2012

S. Haberman
Get access Rights & Permissions [Opens in a new window]

Abstract

The paper reviews the mathematical models of transmission of infection that have been put forward for representing the spread of HIV infection and AIDS. It describes and compares the main models that have been proposed and thereby provides some guidance on how such models might be constructed and utilised. There is also discussion of the importance of constructing such mathematical models of transmission of infection which further our understanding of the transmission dynamics of the epidemic and help to identify important epidemiological parameters and their likely influence on the epidemic's course.

Keywords

Mathematical modelsAIDSPrediction

Information

Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 117 , Issue 2 , September 1990 , pp. 319 - 405
Copyright
Copyright © Institute and Faculty of Actuaries 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Anderson, R. M. (1988). The epidemiology of HIV infection; variable incubation plus infectious periods and heterogeneity in sexual activity. J.R.S.S. Series A. 151, 66–93.Google Scholar
Anderson, R. M. & May, R. M. (1986). The invasion, persistence and spread of infectious diseases within animal and plant communities. Phil. Trans. Roy. Soc. B. 314, 533–570.Google ScholarPubMed
Anderson, R. M. & May, R. M. (1987). Plotting the spread of AIDS. New Scientist, 26 March 1987, 54-59.Google Scholar
Anderson, R. M. & May, R. M. (1988). Epidemiological parameters of HIV transmission. Nature, 333, 514–519.CrossRefGoogle ScholarPubMed
Anderson, R. M., May, R. M. & Mclean, A. R. (1988). Possible demographic consequences of AIDS in developing countries. Nature, 332, 228–234.CrossRefGoogle ScholarPubMed
Anderson, R. M., May, R. M., Medley, G. F. & Johnson, A. E. (1986). A preliminary study of the transmission dynamics of the Human Immunodeficiency Virus (HIV). the causative agent of AIDS. I.M.A.J. Math. Appl. Med. & Biol. 3, 229–263.CrossRefGoogle ScholarPubMed
Anderson, R. M., Medley, G. F., Blythe, S. P. & Johnson, A. E. (1987). Is it possible to predict the minimum size of the AIDS epidemic in the U.K.? Lancet, 1, 1073–1075.CrossRefGoogle Scholar
Anderson, R. M. & Medley, G. F. (1988). Epidemiology, HIV infection and AIDS: the incubation and infectious periods, survival and vertical transmission. AIDS, 2, S57–S63.CrossRefGoogle ScholarPubMed
Artzrouni, M. & Wykoff, R. (1988). ‘A two state infective age-structured model for the spread of AIDS in the U.S.A.’ Poster presentation at the IVth International Conference on AIDS, Stockholm. June 1988. Abstract 4695.Google Scholar
Bailey, N. T. J. (1975). The Mathematical Theory of Infectious Diseases. Griffin, London.Google Scholar
Bailey, N. T. J. (1988). Simplified modelling of the population dynamics of HIV/AIDS. J.R.S.S. Series A 151, 31–43.Google Scholar
BAILEY, N. T. J. & Estreicher, J. (1987). ‘Epidemic prediction and public health control. with special reference to influenza and AIDS.’ Proc. 1st World Congress of Bernoulli Society (Tashkent, September 1986).Google Scholar
Barrett, J. C. (1988). Monte Carlo simulation of the heterosexual spread of the human immunodeficiency virus. Journal of Medical Virology, 26, 99–109.CrossRefGoogle ScholarPubMed
Barton, D. E. (1987). Striking the balance on AIDS. Nature, 326, 734.CrossRefGoogle Scholar
