diff --git a/testfile.sh b/testfile.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c219dfad5894b2194c19becc869f5eef1a3f2d95
--- /dev/null
+++ b/testfile.sh
@@ -0,0 +1 @@
+java -cp /exlibris/dps/d4_1/system.dir/dps-sdk-7.3.0/lib//../dps-sdk-projects/dps-sdk-deposit/lib/dps-sdk-7.3.0.jar::./java/:/usr/share/java/junit4.jar:/exlibris/dps/d4_1/system.dir/dps-sdk-7.3.0/lib//../dps-sdk-projects/dps-sdk-deposit/lib/commons-codec-1.10.jar:/exlibris/dps/d4_1/system.dir/dps-sdk-7.3.0/lib//../dps-sdk-projects/dps-sdk-deposit/lib/log4j-core-2.17.1.jar:/exlibris/dps/d4_1/system.dir/dps-sdk-7.3.0/lib//../dps-sdk-projects/dps-sdk-deposit/lib/xpath2.processor-1.1.0.jar:/exlibris/dps/d4_1/system.dir/dps-sdk-7.3.0/lib//../dps-sdk-projects/dps-sdk-deposit/lib/xml-apis-1.4.01.jar:/exlibris/dps/d4_1/system.dir/dps-sdk-7.3.0/lib//../dps-sdk-projects/dps-sdk-deposit/lib/dps-sdk-7.3.0.jar:/exlibris/dps/d4_1/system.dir/dps-sdk-7.3.0/lib//../dps-sdk-projects/dps-sdk-deposit/lib/dom4j-1.6.1.jar:/exlibris/dps/d4_1/system.dir/dps-sdk-7.3.0/lib//../dps-sdk-projects/dps-sdk-deposit/lib/xmlbeans-2.3.0.jar:/exlibris/dps/d4_1/system.dir/dps-sdk-7.3.0/lib//../dps-sdk-projects/dps-sdk-deposit/lib/dps-sdk-7.3.0-javadoc.jar:/exlibris/dps/d4_1/system.dir/dps-sdk-7.3.0/lib//../dps-sdk-projects/dps-sdk-deposit/lib/commons-lang-2.6.jar:/exlibris/dps/d4_1/system.dir/dps-sdk-7.3.0/lib//../dps-sdk-projects/dps-sdk-deposit/lib/xercesImpl-2.11.0.beta.jar:/exlibris/dps/d4_1/system.dir/dps-sdk-7.3.0/lib//../dps-sdk-projects/dps-sdk-deposit/lib/log4j-api-2.17.1.jar:/exlibris/dps/d4_1/system.dir/dps-sdk-7.3.0/lib//../dps-sdk-projects/dps-sdk-deposit/lib/xalan-2.7.2.jar:/exlibris/dps/d4_1/system.dir/dps-sdk-7.3.0/lib//../dps-sdk-projects/dps-sdk-deposit/lib/jaxen-1.1-beta-6.jar:/exlibris/dps/d4_1/system.dir/dps-sdk-7.3.0/lib//../dps-sdk-projects/dps-sdk-deposit/lib/jxl-2.6.9.jar:/usr/share/java/xml-resolver-1.2.jar:XmlFormatValidationPlugin.jar org.slub.rosetta.dps.repository.plugin.XmlFormatValidationPlugin testfile.xml
diff --git a/testfile.xml b/testfile.xml
new file mode 100644
index 0000000000000000000000000000000000000000..aa601cc15c346899ff28ca2c920d7aceb99234fb
--- /dev/null
+++ b/testfile.xml
@@ -0,0 +1,3661 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
+<article article-type="research-article" dtd-version="1.3" xml:lang="en"
+ xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"
+ xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
+ <front>
+ <journal-meta>
+ <journal-id journal-id-type="pmc">pnas</journal-id>
+ <journal-id journal-id-type="pubmed">Proc Natl Acad Sci U S A</journal-id>
+ <journal-id journal-id-type="publisher">PNAS</journal-id>
+ <issn>0027-8424</issn>
+ <publisher>
+ <publisher-name>The National Academy of Sciences</publisher-name>
+ </publisher>
+ </journal-meta>
+ <article-meta>
+ <article-id pub-id-type="publisher-id">181325198</article-id>
+ <article-id pub-id-type="publisher-id">3251</article-id>
+ <article-id pub-id-type="doi">10.1073/pnas.181325198</article-id>
