zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Effects of public health educational campaigns and the role of sex workers on the spread of HIV/AIDS among heterosexuals. (English) Zbl 1147.92317
Summary: A sex-structured model for heterosexual transmission of HIV/AIDS is presented in which the population is divided into three subgroups: susceptibles, infectives and AIDS cases. The subgroups are further divided into two classes, consisting of individuals involved in high-risk sexual activities and individuals involved in low-risk sexual activities. The model considers the movement of individuals from high to low sexual activity groups as a result of public health educational campaigns. Thus, in this case public health educational campaigns are resulting in the split of the population into risk groups. The equilibrium and epidemic threshold, which is known as the basic reproductive number $({\cal R}_0)$, are obtained, and stability (local and global) of the disease-free equilibrium is investigated. The model is extended to incorporate sex workers, and their role in the spread of HIV/AIDS in settings with heterosexual transmission is explored. Comprehensive analytic and numerical techniques are employed in assessing the possible community benefits of public health educational campaigns in controlling HIV/AIDS. From the study, we conclude that the presence of sex workers enlarges the epidemic threshold ${\cal R}_0$, thus fuels the epidemic among the heterosexuals, and that public health educational campaigns among the high-risk heterosexual population reduces ${\cal R}_0$, and thus can help to slow or eradicate the epidemic.

34K20Stability theory of functional-differential equations
34K60Qualitative investigation and simulation of models
Full Text: DOI
[1] Anderson, R. M.; May, R. M.: Infectious diseases of humans. (1991)
[2] 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 (1991)
[3] Baggaley, R. F.; Garnett, G. P.; Ferguson, N. M.: Modelling the impact of antiretroviral use in resource-poor settings. Plos med. 3, No. 4, e124 (2006)
[4] Blower, S. M.; Mclean, A. R.: Prophylactic vaccines, risk behaviour change, and the probability of eradicating HIV in San Francisco. Science 265, 1451-1454 (1994)
[5] Blower, S. M.; Gershengorn, H. B.; Grant, R. M.: A tale of two futures: HIV and antiretroviral therapy in San Francisco. Science 287, 650-654 (2000)
[6] Blower, S.; Aschenbach, A.; Gershengorn, H.; Kahn, J.: Predicting the unpredictable: transmission of drug resistant HIV. Nat. med. 7, 1016-1020 (2001)
[7] Blower, S. M.; Koelle, K.; Mills, J.: Health policy modeling: epidemic control, HIV vaccines and risky behavior. Quantitative evaluation of HIV prevention programs, 260-289 (2002)
[8] Blower, S.; Moss, R. B.; Fernandez-Cruz, E.: Calculating the potential epidemic-level impact of therapeutic vaccination on the San Francisco HIV epidemic. Aidsci. 3, No. 21 (2003)
[9] Blower, S.; Schwartz, E. J.; Mills, J.: Forecasting the future of HIV epidemics: the impact of antiretroviral therapies and imperfect vaccines. AIDS rev. 5, 113-125 (2003)
[10] Blower, S.; Bodine, E.; Kahn, J.; Mcfarland, W.: The antiretroviral rollout and drug-resistant HIV in africa: insights from empirical data and theoretical models. AIDS rev. 19, No. 1, 1-14 (2005)
[11] Busenberg, S.; Cooke, K.: Vertically transmitted diseases models and dynamics. Biomathematics. 23 (1993) · Zbl 0837.92021
[12] Caldwell, J. P.; Quiggin, P.: The social context of AIDS in sub-saharan africa. Popul. dev. Rev., 185-234 (1989)
[13] Campbell, C.: Selling sex in the time of AIDS: the psycho-social context of condom use by sex workers on a south african mine. Soc. sci. Med., 479-494 (2000)
[14] Castillo-Chavez, C., Busenberg, S., 1991. On the solution of the two-sex mixing problem. In: Busenberg, S., Martelli, M., (Eds.), Differential Equations Models in Biology, Epidemiology and Ecology, Proceedings, Claremont 1990. Lecture Notes in Biomathematics, vol. 92. Springer, New York, pp. 80 -- 98. · Zbl 0753.92024
