item-0 at level 0: unspecified: group _root_
  item-1 at level 1: title: The coreceptor mutation CCR5Δ32  ... V epidemics and is selected for by HIV
    item-2 at level 2: paragraph: Amy D. Sullivan, Janis Wigginton, Denise Kirschner
    item-3 at level 2: paragraph: Department of Microbiology and I ... dical School, Ann Arbor, MI 48109-0620
    item-4 at level 2: section_header: Abstract
      item-5 at level 3: text: We explore the impact of a host  ... creasing the frequency of this allele.
    item-6 at level 2: text: Nineteen million people have die ...  factors such as host genetics (4, 5).
    item-7 at level 2: text: To exemplify the contribution of ...  follow the CCR5Δ32 allelic frequency.
    item-8 at level 2: text: We hypothesize that CCR5Δ32 limi ... g the frequency of this mutant allele.
    item-9 at level 2: text: CCR5 is a host-cell chemokine re ... iral strain (such as X4 or R5X4) (30).
    item-10 at level 2: section_header: The Model
      item-11 at level 3: text: Because we are most concerned wi ... t both economic and social conditions.
      item-12 at level 3: picture
        item-12 at level 4: caption: Figure 1 A schematic representation of the basic compartmental HIV epidemic model. The criss-cross lines indicate the sexual mixing between different compartments. Each of these interactions has a positive probability of taking place; they also incorporate individual rates of transmission indicated as λ, but in full notation is λ î,,→i,j, where i,j,k is the phenotype of the infected partner and î, is the phenotype of the susceptible partner. Also shown are the different rates of disease progression, γ i,j,k , that vary according to genotype, gender, and stage. Thus, the interactions between different genotypes, genders, and stages are associated with a unique probability of HIV infection. M, male; F, female.
      item-13 at level 3: table with [6x5]
        item-13 at level 4: caption: Table 1 Children's genotype
      item-14 at level 3: section_header: Parameter Estimates for the Model.
        item-15 at level 4: text: Estimates for rates that govern  ... d in Fig. 1 are summarized as follows:
        item-16 at level 4: formula:  \frac{dS_{i,j}(t)}{dt}={\chi}_{ ... ,\hat {k}{\rightarrow}i,j}S_{i,j}(t), 
        item-17 at level 4: formula:  \hspace{1em}\hspace{1em}\hspace ... j,A}(t)-{\gamma}_{i,j,A}I_{i,j,A}(t), 
        item-18 at level 4: formula:  \frac{dI_{i,j,B}(t)}{dt}={\gamm ... j,B}(t)-{\gamma}_{i,j,B}I_{i,j,B}(t), 
        item-19 at level 4: formula:  \frac{dA(t)}{dt}={\gamma}_{i,j, ...  \right) -{\mu}_{A}A(t)-{\delta}A(t), 
        item-20 at level 4: text: where, in addition to previously ... on of the infected partner, and j ≠ .
        item-21 at level 4: table with [14x5]
          item-21 at level 5: caption: Table 2 Transmission probabilities
        item-22 at level 4: table with [8x3]
          item-22 at level 5: caption: Table 3 Progression rates
        item-23 at level 4: table with [20x3]
          item-23 at level 5: caption: Table 4 Parameter values
        item-24 at level 4: text: The effects of the CCR5 W/Δ32 an ... nting this probability of infection is
        item-25 at level 4: formula:  {\lambda}_{\hat {i},\hat {j},\h ... \hat {i},\hat {j},\hat {k}} \right] , 
        item-26 at level 4: text: where j ≠  is either male or fe ... e those with AIDS in the simulations).
        item-27 at level 4: text: The average rate of partner acqu ... owing the male rates to vary (36, 37).
        item-28 at level 4: section_header: Transmission probabilities.
          item-29 at level 5: text: The effect of a genetic factor i ... reported; ref. 42) (ref. 43, Table 2).
          item-30 at level 5: text: Given the assumption of no treat ... ases during the end stage of disease).
        item-31 at level 4: section_header: Disease progression.
          item-32 at level 5: text: We assume three stages of HIV in ... ssion rates are summarized in Table 3.
      item-33 at level 3: section_header: Demographic Setting.
        item-34 at level 4: text: Demographic parameters are based ... [suppressing (t) notation]: χ1,j 1,j =
        item-35 at level 4: formula:  B_{r}\hspace{.167em}{ \,\substa ... }+I_{2,M,k})}{N_{M}} \right] + \right 
        item-36 at level 4: formula:  p_{v} \left \left( \frac{(I_{1, ... ght] \right) \right] ,\hspace{.167em} 
        item-37 at level 4: text: where the probability of HIV ver ... heir values are summarized in Table 4.