Beale, S. (1987). On the sombre view of AIDS. Nature, 328, 673.CrossRefGoogle Scholar
Birkhead, B. G. (1987). ‘A mathematical model of the transmission of the HIV under diminishing recruitment—an exact solution.’ Department of Statistical Science, University College, London. Technical Note.Google Scholar
Blythe, S. P. & Anderson, R. M. (1988). Distributed incubation and infectious periods in models of the transmission dynamics of the human immunodeficiency virus (HIV). I.M.A.J. Math. Appl. Med. & Biol. 5, 1 19.Google ScholarPubMed
Blythe, S. P. & Anderson, R. M. (1988a). Variable infectiousness in HIV transmission models. I.M.A.J. Math. Appl. Med. & Biol. 5, 181–200.CrossRefGoogle ScholarPubMed
Blythe, S. P. & Anderson, R. M. (1988b). Heterogeneous sexual activity models of HIV transmission in male homosexual populations. I.M.A.J. Math. Appl. Med. & Biol. 5, 237–260.CrossRefGoogle ScholarPubMed
Boldsen, J. L., Jensen, J. L., Sogaard, J. & Sorensen, M. (1988). On the incubation time distribution and the Danish AIDS data. J.R.S.S. Series A, 151, 42–43.Google Scholar
Bongaarts, J. (1989). A model of the spread of HIV infection and the demographic impact of AIDS. Statistics in Medicine, 8, 103–120.CrossRefGoogle Scholar
Box, G. E. P. & Cox, D. R. (1964). An analysis of transformations. J.R.S.S. Series B, 26, 211–252.Google Scholar
Brodt, H. R., Helm, E. B., Werner, A. et al. , (1986). Spontanverlauf der LAV/HTLV-III Infektion. Deutsche Medizinische Wochenschrift, 111, 1175–1180.CrossRefGoogle Scholar
Brookmeyer, R. & Damiano, A. (1989). Statistical methods for short-term projections of AIDS incidence. Statistics in Medicine, 8, 23–34.CrossRefGoogle ScholarPubMed
Brookmeyer, R. & Gail, M. H. (1986). Minimum size of the AIDS epidemic in the United States. Lancet, 2, 1320–1322.CrossRefGoogle ScholarPubMed
Brookmeyer, R. & Gail, M. H. (1987). Methods for projecting the AIDS epidemic. Lancet, 2, 99.CrossRefGoogle ScholarPubMed
Brookmeyer, R. & Gail, M. H. (1987a). Biases in prevalent cohorts. Biometrics, 43, 739–749.CrossRefGoogle ScholarPubMed
Brookmeyer, R., Gail, M. H. & Polk, B. F. (1987). The prevalent cohort study and the acquired immunodeficiency syndrome. American Journal of Epidemiology, 126, 14–24.CrossRefGoogle ScholarPubMed
Brookmeyer, R. & Goedert, J. J. (1989). Censoring in an epidemic with an application to hemophilia-associated AIDS. Biometrics, 45, 325–335.CrossRefGoogle Scholar
Canadian Institute of Actuaries Task Force On Aids (1988). First report of the Subcommittee on Modelling. November 1988.Google Scholar
Canadian Institute of Actuaries Task Force On Aids (1988a). Second report of the Subcommittee on Modelling. An analysis of U.S.A. data. November 1988.Google Scholar
Centres For Disease Control (1986). Update: acquired immunodeficiency syndrome (AIDS)— United States. Morbidity and Mortality Weekly Reports, 32, 17–21.Google Scholar
Centres For Disease Control (1987). Human immunodeficiency virus infection in the United States: a review of current knowledge. Mortality and Morbidity Weekly Reports, 36, 1–48.Google Scholar
Chin, J. & Mann, J. (1989). Global surveillance and forecasting of AIDS. Bulletin of WHO, 67, 1–7.Google ScholarPubMed
Colgate, S. A., Stanley, E. A., Hyman, J. M. et al. (1989). A behaviour based model of the cubic growth of AIDS in the United States. Proc. Nat. Acad. Sci. U.S.A. 86, 4793–4797.CrossRefGoogle ScholarPubMed