+ <article-id pub-id-type="other">jPNAS.v98.i18.pg10214</article-id>
+ <article-id pub-id-type="pmid">11517319</article-id>
+ <article-categories>
+ <subj-group>
+ <subject>Physical Sciences</subject>
+ <subj-group>
+ <subject>Applied Mathematics</subject>
+ </subj-group>
+ </subj-group>
+ <subj-group>
+ <subject>Biological Sciences</subject>
+ <subj-group>
+ <subject>Genetics</subject>
+ </subj-group>
+ </subj-group>
+ </article-categories>
+ <title-group>
+ <article-title>The coreceptor mutation CCR5Δ32 influences the dynamics of HIV
+ epidemics and is selected for by HIV</article-title>
+ </title-group>
+ <contrib-group>
+ <contrib contrib-type="author">
+ <name>
+ <surname>Sullivan</surname>
+ <given-names>Amy D.</given-names>
+ </name>
+ <xref ref-type="author-notes" rid="FN150">*</xref>
+ <xref ref-type="aff" rid="aff-1"/>
+ </contrib>
+ <contrib contrib-type="author">
+ <name>
+ <surname>Wigginton</surname>
+ <given-names>Janis</given-names>
+ </name>
+ <xref ref-type="aff" rid="aff-1"/>
+ </contrib>
+ <contrib contrib-type="author">
+ <name>
+ <surname>Kirschner</surname>
+ <given-names>Denise</given-names>
+ </name>
+ <xref ref-type="author-notes" rid="FN151">†</xref>
+ <xref ref-type="aff" rid="aff-1"/>
+ </contrib>
+ </contrib-group>
+ <aff id="aff-1">Department of Microbiology and Immunology, University of Michigan
+ Medical School, Ann Arbor, MI 48109-0620</aff>
+ <author-notes>
+ <fn id="FN150">
+ <p>* Present address: Centers for Disease Control and Prevention
+ Epidemiology Program Office, State Branch Oregon Health Division, 800 NE
+ Oregon Street, Suite 772, Portland, OR 97232.</p>
+ </fn>
+ <fn id="FN151">
+ <p>† To whom reprint requests should be addressed. E-mail:
+ <email>kirschne@umich.edu</email>.</p>
+ </fn>
+ <fn fn-type="com">
+ <p>Communicated by Avner Friedman, University of Minnesota, Minneapolis, MN</p>
+ </fn>
+ </author-notes>
+ <pub-date date-type="pub" publication-format="print" iso-8601-date="2001-08-28">
+ <day>28</day>
+ <month>8</month>
+ <year>2001</year>
+ </pub-date>
+ <pub-date date-type="pub" publication-format="electronic" iso-8601-date="2001-08-21">
+ <day>21</day>
+ <month>8</month>
+ <year>2001</year>
+ </pub-date>
+ <volume>98</volume>
+ <issue>18</issue>
+ <fpage>10214</fpage>
+ <lpage>10219</lpage>
+ <history>
+ <date date-type="received" iso-8601-date="2000-05-30">
+ <day>30</day>
+ <month>5</month>
+ <year>2000</year>
+ </date>
+ <date date-type="accepted" iso-8601-date="2001-06-27">
+ <day>27</day>
+ <month>6</month>
+ <year>2001</year>
+ </date>
+ </history>
+ <permissions>
+ <copyright-statement>Copyright © 2001, The National Academy of
+ Sciences</copyright-statement>
+ <copyright-year>2001</copyright-year>
+ </permissions>
+ <abstract>
+ <p>We explore the impact of a host genetic factor on heterosexual HIV epidemics by
+ using a deterministic mathematical model. A protective allele unequally
+ distributed across populations is exemplified in our models by the 32-bp
+ deletion in the host-cell chemokine receptor CCR5, CCR5Δ32. Individuals
