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**Effects of education, vaccination and treatment on HIV transmission in homosexuals with genetic heterogeneity.**
*(English)*
Zbl 1047.92042

Summary: 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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