×

zbMATH — the first resource for mathematics

Modeling the HIV/AIDS epidemic among injecting drug users and sex workers in Kunming, China. (English) Zbl 1334.92389
Summary: This paper presents a mathematical model of the HIV/AIDS epidemic in Kunming, the provincial capital of Yunnan, China. The population is divided into several groups, with individuals possibly changing group. Two transmission routes of HIV are considered: needle sharing between injecting drug users (IDUs) and commercial sex between female sex workers (FSWs) and clients. The model includes male IDUs who are also clients and female IDUs who are also FSWs. Groups are split in two – risky and safe – according to condom use and needle sharing. A system of partial differential equations is derived to describe the spread of the disease. For the simulation, parameters are chosen to fit as much as possible data publicly available for Kunming. Some mathematical properties of the model – in particular the epidemic threshold \(R_0\) which determines the goal of public health interventions – are also presented. Though the model couples two transmission routes of HIV, the approximation \(R_0\simeq \max\{R^{\mathrm{IDU}}_0, R^{\mathrm{sex}}_0\}\), with closed formulas for \(R^{\mathrm{IDU}}_0\) and \(R^{\mathrm{sex}}_0\), appears to be quite good. The critical levels of condom use and clean needle use necessary to stop both the sexual transmission and the transmission among IDUs can therefore be determined independently.

MSC:
92D30 Epidemiology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Anderson, R.M., Medley, G.F., May, R.M., and Johnson, A.M., 1986. A preliminary study of the transmission dynamics of the human immunodeficiency virus (HIV), the causative agent of AIDS. IMA J. Math. Appl. Med. Biol. 3, 229–263. · Zbl 0609.92025
[2] Bacaër, N., 2003. The asymptotic behavior of the McKendrick equation with immigration. Math. Popul. Stud. 10, 1–20. · Zbl 1046.91101
[3] Berman, A., Plemmons, R.J., 1994. Nonnegative Matrices in the Mathematical Sciences. Society for Industrial and Applied Mathematics, Philadelphia. · Zbl 0815.15016
[4] Bignami-Van Assche, S., 2004. Estimates and projections of HIV/AIDS for Yunnan province, China. Popul. Rev. 43, No. 2, Section 1.
[5] Brown, T., Peerapatanapokin, W., 2004. The Asian epidemic model: a process model for exploring HIV policy and programme alternatives in Asia. Sex. Transm. Infect. 80, i19–i24.
[6] Capasso, V., Morale, D., Di Somma, M., Villa, M., Nicolisi A., Sicurello, F., 1997. Multistage models of HIV transmission among injecting drug users via shared drug injection equipment, in Arino O. et al. (Eds.), Advances in Mathematical Population Dynamics–Molecules, Cells and Man. World Scientific, Singapore, pp. 511–527. · Zbl 0929.92030
[7] Castillo-Chavez, C., Cooke, K., Huang, W., Levin, S.A., 1989a. On the role of long incubation periods in the dynamics of acquired immunodeficiency syndrome (AIDS)-part 1: Single population models. J. Math. Biol. 27, 373–398. · Zbl 0715.92029
[8] Castillo-Chavez, C.,Cooke, K., Huang, W., Levin, S.A., 1989b. On the role of long incubation periods in the dynamics of acquired immunodeficiency syndrome (AIDS)-part 2: multiple group models. In: Castillo-Chavez, C., (Ed.), Mathematical and Statistical Approaches to AIDS Epidemiology. Springer-Verlag, New York, pp. 200–217. · Zbl 0705.92018
[9] Cheng, H., Zhang, J., Kou, J., Zhang, Y., Zhang, X., Jia, M., Bi, X., Ma, Y., Liang, Y., Yang, Z., Pan, S., An, X., 1996. HIV infection tends to spread to whole Yunnan province. Chin. J. STD/AIDS Prev. Cont. 2, 54–57.
[10] China AIDS Info, 2004. Yunnan passes new AIDS policy, will provide clean needles to drug users. Online: http://www.china-aids.org .
[11] Cohen, J., 2004a. HIV/AIDS in China–Poised for takeoff? Science 304, 1430–1432.
[12] Cohen, J., 2004b. HIV/AIDS in China–Changing course to break the HIV-heroin connection. Science 304, 1434–1435.
[13] Cohen, J., 2004c. HIV/AIDS in Asia–Asia and Africa: On different trajectories? Science 304, 1932–1938.