+ homozygous for CCR5Δ32 are protected against HIV infection whereas those
+ heterozygous for CCR5Δ32 have lower pre-AIDS viral loads and delayed
+ progression to AIDS. CCR5Δ32 may limit HIV spread by decreasing the
+ probability of both risk of infection and infectiousness. In this work, we
+ characterize epidemic HIV within three dynamic subpopulations: CCR5/CCR5
+ (homozygous, wild type), CCR5/CCR5Δ32 (heterozygous), and
+ CCR5Δ32/CCR5Δ32 (homozygous, mutant). Our results indicate
+ that prevalence of HIV/AIDS is greater in populations lacking the
+ CCR5Δ32 alleles (homozygous wild types only) as compared with populations
+ that include people heterozygous or homozygous for CCR5Δ32. Also, we show
+ that HIV can provide selective pressure for CCR5Δ32, increasing the
+ frequency of this allele.</p>
+ </abstract>
+ </article-meta>
+ </front>
+ <body>
+ <p>Nineteen million people have died of AIDS since the discovery of HIV in the 1980s. In
+ 1999 alone, 5.4 million people were newly infected with HIV (ref. <xref ref-type="bibr"
+ rid="B1">1</xref> and <ext-link ext-link-type="url"
+ xmlns:xlink="http://www.w3.org/1999/xlink"
+ xlink:href="http://www.unaids.org/epidemicupdate/report/Epireport.html"
+ >http://www.unaids.org/epidemicupdate/report/Epireport.html</ext-link>). (For
+ brevity, HIV-1 is referred to as HIV in this paper.) Sub-Saharan Africa has been hardest
+ hit, with more than 20% of the general population HIV-positive in some countries
+ (<xref ref-type="bibr" rid="B2">2</xref>, <xref ref-type="bibr" rid="B3">3</xref>).
+ In comparison, heterosexual epidemics in developed, market-economy countries have not
+ reached such severe levels. Factors contributing to the severity of the epidemic in
+ economically developing countries abound, including economic, health, and social
+ differences such as high levels of sexually transmitted diseases and a lack of
+ prevention programs. However, the staggering rate at which the epidemic has spread in
+ sub-Saharan Africa has not been adequately explained. The rate and severity of this
+ epidemic also could indicate a greater underlying susceptibility to HIV attributable not
+ only to sexually transmitted disease, economics, etc., but also to other more ubiquitous
+ factors such as host genetics (<xref ref-type="bibr" rid="B4">4</xref>, <xref
+ ref-type="bibr" rid="B5">5</xref>).</p>
+ <p>To exemplify the contribution of such a host genetic factor to HIV prevalence trends, we
+ consider a well-characterized 32-bp deletion in the host-cell chemokine receptor CCR5,
+ CCR5Δ32. When HIV binds to host cells, it uses the CD4 receptor on the surface of
+ host immune cells together with a coreceptor, mainly the CCR5 and CXCR4 chemokine
+ receptors (<xref ref-type="bibr" rid="B6">6</xref>). Homozygous mutations for this 32-bp
+ deletion offer almost complete protection from HIV infection, and heterozygous mutations
+ are associated with lower pre-AIDS viral loads and delayed progression to AIDS (<xref
+ ref-type="bibr" rid="B7">7</xref>–<xref ref-type="bibr" rid="B14">14</xref>).
