Effects of education, vaccination and treatment on HIV transmission in homosexuals with genetic heterogeneity.

*(English)*Zbl 1047.92042Summary: Genetic studies report the existence of a mutant allele \(\Delta\)32 of CCR5 chemokine receptor gene at high allele frequencies (\(\sim 10\%\)) in Caucasian populations. The presence of this allele is believed to provide partial or full resistance to HIV. We look at the impact of education, temporarily effective vaccines and therapies on the dynamics of HIV in homosexually active populations. In our model, it is assumed that some individuals possess one or two mutant alleles (like \(\Delta\)32 of CCR5) that prevent the successful invasion or replication of HIV. Our model therefore differentiates by genetic and epidemiological status and naturally ignores the reproduction process.

Furthermore, HIV infected individuals are classified as rapid, normal or slow progressors. In this complex setting, the basic reproductive number \(\mathcal R_0\) is derived in various situations. The separate or combined effects of therapies, education, vaccines, and genetic resistance are analyzed. Our results support the conclusions of S.-F. Hsu Schmitz [J. Theor. Med. 2, 285 ff (2000); Math. Biosci. 167, 1–18 (2000; Zbl 0979.92023); IMA Vol. Math. Appl. 126, 245–260 (2002; Zbl 1023.92029)] that some integrated intervention strategies are far superior to those based on a single approach. However, treatment programs may have effects which counteract each other, as may genetic resistance.

Furthermore, HIV infected individuals are classified as rapid, normal or slow progressors. In this complex setting, the basic reproductive number \(\mathcal R_0\) is derived in various situations. The separate or combined effects of therapies, education, vaccines, and genetic resistance are analyzed. Our results support the conclusions of S.-F. Hsu Schmitz [J. Theor. Med. 2, 285 ff (2000); Math. Biosci. 167, 1–18 (2000; Zbl 0979.92023); IMA Vol. Math. Appl. 126, 245–260 (2002; Zbl 1023.92029)] that some integrated intervention strategies are far superior to those based on a single approach. However, treatment programs may have effects which counteract each other, as may genetic resistance.

##### MSC:

92D30 | Epidemiology |

92D10 | Genetics and epigenetics |

34D23 | Global stability of solutions to ordinary differential equations |

##### Keywords:

HIV/AIDS; Genetic resistance; Vaccination; Treatment programs; Public education; Reproductive number
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\textit{S. Del Valle} et al., Math. Biosci. 187, No. 2, 111--133 (2004; Zbl 1047.92042)

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##### References:

[1] | Begley, S., AIDS at 20, Newsweek, June 11, 34, (2001) |

[2] | Freeman, S.; Herron, J.C., Evolutionary analysis, (1998), Prentice Hall Upper Saddle River, NJ |

[3] | Sheppard, H.W.; Lang, W.; Ascher, M.S., The characterization of non-progressors: long-term HIV-1 infection with stable CD4+ T-cell levels, Aids, 7, 1159, (1993) |

[4] | Phair, J.P., Keynote address: variations in the natural history of HIV infection, AIDS res. hum. retrov., 10, 883, (1994) |

[5] | Detels, R.; Liu, Z.; Hennessey, K., Resistance to HIV-1 infection: multicenter AIDS cohort study, J. acq. immun. def. synd. hum. retrovirol., 7, 1263, (1994) |

[6] | Paxton, W.A.; Martin, S.R.; Tse, D., Relative resistance to HIV-1 infection of CD4 lymphocytes from persons who remain uninfected despite multiple high-risk sexual exposure, Nat. med., 2, 412, (1996) |

[7] | Fowke, K.R.; Nagelkerke, N.J.D.; Kimani, J., Resistance to HIV-1 infection among persistently seronegative prostitutes in nairobi, kenya, Lancet, 348, 1347, (1996) |

[8] | Dean, M.; Carrington, M.; Winkler, C., Genetic restriction of HIV-1 infection and progression to AIDS by a deletion allele of the CKR5 structural gene, Science, 273, 1856, (1996) |

[9] | Samson, M.; Libert, F.; Doranz, B.J., Resistance to HIV-1 infection in Caucasian individuals bearing mutant alleles of the CCR-5 chemokine receptor gene, Nature, 382, 722, (1996) |