[14] Diekmann, O., Heesterbeek, J.A.P., 2000. Mathematical Epidemiology of Infectious Diseases. John Wiley Chichester. · Zbl 0997.92505
[15] Duan, Y., Zheng, X., Zhen, C., 1995. Investigation of mortality among HIV-infected intravenous drug users in Ruili region of Yunnan province. Zhonghua Liu Xing Bing Xue Za Zhi 16, 71–73.
[16] Greenhalgh, D., Lewis, F., 2002. The general mixing of addicts and needles in a variable-infectivity needle-sharing environment. J. Math. Biol. 44, 561–598. · Zbl 0992.92037
[17] Hethcote, H.W., Thieme, H.R., 1985. Stability of the endemic equilibrium in epidemic models with subpopulations. Math. Biosci. 75, 205–227. · Zbl 0582.92024
[18] Horizon Market Research and Futures Group Europe, 2002a. 2001 behavioural surveillance survey in Yunnan and Sichuan–adult male report. Online: http://www.futures-group.com/Documents/2001BSSadultmale.pdf .
[19] Horizon Market Research and Futures Group Europe, 2002b. 2001 behavioural surveillance survey in Yunnan and Sichuan–sex worker report. Online: http://www.fu-turesgroup.com/Documents/2001BSSsexworker.pdf .
[20] Horn, R.A., Johnson, C.R., 1985. Matrix Analysis. Cambridge University Press, Cambridge. · Zbl 0576.15001
[21] Huang, W., Cooke, K.L., Castillo-Chavez, C., 1992. Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission. SIAM J. Appl. Math. 52, 833–854. · Zbl 0769.92023
[22] Hyman, J.M., Stanley, E.A., 1988. Using mathematical models to understand the AIDS epidemic. Math. Biosci. 90, 415–473. · Zbl 0727.92025
[23] Iannelli, M., Milner, F.A., Pugliese, A., Gonzo, M. 1997. The HIV/AIDS epidemics among drug injectors: A study of contact structure through a mathematical model. Math. Biosci. 139, 25–58. · Zbl 0893.92025
[24] Ka, K., 2004. Voluntary counseling and testing among injecting drug users in Kunming city, Yunnan Province. 15th International AIDS Conference, Bangkok, abstract no. WePeC5999.
[25] Kermack, W.O., McKendrick, A.G., 1933. Contributions to the mathematical theory of epidemics - III. Further studies of the problem of endemicity. Proc. Roy. Soc. London Ser. A 141, 94–122. (Reprinted in Bull. Math. Biol. 53 (1991), 89–118. · Zbl 0007.31502
[26] Lu, L., Jia, M., Zhang, X., Luo, H., Ma, Y., Fu. L., Lu, J., 2004. Analysis for epidemic trend of acquired immunodeficiency syndrome in Yunnan Province of China. Chin. J. Prev. Med. 38, 309–312.
[27] Mastro, T.D., Satten, G.A., Nopkesorn, T., Sangkharomya, S., Longini, I.M., 1994. Probability of female-to-male transmision of HIV-1 in Thailand. Lancet 434, 204–207.
[28] McCoy, C.B., Lai, S., Metsch, L.R., Wang, X., Li, C., Yang, M., Yulong, L., 1997. No pain no gain, establishing the Kunming, China, drug rehabilitation center. Journal of Drug Issues 27, 73–85.
[29] Merli, M.G., Hertog, S., Wang, B., Li, J., 2004. Modelling the course of the HIV/AIDS epidemic in China: An application of a bio-behavioral macrosimulation model of the spread of HIV/AIDS. Center for Demography and Ecology Working Paper No. 2004–14, University of Wisconsin-Madison.
[30] Motulsky, H.J., Christopoulos, A., 2003. Fitting models to biological data using linear and nonlinear regression. A practical guide to curve fitting. GraphPad Software Inc., San Diego, CA, Online: http://www.graphpad.com . · Zbl 1081.62100
[31] Monitoring the AIDS Pandemic Network 2004. AIDS in Asia: face the facts–a comprehensive analysis of the AIDS epidemics in Asia. Online: http://www.mapnet-work.org/docs/MAP_AIDSinAsia2004.pdf .
[32] National Bureau of Statistics of China, 1994–2003. China Population Statistics Yearbook. China Statistic Press, Beijing.
[33] Pan, S., Cheng, H., Zhang, J., Jia, M., Bi, X., Zhang, Y., Zhang, X., An, J., Ma, Y., Yang, Z., Liang, Y., Kou, J., 1997. Survey of the current situation of the HIV infection epidemic in Yunnan province. Chin. J. STD/AIDS Prev. Cont. 3, 244–247.