Costagliola, D. & Downs, A. M. (1987). Incubation time for AIDS. Nature, 328, 582.CrossRefGoogle ScholarPubMed
Costagliola, D., Mary, J.-Y., Brouard, N. et al. (1989). Incubation Time for AIDS from French transfusion-associated cases. Nature, 338, 768–769.CrossRefGoogle ScholarPubMed
Cowell, M. J. & Hoskins, W. H. (1987). ‘AIDS, HIV mortality and life insurance.’ Society of Actuaries special report, August 1987 (also in report of the Society of Actuaries Task Force on AIDS).Google Scholar
Cox, D. R. & Medley, G. F. (1989). A process of events with notification delay and the forecasting of AIDS. Phil. Trans. Roy. Soc. B, 325, 135–145.Google ScholarPubMed
Cox, D. R. & Davison, A. C. (1989). Prediction for small subgroups. Phil. Trans. Roy. Soc. B, 325, 185–187.Google ScholarPubMed
Curran, J. W., Morgan, W. M., Hardy, A. M. et al. (1985). The epidemiology of AIDS: current status and future prospects. Science, 229, 1352–1357.CrossRefGoogle ScholarPubMed
Dahlman, G. E., Bergstrom, R. L. & Mathes, R. W. (1987). ‘Projecting extra AIDS mortality for individual ordinary life insurance in force as of December 31 1986.’ Milliman & Robertson Research Report (revised version in Report of Society of Actuaries Task Force on AIDS).Google Scholar
Dangerfield, B. & Roberts, C. (1990). A role for system dynamics in modelling the spread of AIDS. Trans. of Institute of Measurement and Control. (To appear.)Google Scholar
Day, N. E., Gore, S. M., McGee, M. A. & South, M. (1989). Predictions of the AIDS epidemic in the U.K.: The use of the back projection method. Phil. Trans. Roy. Soc. B, 325, 123–134.Google ScholarPubMed
Daykin, C. D., Clark, P. N. S., Eves, M. J., Haberman, S., Le Grys, D. J., Lockyer, J., Michaelson, R. W. & Wilkie, A. D. (1987). AIDS Bulletin No. 1. Institute of Actuaries AIDS Working Party.Google Scholar
Daykin, C. D., Clark, P. N. S., Eves, M. J., Haberman, S., Le Grys, D. J., Lockyer, J., Michaelson, R. W. & Wilkie, A. D. (1987a). AIDS Bulletin No. 2. Institute of Actuaries.Google Scholar
Daykin, C. D., Clark, P. N. S., Eves, M. J., Haberman, S., Le Grys, D. J., Lockyer, J., Michaelson, R. W. & Wilkie, A. D. (1987b). The implications of AIDS for life insurance companies (Supplement to AIDS Bulletin No. 2). Proceedings of a seminar on 1 February 1988. Institute of Actuaries.Google Scholar
Daykin, C. D., Clark, P. N. S., Eves, M. J., Haberman, S., Le Grys, D. J., Lockyer, J., Michaelson, R. W. & Wilkie, A. D. (1988). AIDS Bulletin No 3. Institute of Actuaries AIDS Working Party.Google Scholar
Daykin, C. D., Clark, P. N. S., Eves, M. J., Haberman, S., Le Grys, D. J., Lockyer, J., Michaelson, R. W. & Wilkie, A. D. (1988a). The Impact of HIV Infection and AIDS on Insurance in the United Kingdom. J.I.A. 115, 727–837.Google Scholar
Daykin, C. D., Clark, P. N. S., Eves, M. J., Haberman, S., Le Grys, D. J., Lockyer, J., Michaelson, R. W. & Wilkie, A. D. (1989). AIDS Bulletin No. 4. Institute of Actuaries.Google Scholar
Daykin, C. D. (1990). Epidemiology of HIV Infection and AIDS. J.I.A. 117, 51–94.Google Scholar
De Gruttola, V. & Mayer, K. H. (1988). Assessing and modelling heterosexual spread of the human immunodeficiency virus in the United States. Review of Infectious Diseases, 10, 138–150.CrossRefGoogle ScholarPubMed