[15] Del Valle, S.; Evangelista, A. M.; Velasco, M. C.; Kribs-Zaleta, C. M.; Schmitz, S. F. Hsu: Effects of education, vaccination and treatment on HIV transmission in homosexuals with genetic heterogeneity. Math. biosci. 187, 111-133 (2004) · Zbl 1047.92042
[16] Diekmann, O.; Heesterbeek, J. A. P.; Metz, J. A. P.: On the definition and computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. J. math. Biol., 365-382 (1990) · Zbl 0726.92018
[17] Doyle, M. T.; Greenhalgh, D.: Asymmetry and multiple endemic equilibria in a model for HIV transmission in a heterosexual population. Math. comput. Model. 29, 43-61 (1999) · Zbl 1027.68731
[18] Doyle, M. T.; Greenhalgh, D.; Blythe, S.: Equilibrium analysis of a mathematical model for the spread of AIDS in a two sex population with mixing constraints. J. biol. Syst. 6, No. 2, 159-185 (1998)
[19] Elbasha, E. H.; Gumel, A. B.: Theoretical assessment of public health impact of imperfect prophylactic HIV vaccines with therapeutic benefits. Bull. Math. biol. 68, 577-614 (2006)
[20] Gray, R. H.; Xianbin, L.; Wawer, M. J.; Gange, S. J.; Serwadda; Sewankambo, N. K.; Moore, R.; Wabwire-Mangen, F.; Lutalo, T.; Quinn, T. C.: Stochastic simulation of the impact of antiretroviral therapy and HIV vaccines on HIV transmission, rakai, uganda. Aids 17, 1941-1951 (2003)
[21] Griffiths, J.; Lowrie, D.; Williams, J.: An age-structured model for the AIDS epidemic. Eur. J. Oper. res., 1-14 (2000) · Zbl 0955.92032
[22] Griffiths, J.; England, T.; Williams, J.: Analytic solutions to compartment models of the HIV/AIDS epidemic. IMA J. Math. appl. Med. biol., 295-310 (2000) · Zbl 0966.92021
[23] Gysels, M.; Pool, R.; Nnalusiba, B.: Women who sell sex in a ugandan trading town: life histories, survival strategies and risk. Soc. sci. Med. 54, 179-192 (2002)
[24] Hall, J.: Sex workers join efforts to contain spread of AIDS. (2003)
[25] Heesterbeek, J. A. P.; Metz, J. A. J.: The saturating contact rate in marriage- and epidemic models. J. math. Biol. 31, 529-539 (1993) · Zbl 0770.92021
[26] Hethcote, H. W.: The mathematics of infectious disease. SIAM rev. 42, 599 (2000) · Zbl 0993.92033
[27] Hethcote, H. W.; Van Ark, J. W.: Modelling HIV transmission and AIDS in the united states. Lecture notes in biomathematics. (1980)
[28] Hsieh, Y. -H.; Velasco-Hernandez, J. X.: Community treatment of HIV-1: initial stage and asymptotic dynamics. Biosystems 23, 75-81 (1995)
[29] Schmitz, S. F. Hsu: Effects of treatment or/and vaccination on HIV transmission in homosexuals with genetic heterogeneity. Math. biosci. 167, 1-18 (2000) · Zbl 0979.92023
[30] Schmitz, S. F. Hsu: Effects of genetic heterogeneity on HIV transmission in homosexual populations. Mathematical approaches for emerging and reemerging infectious diseases: models, methods and theory, 245-260 (2002) · Zbl 1023.92029
[31] Hyman, J. M.; Li, J.; Stanley, E. A.: The differential infectivity and staged progression models for the transmission of HIV. Math. biosci. 155, 77-109 (1999) · Zbl 0942.92030
[32] Kermack, W.O., McKendrick, A.G., 1927. Contributions to the mathematical theory of epidemics-I. In: Proceedings of the Royal Society 115A, pp. 700 -- 721 (reprint in Bull. Math. Biol. 53(1/2), 33 -- 55, 1991). · Zbl 53.0517.01
[33] Kribs-Zaleta, C. M.: Structured models for heterosexual disease transmission. Math. biosci. 160, 83 (1999) · Zbl 0980.92031
[34] Kribs-Zaleta, C. M.: The effect of the HIV/AIDS epidemic on africa’s truck drivers. Math. biosci. Eng. 2, No. 4, 771-788 (2005) · Zbl 1097.92044
[35] Lansky, A.; Nakashima, A.; Jones, J.: Risk behaviors related to heterosexual transmission from HIV-infected persons. Sex. transm. Dis., 483-489 (2000)
[36] Matlin, S., Spence, N., 2000. The gender aspects of the HIV/AIDS pandemic, EGM / HIV-AIDS /2000/OP1.