+ CCR5Δ32 generally is found in populations of European descent, with allelic
+ frequencies ranging from 0 to 0.29 (<xref ref-type="bibr" rid="B13">13</xref>). African
+ and Asian populations studied outside the United States or Europe appear to lack the
+ CCR5Δ32 allele, with an allelic frequency of almost zero (<xref ref-type="bibr"
+ rid="B5">5</xref>, <xref ref-type="bibr" rid="B13">13</xref>). Thus, to understand
+ the effects of a protective allele, we use a mathematical model to track prevalence of
+ HIV in populations with or without CCR5Δ32 heterozygous and homozygous people and
+ also to follow the CCR5Δ32 allelic frequency.</p>
+ <p>We hypothesize that CCR5Δ32 limits epidemic HIV by decreasing infection rates, and
+ we evaluate the relative contributions to this by the probability of infection and
+ duration of infectivity. To capture HIV infection as a chronic infectious disease
+ together with vertical transmission occurring in untreated mothers, we model a dynamic
+ population (i.e., populations that vary in growth rates because of fluctuations in birth
+ or death rates) based on realistic demographic characteristics (<xref ref-type="bibr"
+ rid="B18">18</xref>). This scenario also allows tracking of the allelic frequencies
+ over time. This work considers how a specific host genetic factor affecting HIV
+ infectivity and viremia at the individual level might influence the epidemic in a
+ dynamic population and how HIV exerts selective pressure, altering the frequency of this
+ mutant allele.</p>
+ <p>CCR5 is a host-cell chemokine receptor, which is also used as a coreceptor by R5 strains
+ of HIV that are generally acquired during sexual transmission (<xref ref-type="bibr"
+ rid="B6">6</xref>, <xref ref-type="bibr" rid="B19">19</xref>–<xref
+ ref-type="bibr" rid="B25">25</xref>). As infection progresses to AIDS the virus
+ expands its repertoire of potential coreceptors to include other CC-family and
+ CXC-family receptors in roughly 50% of patients (<xref ref-type="bibr" rid="B19"
+ >19</xref>, <xref ref-type="bibr" rid="B26">26</xref>, <xref ref-type="bibr"
+ rid="B27">27</xref>). CCR5Δ32 was identified in HIV-resistant people (<xref
+ ref-type="bibr" rid="B28">28</xref>). Benefits to individuals from the mutation in
+ this allele are as follows. Persons homozygous for the CCR5Δ32 mutation are
+ almost nonexistent in HIV-infected populations (<xref ref-type="bibr" rid="B11"
+ >11</xref>, <xref ref-type="bibr" rid="B12">12</xref>) (see ref. <xref
+ ref-type="bibr" rid="B13">13</xref> for review). Persons heterozygous for the mutant
+ allele (CCR5 W/Δ32) tend to have lower pre-AIDS viral loads. Aside from the
+ beneficial effects that lower viral loads may have for individuals, there is also an
+ altruistic effect, as transmission rates are reduced for individuals with low viral
+ loads (as compared with, for example, AZT and other studies; ref. <xref ref-type="bibr"
+ rid="B29">29</xref>). Finally, individuals heterozygous for the mutant allele (CCR5
+ W/Δ32) also have a slower progression to AIDS than those homozygous for the
+ wild-type allele (CCR5 W/W) (<xref ref-type="bibr" rid="B7">7</xref>–<xref
+ ref-type="bibr" rid="B10">10</xref>), remaining in the population 2 years longer, on
+ average. Interestingly, the dearth of information on HIV disease progression in people
+ homozygous for the CCR5Δ32 allele (CCR5 Δ32/Δ32) stems from the
+ rarity of HIV infection in this group (<xref ref-type="bibr" rid="B4">4</xref>, <xref
+ ref-type="bibr" rid="B12">12</xref>, <xref ref-type="bibr" rid="B28">28</xref>).