[10] | Quillent, C.; Oberlin, E.; Braun, J., HIV-1-resistance phenotype conferred by combination of two separate inherited mutations of CCR5 gene, Lancet, 351, 14, (1998) |

[11] | Hsu Schmitz, S.-F., A mathematical model of HIV transmission in homosexuals with genetic heterogeneity, J. theor. med., 2, 285, (2000) · Zbl 0962.92035 |

[12] | Hsu Schmitz, S.-F., Effects of treatment and/or vaccination on HIV transmission in homosexuals with genetic heterogeneity, Math. biosci., 167, 1, (2000) · Zbl 0979.92023 |

[13] | Blower, S.M.; Gershengorn, H.B.; Grant, R.M., A tale of two futures: HIV and antiretroviral therapy in San Francisco, Science, 287, 650, (2000) |

[14] | Blower, S.M.; Aschenbach, A.N.; Gershengorn, H.B.; Kahn, J.O., Predicting the unpredictable: transmission of drug-resistant HIV, Nat. med., 7, 1016, (2001) |

[15] | McLean, A.R.; Blower, S.M., Imperfect vaccines and herd immunity to HIV, Proc R. soc. lond. B, 253, 9, (1993) |

[16] | Blower, S.M.; McLean, A.R., Prophylactic vaccines, risk behavior change, and the probability of eradicating HIV in San Francisco, Science, 265, 1451, (1994) |

[17] | McLean, A.R.; Blower, S.M., Modelling HIV vaccination, Trends microbiol., 3, 458, (1995) |

[18] | Anderson, R.M.; May, R.M., Epidemiological parameters of HIV transmission, Nature, 333, 514, (1988) |

[19] | Anderson, R.M.; Gupta, S.; May, R.M., Potential of community-wide chemotherapy of immunotherapy to control the spread of HIV-1, Nature, 350, 356, (1991) |

[20] | Castillo-Chávez, C.; Cooke, K.; Huang, W.; Levin, S.A., The role of long incubation periods in the dynamics of HIV/AIDS. part 1: single populations models, J. math. biol., 27, 373, (1989) · Zbl 0715.92029 |

[21] | Castillo-Chávez, C.; Cooke, K.L.; Huang, W.; Levin, S.A., Results on the dynamics for models for the sexual transmission of the human immunodeficiency virus, J. appl. math. lett., 2, 4, 327, (1989) · Zbl 0703.92022 |

[22] | Busenberg, S.; Castillo-Chávez, C., A general solution of the problem of mixing of subpopulations and its application to risk- and age-structured epidemic models for the spread of AIDS, IMA J. math. appl. med. biol., 8, 1, (1991) · Zbl 0764.92017 |

[23] | Diekmann, O.; Heesterbeek, J.A.P.; Metz, J.A.J., On the definition and the computation of the basic reproduction ratio \(R0\) in models for infectious diseases in heterogeneous populations, J. math. biol., 28, 365, (1990) · Zbl 0726.92018 |

[24] | Castillo-Chávez, C.; Feng, Z.; Huang, W., On the computation of \(R0\) and role on global stability, (), 229 |

[25] | Diekmann, O.; Dietz, K.; Heesterbeek, J.A.P., The basic reproduction ratio for sexually transmitted diseases, part 1: theoretical considerations, Math. biosci., 107, 325, (1991) · Zbl 0748.92010 |

[26] | Dietz, K.; Heesterbeek, J.A.P.; Tudor, D.W., The basic reproduction ratio for sexually transmitted diseases, part 2: effects of variable HIV-infectivity, Math. biosci., 117, 35, (1993) · Zbl 0805.92024 |

[27] | Kegeles, S.M.; Hays, R.B.; Pollack, L.M.; Coates, T.J., Mobilizing Young gay and bisexual men for HIV prevention: a two-community study, Aids, 13, 1753, (1999) |

[28] | Hadeler, K.P.; Castillo-Chávez, C., A core group model for disease transmission, Math. biosci., 128, 41, (1995) · Zbl 0832.92021 |

[29] | Kribs-Zaleta, C.M.; Velasco-Hernández, J.X., A simple vaccination model with multiple endemic states, Math. biosci., 164, 2, 183, (2000) · Zbl 0954.92023 |

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