A stochastic model of the HIV epidemic and the HIV infection distribution in a homosexual population. (English) Zbl 0767.92027
Summary: We develop a stochastic model for the HIV epidemic in a homosexual population and use the model to characterize the HIV infection distribution and seroconversion distribution. Through computer-generated infection distributions and seroconversion distributions, we assess the effects of various risk factors on these distributions. The fitting of some data sets generated by computer suggests that the three-parameter generalized log-logistic distribution should be assumed as the infection distribution for the proposed stochastic model of HIV epidemics.
Keywords:
stochastic model; homosexual population; HIV infection distribution; computer-generated infection distributions; seroconversion distributions; three-parameter generalized log-logistic distribution; HIV epidemicsReferences:
| [1] | Akaike, H.; Atkinson, C.; Feinberg, S. E., Prediction and entropy, A Celebration of Statistics (1985), Springer-Verlag: Springer-Verlag New York · Zbl 0576.62009 |
| [2] | Anderson, R. M.; Medley, G. G.; May, R. M.; Johnson, A. M., A preliminary study of the transmission dynamics of the human immunodeficiency virus (HIV), the causitive agent of AIDS, IMA J. Math. Appl. Med. Biol., 3, 229-263 (1986) · Zbl 0609.92025 |
| [3] | Anderson, R. M.; Blythe, S. P.; Gupta, S.; Konings, E., The transmission dynamics of the human immunodeficiency virus type 1 in the United Kingdom: the influence of changes in sexual behavior, Phil. Trans. Roy. Soc. Lond. B, 325, 7-60 (1989) |
| [4] | Baccheeti, P., Estimating the incubation period of AIDS by comparing population infection and diagnosis patterns, J. Am. Stat. Assoc., 85, 1002-1008 (1990) |
| [5] | Byers, R. H.; Morgan, W. M.; Darrow, W. W.; Doll, L.; Jaffe, H. W.; Rutherford, G. W.; Hessol, N.; O’Malley, P. M., Estimating AIDS infection rates in the San Francisco Cohort, AIDS, 2, 207-210 (1988) |
| [6] | Day, N. E.; Gore, S. M.; McGee, M. A.; South, M., Prediction of the AIDS epidemic in the U.K.: the use of the back projection method, Phil. Trans. Roy. Soc. Lond. B, 325, 85-96 (1989) |
| [7] | DeGruttola, V.; Lagakos, S. W., The value of AIDS incidence data in assessing the spread of HIV infection, Stat. Med., 8, 35-44 (1989) |
| [8] | Doll, L.; Byers, R. H.; Bolan, G.; Douglas, J.; Moss, P.; Weller, P., Persistence of high-risk sexual behavior in homosexual/bisexual men: a multi-center study, Fifth International AIDS Conference (1989) |
| [9] | Gail, M. H.; Brookmeyer, R., Methods for projecting course of acquired immunodeficiency syndrome epidemic, J. Natl. Cancer Inst., 80, 900-911 (1988) |
| [10] | Haseltine, W. A.; Wong-Staal, F., The molecular biology of the AIDS virus, Sci. Am., 259, 52-63 (1988) |
| [11] | Isham, V., Mathematical modelling of the transmission dynamics of HIV infection and AIDS: a review, J. Roy. Stat., Soc. A, 151, 5-30 (1988) · Zbl 1001.92550 |
| [12] | Isham, V., Assessing the variability of stochastic epidemics, Math. Biosci., 107, 209-224 (1991) · Zbl 0739.92015 |
| [13] | Jacquez, J. A.; Simon, C. P.; Koopman, J.; Sattenspiel, L.; Perry, T., Modelling and analyzing HIV transmission: the effect of contact patterns, Math. Biosci., 92, 119-199 (1988) · Zbl 0686.92016 |
| [14] | Mode, C. J.; Gollwitzer, H. E.; Herrmann, N., A methodological study of a stochastic model of an AIDS epidemic, Math. Biosci., 92, 201-229 (1988) · Zbl 0659.92016 |
| [15] | Ng, J.; Orav, E. J., A generalized chain binomial model with application of HIV infection, Math. Biosci., 101, 99-119 (1990) · Zbl 0702.92019 |
| [16] | Redfield, R. R.; Burke, D. S., HIV infection: the clinical picture, Sci. Am., 259, 90-99 (1988) |
| [17] | Rosenberg, P. S.; Gail, M. H., Back-calculation of flexible linear models of the HIV infection curve, Appl. Stat., 40, 269-282 (1991) · Zbl 0825.62871 |
| [18] | Singh, K.; George, E. O., Generalized log-logistic model for survival data, (Tech. Rep. 87-3. Tech. Rep. 87-3, Orlando, Fla.. Tech. Rep. 87-3. Tech. Rep. 87-3, Orlando, Fla., Winter ASA Conference (Jan. 7-9, 1987), Dept. of Mathematics, Central Michigan Univ: Dept. of Mathematics, Central Michigan Univ Mt. Pleasant, Mich), paper presented at the |
| [19] | Singh, K.; Lee, C. M.-S.; George, E. O., On generalized log-logistic model for censored survival data, Biomed. J., 30, 843-850 (1988) |
| [20] | Tan, W. Y.; Byers, R. H., Some Monte Carlo studies of the incubation distribution in a homosexual population, Joint Statistical Meetings in Atlanta, Ga. (Aug. 19-22, 1991), paper presented at the |
| [21] | Tan, W. Y.; Hsu, H., Some stochastic models of AIDS spread, Stat. Med., 8, 121-136 (1989) |
| [22] | Tan, W. Y.; Hsu, H., A stochastic model for the AIDS epidemic in a homosexual population, (Arino, D. E.; Kimmel, M., Mathematical Population Dynamics (1991), Marcel Dekker: Marcel Dekker New York), Chap. 24 · Zbl 0729.92540 |
| [23] | Tan, W. Y.; Byers, R. H.; Karon, J.; Longini, I., Monte Carlo studies of the HIV infection distribution in a homosexual population, (Tech. Rep. 90-13 (1990), Dept. of Mathematical Sciences, Memphis State Univ: Dept. of Mathematical Sciences, Memphis State Univ Memphis, Tenn) |
| [24] | Taylor, J. M.G., Models for the HIV infection and AIDS epidemic in the United States, Stat. Med., 8, 45-58 (1989) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