+ However, in case reports of HIV-infected CCR5 Δ32/Δ32 homozygotes, a rapid
+ decline in CD4<sup>+</sup> T cells and a high viremia are observed, likely
+ because of initial infection with a more aggressive viral strain (such as X4 or R5X4)
+ (<xref ref-type="bibr" rid="B30">30</xref>).</p>
+ <sec>
+ <title>The Model</title>
+ <p>Because we are most concerned with understanding the severity of the epidemic in
+ developing countries where the majority of infection is heterosexual, we consider a
+ purely heterosexual model. To model the effects of the allele in the population, we
+ examine the rate of HIV spread by using an enhanced susceptible-infected-AIDS model
+ of epidemic HIV (for review see ref. <xref ref-type="bibr" rid="B31">31</xref>). Our
+ model compares two population scenarios: a CCR5 wild-type population and one with
+ CCR5Δ32 heterozygotes and homozygotes in addition to the wild type. To model
+ the scenario where there are only wild-type individuals present in the population
+ (i.e., CCR5 W/W), we track the sexually active susceptibles at time
+ <italic>t</italic> [<italic>S<sub>i,j</sub>
+ </italic>(<italic>t</italic>)], where <italic>i</italic> = 1 refers to
+ genotype (CCR5 W/W only in this case) and <italic>j</italic> is either the male or
+ female subpopulation. We also track those who are HIV-positive at time
+ <italic>t</italic> not yet having AIDS in <italic>I<sub>i,j,k</sub>
+ </italic>(<italic>t</italic>) where <italic>k</italic> refers to stage of HIV
+ infection [primary (<italic>A</italic>) or asymptomatic
+ (<italic>B</italic>)]. The total number of individuals with AIDS at time
+ <italic>t</italic> are tracked in <italic>A</italic>(<italic>t</italic>). The
+ source population are children, χ<sub>
+ <italic>i,j</italic>
+ </sub>(<italic>t</italic>), who mature into the sexually active population at time
+ <italic>t</italic> (Fig. <xref ref-type="fig" rid="F1">1</xref>, Table <xref
+ ref-type="table" rid="T1">1</xref>). We compare the model of a population
+ lacking the CCR5Δ32 allele to a demographically similar population with a
+ high frequency of the allele. When genetic heterogeneity is included, male and
+ female subpopulations are each further divided into three distinct genotypic groups,
+ yielding six susceptible subpopulations, [<italic>S<sub>i,j</sub>
+ </italic>(<italic>t</italic>), where <italic>i</italic> ranges from 1 to 3, where 1
+ = CCR5W/W; 2 = CCR5 W/Δ32; 3 = CCR5 Δ32/Δ32]. The
+ infected classes, <italic>I<sub>i,j,k</sub>
+ </italic>(<italic>t</italic>), also increase in number to account for these new
+ genotype compartments. In both settings we assume there is no treatment available
+ and no knowledge of HIV status by people in the early acute and middle asymptomatic
+ stages (both conditions exist in much of sub-Saharan Africa). In addition, we assume
+ that sexual mixing in the population occurs randomly with respect to genotype and
+ HIV disease status, all HIV-infected people eventually progress to AIDS, and no
+ barrier contraceptives are used. These last assumptions reflect both economic and
+ social conditions. </p>
+ <fig id="F1">
+ <label>Figure 1</label>
+ <caption>
+ <p>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<sub>