De Gruttola, V. & Lagakos, S. W. (1989). The value of AIDS incidence data in assessing the spread of HIV infection. Statistics in Medicine, 8, 35–43.CrossRefGoogle ScholarPubMed
De Gruttola, V. & Lagakos, S. W. (1989a). Analysis of doubly-censored survival data, with application to AIDS. Biometrics, 45, 1–11.CrossRefGoogle ScholarPubMed
Department of Health/Welsh Office (1988). ‘Short-term prediction of HIV infection and AIDS in England and Wales.’ Report of a Working Group. HMSO. London.Google Scholar
Dietz, K. (1987). ‘Epidemiological models for sexually transmitted infections.’ Proc. 1st World Congress of Bernoulli Society (Tashkent, 1986).Google Scholar
Dietz, K. (1988). On the transmission dynamics of HIV. Mathematical Biosciences, 90, 397–414.CrossRefGoogle Scholar
Dietz, K. & Hadeler, K. P. (1988). Epidemiological models for sexually transmitted diseases. Journal of Math. Biology, 26, 1–25.CrossRefGoogle ScholarPubMed
Dietz, K. & Schenzle, D. (1985). Mathematical models for infectious disease statistics. In: A Celebration of Statistics, eds. Atkinson, A. C. & Fienberg, S. E., pp. 167–204. Springer, New York.CrossRefGoogle Scholar
Downs, A. M., Ancelle, R. & Brunet, J. B. (1987). AIDS in Europe: Current trends and short-term predictions estimated from surveillance data, January 1981-June 1986. AIDS, 1, 53–57.Google ScholarPubMed
Eisenberg, B. (1989). The number of partners and the probability of HIV infection. Statistics in Medicine, 8, 83–92.CrossRefGoogle ScholarPubMed
Farmer, R. D. T. & Emami, J. (1987). ‘The transmission of HIV and the evolution of the AIDS epidemic—sexual transmission model.’ (Unpublished.)Google Scholar
Fuhrer, C. (1988). ‘Projecting the number of AIDS Cases.’ Presented to the Society of Actuaries Symposium “Insurance and the AIDS Epidemic”. Chicago, Illinois. May, 1988.Google Scholar
Fuxman, Y. L. (1989). ‘Generating relations in the mathematical modelling of the AIDS epidemic.’ (Unpublished manuscript.)Google Scholar
Gail, M. H. & Brookmeyfr, R. (1988). Methods for projecting course of acquired immunodefi-ciency syndrome epidemic. J. Nat. Cancer Inst. 80, 900–911.CrossRefGoogle Scholar
Gail, M. H., Preston, D. & Piantadosi, S. (1989). Disease prevention models of voluntary confidential screening for human immunodeficiency syndrome. Statistics in Medicine, 8, 59–81.CrossRefGoogle Scholar
Gani, J. (1978). Some problems of epidemic theory. J.R.S.S. Series A, 140, 323–347.Google Scholar
General Accounting Office (1989). ‘AIDS forecasting: undercount of cases and lack of key data weaken existing estimates.‘ Report to Congress. GAO PEMD 89-13. Washington DC, U.S.A.Google Scholar
Gonzalez, J. J., Koch, M. G., Dorner, D., L'age-Stehr, J., Myrtveit, M. & Vavik, L. (1987). ‘The prognostic analysis of the AIDS epidemic: mathematical modelling and computer simulation.’ Proc. E.C. Workshop on Statistical Analysis and Mathematical Modelling of AIDS (Bilthoven, December 1986). Oxford University Press.Google Scholar
Gonzalez, J. J. & Koch, M. G. (1987). On the role of transients for the prognostic analysis of the AIDS epidemic. American Journal of Epidemiology, 126, 985–1005.CrossRefGoogle ScholarPubMed
Harris, J. E. (1987). ‘Delay in reporting acquired immune deficiency syndrome.’ M.I.T. Technical report No. 452, M.I.T.. Mass.. U.S.A.CrossRefGoogle Scholar
Harris, J. E. (1988). ‘The incubation period for human immunodeficiency virus (HIV)‘, in Kulstad, R. (ed.) AIDS 1988: AAAS Symposia Papers. AAAS, Washington DC.Google Scholar