    item-38 at level 2: section_header: Prevalence of HIV
      item-39 at level 3: section_header: Demographics and Model Validation.
        item-40 at level 4: text: The model was validated by using ... 5% to capture early epidemic behavior.
        item-41 at level 4: text: In deciding on our initial value ... n within given subpopulations (2, 49).
        item-42 at level 4: text: In the absence of HIV infection, ... those predicted by our model (Fig. 2).
        item-43 at level 4: picture
          item-43 at level 5: caption: Figure 2 Model simulation of HIV infection in a population lacking the protective CCR5Δ32 allele compared with national data from Kenya (healthy adults) and Mozambique (blood donors, ref. 17). The simulated population incorporates parameter estimates from sub-Saharan African demographics. Note the two outlier points from the Mozambique data were likely caused by underreporting in the early stages of the epidemic.
      item-44 at level 3: section_header: Effects of the Allele on Prevalence.
        item-45 at level 4: text: After validating the model in th ... among adults for total HIV/AIDS cases.
        item-46 at level 4: text: Although CCR5Δ32/Δ32 homozygosit ... frequency of the mutation as 0.105573.
        item-47 at level 4: text: Fig. 3 shows the prevalence of H ... mic, reaching 18% before leveling off.
        item-48 at level 4: picture
          item-48 at level 5: caption: Figure 3 Prevalence of HIV/AIDS in the adult population as predicted by the model. The top curve (○) indicates prevalence in a population lacking the protective allele. We compare that to a population with 19% heterozygous and 1% homozygous for the allele (implying an allelic frequency of 0.105573. Confidence interval bands (light gray) are shown around the median simulation () providing a range of uncertainty in evaluating parameters for the effect of the mutation on the infectivity and the duration of asymptomatic HIV for heterozygotes.
        item-49 at level 4: text: In contrast, when a proportion o ... gins to decline slowly after 70 years.
        item-50 at level 4: text: In the above simulations we assu ...  in the presence of the CCR5 mutation.
        item-51 at level 4: text: Because some parameters (e.g., r ... s a major influence on disease spread.
    item-52 at level 2: section_header: HIV Induces Selective Pressure on Genotype Frequency
      item-53 at level 3: text: To observe changes in the freque ...  for ≈1,600 years before leveling off.
      item-54 at level 3: picture
        item-54 at level 4: caption: Figure 4 Effects of HIV-1 on selection of the CCR5Δ32 allele. The Hardy-Weinberg equilibrium level is represented in the no-infection simulation (solid lines) for each population. Divergence from the original Hardy-Weinberg equilibrium is shown to occur in the simulations that include HIV infection (dashed lines). Fraction of the total subpopulations are presented: (A) wild types (W/W), (B) heterozygotes (W/Δ32), and (C) homozygotes (Δ32/Δ32). Note that we initiate this simulation with a much lower allelic frequency (0.00105) than used in the rest of the study to better exemplify the actual selective effect over a 1,000-year time scale. (D) The allelic selection effect over a 2,000-year time scale.
    item-55 at level 2: section_header: Discussion
      item-56 at level 3: text: This study illustrates how popul ... pulations where the allele is present.
      item-57 at level 3: text: We also observed that HIV can pr ... is) have been present for much longer.
      item-58 at level 3: text: Two mathematical models have con ... ce of the pathogen constant over time.
      item-59 at level 3: text: Even within our focus on host pr ... f a protective allele such as CCR5Δ32.
      item-60 at level 3: text: Although our models demonstrate  ... f the population to epidemic HIV (16).
      item-61 at level 3: text: In assessing the HIV/AIDS epidem ... for education and prevention programs.
    item-62 at level 2: section_header: Acknowledgments
      item-63 at level 3: text: We thank Mark Krosky, Katia Koel ... ers for extremely insightful comments.
    item-64 at level 2: section_header: References
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  item-132 at level 1: caption: Figure 1 A schematic representat ...  of HIV infection. M, male; F, female.
  item-133 at level 1: caption: Table 1 Children's genotype
  item-134 at level 1: caption: Table 2 Transmission probabilities
  item-135 at level 1: caption: Table 3 Progression rates
  item-136 at level 1: caption: Table 4 Parameter values
  item-137 at level 1: caption: Figure 2 Model simulation of HIV ... g in the early stages of the epidemic.
  item-138 at level 1: caption: Figure 3 Prevalence of HIV/AIDS  ... of asymptomatic HIV for heterozygotes.
  item-139 at level 1: caption: Figure 4 Effects of HIV-1 on sel ... n effect over a 2,000-year time scale.