+ <italic>î</italic>,<italic></italic>,<italic></italic>→<italic>i</italic>,<italic>j</italic>,</sub>
+ where <italic>i</italic>,<italic>j</italic>,<italic>k</italic> is the
+ phenotype of the infected partner and
+ <italic>î</italic>,<italic></italic> is the phenotype of
+ the susceptible partner. Also shown are the different rates of disease
+ progression, γ<sub>
+ <italic>i</italic>,<italic>j</italic>,<italic>k</italic>
+ </sub>, 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.</p>
+ </caption>
+ <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="pq1813251001"
+ > </graphic>
+ </fig>
+ <table-wrap id="T1">
+ <label>Table 1</label>
+ <caption>
+ <p>Children's genotype</p>
+ </caption>
+ <table>
+ <tr>
+ <th>Parents</th>
+ <th colspan="4">Mother</th>
+ </tr>
+ <tr>
+ <td colspan="5">
+ <hr/>
+ </td>
+ </tr>
+ <tr>
+ <td>Father</td>
+ <td/>
+ <td>W/W</td>
+ <td>W/Δ32</td>
+ <td>Δ32/Δ32</td>
+ </tr>
+ <tr>
+ <td/>
+ <td>W/W</td>
+ <td>χ<sub>1,<italic>j</italic>
+ </sub>1,<italic>j</italic>
+ </td>
+ <td>χ<sub>1,<italic>j</italic>
+ </sub>1,<italic>j</italic>, χ<sub>2,<italic>j</italic>
+ </sub>2,<italic>j</italic>
+ </td>
+ <td>χ<sub>2,<italic>j</italic>
+ </sub>2,<italic>j</italic>
+ </td>
+ </tr>
+ <tr>
+ <td/>
+ <td>W/Δ32</td>
+ <td>χ<sub>1,<italic>j</italic>
+ </sub>1,<italic>j</italic>, χ<sub>2,<italic>j</italic>
+ </sub>2,<italic>j</italic>
+ </td>
+ <td>χ<sub>1,<italic>j</italic>
+ </sub>1,<italic>j</italic>, χ<sub>2,<italic>j</italic>
+ </sub>2,<italic>j</italic>, χ<sub>3,<italic>j</italic>
+ </sub>3,<italic>j</italic>
+ </td>
+ <td>χ<sub>2,<italic>j</italic>
+ </sub>2,<italic>j</italic>, χ<sub>3,<italic>j</italic>
+ </sub>3,<italic>j</italic>
+ </td>
+ </tr>
+ <tr>
+ <td/>
+ <td>Δ32/Δ32</td>
+ <td>χ<sub>2,<italic>j</italic>
+ </sub>2,<italic>j</italic>
+ </td>
+ <td>χ<sub>2,<italic>j</italic>
+ </sub>2,<italic>j</italic>, χ<sub>3,<italic>j</italic>
+ </sub>3,<italic>j</italic>
+ </td>
+ <td>χ<sub>3,<italic>j</italic>
+ </sub>3,<italic>j</italic>
+ </td>
+ </tr>
+ </table>
+ <table-wrap-foot>
+ <fn>
+ <p>χ<sub>1,<italic>j</italic>
+ </sub>1,<italic>j</italic> = wild-type children; (W/W);
+ χ<sub>2,<italic>j</italic>
+ </sub>2,<italic>j</italic> = heterozygous children
+ (W/Δ32); χ<sub>3,<italic>j</italic>
+ </sub>3,<italic>j</italic> = homozygous children
+ (Δ32/Δ32) of gender <italic>j</italic>. Children's
+ genotypes are determined by using Mendelian inheritance patterns.</p>
+ </fn>
+ </table-wrap-foot>
+ </table-wrap>
+ <sec>
+ <title>Parameter Estimates for the Model.</title>
+ <p>Estimates for rates that govern the interactions depicted in Fig. <xref
+ ref-type="fig" rid="F1">1</xref> were derived from the extensive literature
+ on HIV. Our parameters and their estimates are summarized in Tables <xref
+ ref-type="table" rid="T2">2</xref>–<xref ref-type="table" rid="T4"
+ >4</xref>. The general form of the equations describing the rates of
+ transition between population classes as depicted in Fig. <xref ref-type="fig"
+ rid="F1">1</xref> are summarized as follows: <disp-formula id="E1">
+ <tex-math id="M1">\documentclass[12pt]{minimal} \usepackage{wasysym}
+ \usepackage[substack]{amsmath} \usepackage{amsfonts}
+ \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal}
