Abstract
Building on the Weibull distribution, we develop a modeled time-varying density function of the incubation time between exposure to HIV infection and full-blown AIDS. This approach leads to a series of cohort-specific density functions that take into account the increasing impact of new therapies such as zidovudine (AZT). The resulting modeled density functions are studied in detail, particularly with regard to their modes and medians. The mode is sensitive to changes in the period incubation time distribution, with even a possibility of a bimodal distribution for certain combinations of the parameters that determine the rate at which the period median incubation time changes. An important substantive result is that when a period median incubation period slowly increases to some leveling off value, say m(x c ), then it is surprisingly early on that cohorts of infected individuals have a median incubation period very close to that ultimate value m(x c ).
Similar content being viewed by others
References
Anderson, R. M., Gupta, S., May, R. M.: Potential of community-wide chemotherapy or immunotherapy to control the spread of HIV-1. Nature 350, 356–359 (1991)
Bacchetti P., Moss, A. R.: Incubation period of AIDS in San Francisco. Nature 338, 251–253 (1989)
Blythe S. P., Anderson, R. M.: Distributed incubation period and infectious periods in models of the transmission dynamics of the human immunodeficiency virus (HIV). IMA J. Math. Appl. Med. Biol. 5(1), 1–19 (1988)
Brookmeyer R., Liao, J.: Statistical modelling of the AIDS epidemic for forecasting health care needs. Biometrics 46, 1151–1163 (1990)
Brookmeyer, R.: Reconstruction and future trends of the AIDS epidemic in the United States. Science 253, 37–42 (1991)
Castillo-Chavez, C. (ed.) Mathematical and statistical approaches to AIDS epidemiology. (Lect. Notes Biomath., Vol. 83), Berlin Heidelberg New York: Springer 1990
De Gruttola, V., Lange, N.: Modelling progression of HIV infection. Presented at V. International Conference on AIDS, 4–9 June 1989, Montreal, Abstract p. 151 (1989)
Gail, M. H., Rosenberg, P. S., Goedert, J. J.: Therapy may explain recent deficits in AIDS incidence. J. Acq. Immun. Def. Synd. 3, 296–306 (1990)
Lui, K-J, Lawrence, D. N., Morgan, W. M., Peterman, T. A., Haverkos, H. W., Bregman, D. J.: A model-based approach for estimating the mean incubation period for transfusion-associated acquired immunodeficiency syndrome. Proc. Natl. Acad. Sci. USA, 83, 3051–3055 (1986)
Lui, K-J, Darrow, W. W., Rutherford, G. W.: A model-based estimate of the mean incubation period for AIDS in homosexual men. Science 240, 1333–1335 (1988)
Medley, G. F., Anderson, R. M., Cox, D. R., Billard, L.: Incubation period of AIDS in patients infected via blood transfusion. Nature 328, 719–721 (1987)
Schechter, M. T., Craib, K. J. P., Le, T. N., Montaner, J. S. G., McLeod, W. A., Elmslie, K. D., O'Shaughnessy, M. V.: Influence of Zidovidome on progression to AIDS in cohort studies [letter], Lancet, i: 1026–1026 (1989)
Solomon, P. J., Wilson, S. R.: Accommodating change due to treatment in the method of back projection for estimating HIV infection incidence. Biometrics 46, 1165–1170 (1990)
Thieme, H. R., Castillo-Chavez, C.: How many infection-age dependent infectivity affect the dynamics of HIV/AIDS? SIAM J. Appl. Math. (submitted)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Artzrouni, M. A modeled time-varying density function for the incubation period of AIDS. J. Math. Biol. 31, 73–99 (1992). https://doi.org/10.1007/BF00163843
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00163843