Healy, M. J. R. (1988). ‘Extrapolation forecasting. Appendix 6. Short term prediction of HIV infection and AIDS in England and Wales.’ Report of a Working Group. HMSO, London.Google Scholar
Healy, M. J. R. & Tillett, H. E. (1988). Short-term extrapolation of the AIDS epidemic. J.R.S.S. Series A. 151, 50–65.Google Scholar
Hellinger, F. J. (1988). Forecasting the personal medical care costs of AIDS from 1988 through 1991. Public Health Reports, 103, 309–319.Google ScholarPubMed
Hethcote, H. W. & Yorke, J. A. (1984). Gonorrhoea: transmission dynamics and control. Lecture Notes in Biomathematics, 56, 1–105. Springer-Verlag, Berlin.Google Scholar
Hyman, J. M. & Stanley, E. A. (1988). Using mathematical models to understand the AIDS epidemic. Mathematical Biosciences, 90, 415–473.CrossRefGoogle Scholar
Isham, V. (1988). Mathematical modelling of the transmission dynamics of HIV infection and AIDS: A Review. J.R.S.S. Series A, 151, 5–30.Google Scholar
Isham, V. (1989). Estimation of the incidence of HIV infection. Phil. Trans. Roy. Soc. B, 325, 113–121.Google ScholarPubMed
Iversen, O.-J. & Engen, S. (1986). Epidemiology of AIDS-statistical analyses. J. Epidemiol, and Comm. Health, 41, 55–58.CrossRefGoogle Scholar
Jacouez, J. A., Simon, C. P., Koopmu, J., Sattenspiel, L. & Perry, T. (1988). Modelling and analysing transmission: the effect of contact patterns. Mathematical Biosciences, 92, 119–199.CrossRefGoogle Scholar
Kanouse, D. E., Cardell, N. S., Gorman, E. M. et al. (1988). ‘Modelling the spread of HIV infection in the United States.’ (Unpublished working draft.) Presented to the XVth General Assembly of the Geneva Association. The Hague. June 1988. The Rand Corporation.Google Scholar
Kalbfleisch, J. D. & Lawless, J. F. (1988). Estimating the incubation period for AIDS patients. Nature, 333, 504–505.CrossRefGoogle ScholarPubMed
Kermack, W. O. & Mckendrick, A. G. (1927). Contribution to the mathematical theory of epidemics. Proc. Roy. Soc. A, 115, 700–721.Google Scholar
Kiessling, D., Stannat, S., Schedel, I. & Deicher, H. (1986). überlegungen und Hochrechungen zur Epidemiologie des ‘Acquired Immunodeficiency Syndrome’ in der Bundesrepublik Deutsch-land. Infection, 14, 217–222.CrossRefGoogle Scholar
Knox, E. G. (1986). A transmission model for AIDS. European Journal of Epidemiology, 2, 165–177.CrossRefGoogle ScholarPubMed
Kolbye, J. (1987). ‘AIDS mortality and life insurance.’ Baltica-Nordisk Re.Google Scholar
Kremer, E. (1982). IBNR claims and the two-way model of ANOVA. Scandinavian Actuarial Journal, 47–55.CrossRefGoogle Scholar
Lagakos, S. W., Berraj, L. M. & De Gruttola, V. (1988). Nonparametric analysis of truncated survival data with application to AIDS. Biometrika, 75, 515–523.CrossRefGoogle Scholar
Lemp, G. F., Payne, S. F., Rutherford, G. W. et al. (1988). ‘Projections of AIDS morbidity and mortality in San Francisco using epidemic models.’ Poster presentation at the IVth International Conference on AIDS. Stockholm. June 1988. Abstract 4682.Google Scholar
Longini, I. M., Scott Clark, W., Byers, R. H. et al. (1989). Statistical analysis of the stages of HIV infection using a Mark model. Statistics in Mdicine, 8, 831–843.Google Scholar
Lorper, J. (1988). ‘Actuarial studies of the AIDS problems.’ Publications of the Cologne Re. 14.Google Scholar