+ \usepackage{mathrsfs} \DeclareFontFamily{T1}{linotext}{}
+ \DeclareFontShape{T1}{linotext}{m}{n} { <-> linotext }{}
+ \DeclareSymbolFont{linotext}{T1}{linotext}{m}{n}
+ \DeclareSymbolFontAlphabet{\mathLINOTEXT}{linotext} \begin{document} $$
+ \frac{dS_{i,j}(t)}{dt}={\chi}_{i,j}(t)-{\mu}_{j}S_{i,j}(t)-{\lambda}_{\hat
+ {\imath},\hat {},\hat {k}{\rightarrow}i,j}S_{i,j}(t), $$ \end{document}
+ </tex-math>
+ </disp-formula>
+ <disp-formula id="E2">
+ <tex-math id="M2">\documentclass[12pt]{minimal} \usepackage{wasysym}
+ \usepackage[substack]{amsmath} \usepackage{amsfonts}
+ \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal}
+ \usepackage{mathrsfs} \DeclareFontFamily{T1}{linotext}{}
+ \DeclareFontShape{T1}{linotext}{m}{n} { <-> linotext }{}
+ \DeclareSymbolFont{linotext}{T1}{linotext}{m}{n}
+ \DeclareSymbolFontAlphabet{\mathLINOTEXT}{linotext} \begin{document} $$
+ \hspace{1em}\hspace{1em}\hspace{.167em}\frac{dI_{i,j,A}(t)}{dt}={\lambda}_{\hat
+ {\imath},\hat {},\hat
+ {k}{\rightarrow}i,j}S_{i,j}(t)-{\mu}_{j}I_{i,j,A}(t)-{\gamma}_{i,j,A}I_{i,j,A}(t),
+ $$ \end{document} </tex-math>
+ </disp-formula>
+ <disp-formula id="E3">
+ <tex-math id="M3">\documentclass[12pt]{minimal} \usepackage{wasysym}
+ \usepackage[substack]{amsmath} \usepackage{amsfonts}
+ \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal}
+ \usepackage{mathrsfs} \DeclareFontFamily{T1}{linotext}{}
+ \DeclareFontShape{T1}{linotext}{m}{n} { <-> linotext }{}
+ \DeclareSymbolFont{linotext}{T1}{linotext}{m}{n}
+ \DeclareSymbolFontAlphabet{\mathLINOTEXT}{linotext} \begin{document} $$
+ \frac{dI_{i,j,B}(t)}{dt}={\gamma}_{i,j,A}I_{i,j,A}(t)-{\mu}_{j}I_{i,j,B}(t)-{\gamma}_{i,j,B}I_{i,j,B}(t),
+ $$ \end{document} </tex-math>
+ </disp-formula>
+ <disp-formula id="E4">
+ <tex-math id="M4">\documentclass[12pt]{minimal} \usepackage{wasysym}
+ \usepackage[substack]{amsmath} \usepackage{amsfonts}
+ \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal}
+ \usepackage{mathrsfs} \DeclareFontFamily{T1}{linotext}{}
+ \DeclareFontShape{T1}{linotext}{m}{n} { <-> linotext }{}
+ \DeclareSymbolFont{linotext}{T1}{linotext}{m}{n}
+ \DeclareSymbolFontAlphabet{\mathLINOTEXT}{linotext} \begin{document} $$
+ \frac{dA(t)}{dt}={\gamma}_{i,j,B} \left( { \,\substack{ ^{3} \\ {\sum}
+ \\ _{i=1} }\, }I_{i,F,B}(t)+I_{i,M,B}(t) \right)
+ -{\mu}_{A}A(t)-{\delta}A(t), $$ \end{document} </tex-math>
+ </disp-formula> where, in addition to previously defined populations and rates
+ (with <italic>i</italic> equals genotype, <italic>j</italic> equals gender, and
+ <italic>k</italic> equals stage of infection, either <italic>A</italic> or
+ <italic>B</italic>), μ<sub>
+ <italic>j</italic>
+ </sub>, represents the non-AIDS (natural) death rate for males and females
+ respectively, and μ<sub>A</sub> is estimated by the average
+ (μ<sub>F</sub> + μ<sub>M</sub>/2). This approximation
+ allows us to simplify the model (only one AIDS compartment) without compromising
+ the results, as most people with AIDS die of AIDS (δ<sub>AIDS</sub>) and
+ very few of other causes (μ<sub>A</sub>). These estimates include values
+ that affect infectivity (λ<sub>
+ <italic>î</italic>,<italic></italic>,<italic></italic>→<italic>i</italic>,<italic>j</italic>