[37] Mclean, A. R.; Blower, S. M.: Imperfect vaccines and herd immunity to HIV. Proc. R. Soc. London 253, No. 9, 13 (1993)
[38] Mclean, A. R.; Blower, S. M.: Modelling vaccination. Trends microbiol. 3, 458-463 (1995)
[39] Mufune, P., 2004. Social scientific antecedents of HIV/AIDS policies in africa, \langle www.codesria.org/Links/conferences/hiv_aids/mufune.pdf\rangle .
[40] Mukandavire, Z.; Garira, W.: HIV/AIDS model for assessing the effects of prophylactic sterilizing vaccines, condoms and treatment with amelioration. J. biol. Syst. 14, No. 3, 323-355 (2006) · Zbl 1116.92042
[41] Mukandavire, Z.; Garira, W.: Sex-structured HIV/AIDS model to analyse the effects of condom use with application to zimbabwe. J. math. Biol. 54, 669-699 (2007) · Zbl 1114.92060
[42] New Internationalist, 1994. The money market.
[43] O’brien, T.; Busch, M.; Donegan, E.; Ward, J.; Wong, L.: Heterosexual transmission of human imunodeficiency virus type 1 from transfusion recipients to their sex partners. J. acquir. Immune. defic. Syndr. 7, 705-710 (1994)
[44] Roberts, C.; Dangerfield, B.: A system dynamics modelling framework for understanding the epidemiology of HIV/AIDS. OR work in HIV/AIDS -first edition (1990)
[45] Ross, R.: The prevention of malaria. (1911)
[46] Royce, R. A.; Sena, A.; Cates, W.; Cohen, M. S.: Sexual transmission of HIV. N. engl. J. med. 336, No. 15, 1072-1078 (1997)
[47] Smith, R. J.; Blower, S. M.: Could disease-modifying HIV vaccines cause population-level perversity?. Lancet infect. Dis. 4, 636-639 (2004)
[48] UNAIDS, 2004. Report on the global AIDS epidemic, Geneva.
[49] UNAIDS, 2006. Report on the global AIDS epidemic, Geneva.
[50] UNAIDS/WHO, 2003. AIDS epidemic update, Geneva.
[51] UNAIDS/WHO, 2005. AIDS epidemic update, Geneva.
[52] Den Driessche, P. Van; Watmough, J.: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. biosci., 29-48 (2002) · Zbl 1015.92036
[53] Velasco-Hernandez, J. X.; Hsieh, Y. -H.: Modelling the effect of treatment and behavioral change in HIV transmission dynamics. J. math. Biol. 34, 233-249 (1994) · Zbl 0792.92023
[54] WHO, 2005. Zimbabwe WHO estimates of people requiring treatment.
[55] Zimbabwe Ministry of Health and Child Welfare, 2003. CDC Zimbabwe and UNAIDS, Zimbabwe national HIV and AIDS estimates.