Lorper, J. (1989). Projecting the spread of AIDS into the general population-application to life assurance. J.I.A., 116, 625–638.Google Scholar
Lui, K. J., Darrow, W. W. & Rutherford, G. W. III (1988). A model-based estimate of the mean incubation period for AIDS in homosexual men. Science, 240, 1333–1335.CrossRefGoogle ScholarPubMed
Lui, K. J., Lawrence, D. N., Morgan, W. M., Peterman, T. A., Haverkos, H. W. & Bregman, D. J. (1986). A model-based approach for estimating the mean incubation period of transfusion-associated acquired immunodeficiency syndrome. Proc. Nut. Acad. Sci. U.S.A. 83, 3051–3055.CrossRefGoogle ScholarPubMed
Lui, K. J., Peterman, T. A. & Lawrence, D. N. (1987). Comments on the sombre view of AIDS. Nature. 329, 207.CrossRefGoogle ScholarPubMed
May, R. M. & Anderson, R. M. (1987). Transmission dynamics of HIV Infection. Nature, 326, 137–142.CrossRefGoogle ScholarPubMed
Mcevoy, M. & Tillett, H. E. (1985). Some problems in the prediction of the future numbers of cases of the acquired immunodeficiency syndrome in the U.K. Lancet, 2, 541–542.CrossRefGoogle Scholar
Medley, G. F., Anderson, R. M., Cox, D. R. & Billard, L. (1987). Incubation period of AIDS in patients infected via blood transfusion. Nature, 328, 718–721.CrossRefGoogle ScholarPubMed
Medley, G. F., Billard, L., Cox, D. R. & Anderson, R. M. (1988). The distribution of the incubation period for the acquired immunodeficiency syndrome (AIDS). Proc. Roy. Soc. B, 233, 367–377.Google ScholarPubMed
Medley, G. F., Anderson, R. M., Cox, D. R. & Billard, L. (1988a). Estimating the incubation period for AIDS patients. Nature, 333, 505.CrossRefGoogle Scholar
Mode, C. J., Gollwitzer, H. E. & Herrmann, N. (1988). A methodological study of a stochastic model of an AIDS epidemic. Mathematical Biosciences, 92, 201–229.CrossRefGoogle Scholar
Morgan, W. M. & Curran, J. W. (1986). Acquired immunodeficiency syndrome: current and future trends. Public Health Reports, 101, 459 465.Google ScholarPubMed
Mortimer, P. P. (1985). Estimating AIDS, U.K. Lancet, 2, 1065.CrossRefGoogle Scholar
Panjer, H. H. (1987). ‘Survival analysis of persons testing HIV positive.’ Working Paper Series in Actuarial Science ACTSC 87-14, Faculty of Mathematics, University of Waterloo, Canada.Google Scholar
Panjer, H. H. (1988). ‘AIDS: some aspects of modelling the insurance risk.’ Research Report 88 10, Institute of Insurance and Pension Research, University of Waterloo, Canada.Google Scholar
Peterman, T. A., Jafe, H. W., Feorino, P. M., Getchell, J. P., Warfield, D. T., Haverkes, H. W., Stoneburner, R. L. et al. (1985). Transfusion-associated acquired immunodeficiency syndrome. J. Amer. Med. Assoc. 254, 2913–2917.CrossRefGoogle ScholarPubMed
Peto, J. (1986). AIDS promiscuity. Lancet, 2, 979.CrossRefGoogle ScholarPubMed
Plumley, P. W. (1989). Modelling the AIDS Epidemic by Analysis of Sexual and Intravenous Drug Behaviour. Trans. Soc. Act, 41 (to appear).Google Scholar
Rees, M. (1987). The sombre view of AIDS. Nature, 326, 343–345.Google ScholarPubMed
Rees, M. (1987a). Describing the AIDS epidemic. Lancet, 2, 98–99.CrossRefGoogle ScholarPubMed
Roberts, C. A. & Dangerfield, B. C. (1988). ‘Simulation models of the epidemiological consequences of HIV infection and AIDS.’ Working Paper No 8901, Dept. of Business and Management Studies, University of Salford.Google Scholar