[34] Pugliese, A., 1992. Stationary solutions of a multigroup model for AIDS with distributed incubation and variable infectiousness. In Da Prato, G. (Ed.), Mathematical aspects of human diseases, Giardini, Pisa, pp. 110–125.
[35] Razak, M.H., 2002. Situation assessment of injection drug users in Yunnan province - People’s Republic of China. Futures Group Europe Report.
[36] Thieme, H., Castillo-Chavez, C., 1989. On the role of variable infectivity in the dynamics of the human immunodeficiency virus epidemic. In Castillo-Chavez, C. (Ed.), Mathematical and statistical approaches to AIDS epidemiology, Springer-Verlag, New York, pp. 157–177. · Zbl 0687.92009
[37] Thieme, H., Castillo-Chavez, C., 1993. How may infection-age-dependent infectivity affect the dynamics of HIV/AIDS? SIAM J. Appl. Math. 53, 1447–1479. · Zbl 0811.92021
[38] Thieme, H., 2003. Mathematics in Population Biology. Princeton University Press, Princeton. · Zbl 1054.92042
[39] UN Theme Group on HIV/AIDS in China, 2002. HIV/AIDS: China’s Titanic Peril. Online: http://www.youandaids.org/unfiles/chinastitanicperillast.pdf .
[40] UN Theme Group on HIV/AIDS in China and State Council AIDS Working Committee Office, 2004. A Joint Assessment of HIV/AIDS Prevention, Treatment and Care in China. Online: http://www.unchina.org/unaids/JAREng04.pdf .
[41] Wang, S., Li, L., Zhang, L., Ni, Z., Yang, L., 2001. Surveillance and analysis of HIV/AIDS in Kunming in 1999. Guangxi Prev. Med. 7, 157–158.
[42] Wang, S., 2004. Surveillance and control of HIV/AIDS in Kunming. Chin. J. STD/AIDS Prev. Cont. 10, 216–217.
[43] WHO Regional Office for the Western Pacific and Ministry of Health of the People’s Republic of China, 2001. Prevalence survey of sexually transmitted infections among female sex workers and truck drivers in China 1999–2000. Online: http://www.wpro.who.int .
[44] Xinhua News Agency, 2004. Yunnan declares last-ditch war against AIDS. Online: http://news.xinhuanet.com/english/2004-02/23/content_1326621.htm .
[45] Xinhua News Agency, 2004. Yunnan province reports progress in HIV/AIDS prevention. Online: http://english.sina.com/china/1/2004/-1201/12161.html .
[46] Xinhua News Agency, 2005. Kunming conducts AIDS, venereal disease test in service sector. www.sina.com.
[47] Yu, H., An, X., Jia, M., Pan, S., Ma, Y., Zhang, G., Li, H., Zhang, X., Zhang, Y., Liang, Y., Li, J., Zhang, J., Cheng, H., 2001. Report on HIV/AIDS surveillance in Yunnan province in 1999. Chin. J. STD/AIDS Prev. Cont. 7, 74–76.
[48] Yuan, J., Ionita, G., Xu, Y., Jiang, T., Li, J., Zhang, J. 2002. The HIV/AIDS projection in Yunnan. Chin. J. STD/AIDS Prev. Cont. 8, 78–81.
[49] Zhang, J., Cheng, H., Duan, S., 1994. Survey of the current situation of the HIV infection epidemic in Yunnan province. Chin. J. Epidemiol. 5, 259–262.
[50] Zhang, J., Cheng, H., Jia, M., Zhang, Y., 1999. Ten years of experience on AIDS control in Yunnan (1989998). Chin. J. Epidemiol. 20, 377–380.
[51] Zhang, X., Ma, Y., Yu, H., An, J., Liang, Y., Zhang, G., Zhang, Z., Li, H., Wang, W., Pan, S., Zhang, Y., Jia, M., 2002. Analysis on the surveillance result of HIV/AIDS in Yunnan in 2001. Ji Bing Jian Ce 17, 327–330.
[52] Zhang, X., Lu, J., Fu, L., Luo, H., Jia, M., 2004. Analysis on survey results of HIV/AIDS in Yunnan Province in 2003. Ji Bing Jian Ce 19, 409–412.
[53] Zheng, X., Zhang, J., Wang, X., Duan, S., Qu, S., Duan, Y., Zhang, G., 2000. The natural history of HIV infection among IDUs in Ruili, Yunnan province, China. Chin. J. Epidemiol. 21, 17–18.
[54] Zhong, W., 2000. A close look at China’s ”sex industry.” Lianhe Zaobao, Singapore, Online: http://www.usembassy-china.org.cn/sandt/sex-industry.html .
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.