Salzberg, A. M., Dolins, S. L. & Salzberg, C. (1989). HIV incubation times. Lancet, 2, 166.CrossRefGoogle ScholarPubMed
Sattenspiel, L. (1987). Population structure and the spread of disease. Human Biol. 59, 411–438.Google ScholarPubMed
Sattenspiel, L. & Simon, C. (1988). The spread and persistence of infectious diseases in structured populations. Mathematical Biosciences, 90, 341–366.CrossRefGoogle Scholar
Stannat, S., Kiessling, D., Schedel, I. & Deicher, H. (1987). ‘Computer simulations of the AIDS-Epidemic in the Federal Republic of Germany.’Google Scholar
Stigum, H., Groeenesby, J. K., Magnus, P. et al. (1988). ‘The effect of selective partner choice on the spread of HIV.’ Poster presentation at The Global Impact of AIDS Conference, London, March 1988.Google Scholar
Stroniski, K. (1990). ‘Delays in reporting of Canadian AIDS cases.’ ARCH (to appear).Google Scholar
Taylor, J. M. G. (1989). Models for the HIV infection and AIDS epidemic in the United States. Statistics in Medicine, 8, 45–58.CrossRefGoogle Scholar
Tan, W. Y. & Hsu, H. (1989). Some stochastic models of AIDS spread. Statistics in Medicine, 8, 121–136.CrossRefGoogle ScholarPubMed
Thompson, J. R. (1987). ‘AIDS: old disease. new society.’ Technical Report 87-1, Dept. of Statistics. Rice University. Texas.Google Scholar
Tillett, H. E. & Mcevoy, M. (1986). Reassessment of predicted numbers of AIDS cases in the U.K. Lancet, 2, 1104.CrossRefGoogle Scholar
Van Druten, J. A. M., De Boo, Th., Jager, J. C. et al. (1986). AIDS prediction and intervention. Lancet 1 852–853.CrossRefGoogle ScholarPubMed
Van Druten, J. A. M., De Boo, Th., Reintjes, A. G. M., Jager, J. C., Heisterkamp, S. H., Coutinho, R. A., Bos, J. M. & Ruitenberg, E. J. (1987). Reconstruction and prediction of spread of HIV infection in populations of homosexual men. Proc. E.C. Workshop on Statistical Analysis and Mathematical Modelling of AIDS (Bilthoven, December 1986). Oxford University Press.Google Scholar
Verrall, R. J. (1988). ‘Bayesian linear models and the claims run-off triangle.’ Actuarial Research Paper No. City Univercity, London.Google Scholar
Whyte, B. M., Gold, J., Dobson, A. J. & Cooper, D. A. (1987). Epidemiology of acquired immunodeficiency syndrome in Australia. Medical Journal of Australia, 146, 65–69.CrossRefGoogle ScholarPubMed
Wiley, J. A. & Herschom, S. J. (1988). The perils of promiscuity. Journal Infectious Diseases, 158, 500–501.CrossRefGoogle ScholarPubMed
Wiley, J. A., Herschkom, S. J. & Padian, N. S. (1989). Heterogeneity in the probability of HIV transmission per sexual contact: The case of male-to-female transmission in penile-vaginal intercourse. Statistics in Medicine, 8, 93–102.CrossRefGoogle ScholarPubMed
Wilkie, A. D. (1988). An actuarial model for AIDS. J.R.S.S. Series A, 151, 35–39.Google Scholar
Wilkie, A. D. (1988a). An actuarial model for AIDS. J.I.A. 115, 839–853.Google Scholar
Wilkie, A. D. (1989). Population projections for AIDS using an actuarial model. Phil. Trans. Royal Soc. B, 325, 99–112.Google Scholar
Who Collaborating Centre (1988). ‘Results from the latest half-yearly analysis of European AIDS surveillance data: assessment of temporal evolution and predictions to December 1989.’ Paris.Google Scholar
Zeger, S. L., See, L.-C. & Diggle, P. J. (1989). Statistical methods for monitoring the AIDS epidemic. Statistics in Medicine, 8, 3–21.CrossRefGoogle ScholarPubMed