+ </sub>), transmission (β<sub>
+ <italic>î</italic>,<italic></italic>,<italic></italic>→<italic>i</italic>,<italic>j</italic>
+ </sub>), and disease progression (γ<sub>
+ <italic>i</italic>
+ </sub>
+ <sub>,</sub>
+ <sub>
+ <italic>j</italic>
+ </sub>
+ <sub>,</sub>
+ <sub>
+ <italic>k</italic>
+ </sub>) where the
+ <italic>î</italic>,<italic></italic>,<italic></italic>
+ notation represents the genotype, gender, and stage of infection of the infected
+ partner, and <italic>j</italic> ≠ <italic></italic>. </p>
+ <table-wrap id="T2">
+ <label>Table 2</label>
+ <caption>
+ <p>Transmission probabilities</p>
+ </caption>
+ <table>
+ <tr>
+ <th rowspan="3">HIV-infected partner
+ (îıı^^,
+ ^^, <italic>k</italic>
+ <italic>k</italic>^^)</th>
+ <th colspan="4">Susceptible partner (<italic>i</italic>,
+ <italic>j</italic>)</th>
+ </tr>
+ <tr>
+ <td colspan="4">
+ <hr/>
+ </td>
+ </tr>
+ <tr>
+ <th>(^^ to
+ <italic>j</italic>)</th>
+ <th>W/W</th>
+ <th>W/Δ32</th>
+ <th>Δ32/Δ32 </th>
+ </tr>
+ <tr>
+ <td colspan="5">
+ <hr/>
+ </td>
+ </tr>
+ <tr>
+ <td>Acute/primary</td>
+ </tr>
+ <tr>
+ <td> W/W or Δ32/Δ32</td>
+ <td>M to F</td>
+ <td>0.040</td>
+ <td>0.040</td>
+ <td>0.00040 </td>
+ </tr>
+ <tr>
+ <td/>
+ <td>F to M</td>
+ <td>0.020</td>
+ <td>0.020</td>
+ <td>0.00020 </td>
+ </tr>
+ <tr>
+ <td> W/Δ32</td>
+ <td>M to F</td>
+ <td>0.030</td>
+ <td>0.030</td>
+ <td>0.00030 </td>
+ </tr>
+ <tr>
+ <td/>
+ <td>F to M</td>
+ <td>0.015</td>
+ <td>0.015</td>
+ <td>0.00015 </td>
+ </tr>
+ <tr>
+ <td>Asymptomatic </td>
+ </tr>
+ <tr>
+ <td> W/W or Δ32/Δ32</td>
+ <td>M to F</td>
+ <td>0.0010</td>
+ <td>0.0010</td>
+ <td>10 × 10<sup>−6</sup>
+ </td>
+ </tr>
+ <tr>
+ <td/>
+ <td>F to M</td>
+ <td>0.0005</td>
+ <td>0.0005</td>
+ <td>5 × 10<sup>−6</sup>
+ </td>
+ </tr>
+ <tr>
+ <td> W/Δ32</td>
+ <td>M to F</td>
+ <td>0.0005</td>
+ <td>0.0005</td>
+ <td>5 × 10<sup>−6</sup>
+ </td>
+ </tr>
+ <tr>
+ <td/>
+ <td>F to M</td>
+ <td>0.00025</td>
+ <td>0.00025</td>
+ <td>2.5 × 10<sup>−6</sup>
+ </td>
+ </tr>
+ </table>
+ <table-wrap-foot>
+ <fn>
+ <p>Listed are the different transmission probabilities
+ (β<sub>îıı^^,^^,<italic>k</italic>
+ <italic>k</italic>^^→<italic>i</italic>,<italic>j</italic>
+ </sub>) for random sexual mixing between persons where
+ <italic>i</italic>, <italic>j</italic>, <italic>k</italic> is
+ the phenotype of the infected partner and <italic>i</italic>,
+ <italic>j</italic> is the phenotype of the susceptible partner.
+ M, male; F, female.</p>
+ </fn>
+ </table-wrap-foot>
+ </table-wrap>
+ <table-wrap id="T3">
+ <label>Table 3</label>
+ <caption>
+ <p>Progression rates</p>
+ </caption>
+ <table>
+ <tr>
+ <th>Genotype</th>
+ <th>Disease stage</th>
+ <th>Males/females </th>
+ </tr>
+ <tr>
+ <td colspan="3">
+ <hr/>
+ </td>
+ </tr>
+ <tr>
+ <td>W/W</td>
+ <td>A</td>
+ <td>3.5</td>
+ </tr>
+ <tr>
+ <td/>
+ <td>B</td>
+ <td>0.16667 </td>
+ </tr>
+ <tr>
+ <td>W/Δ32</td>
+ <td>A</td>
+ <td>3.5 </td>
+ </tr>
+ <tr>
+ <td/>
+ <td>B</td>
+ <td>0.125</td>
+ </tr>
+ <tr>
+ <td>Δ32/Δ32</td>
+ <td>A</td>
+ <td>3.5 </td>
+ </tr>
+ <tr>
+ <td/>
+ <td>B</td>
+ <td>0.16667</td>
+ </tr>
+ </table>
+ <table-wrap-foot>
+ <fn>
+ <p>Shown are the rates of progression, γ<sub>
+ <italic>i</italic>,<italic>j</italic>,<italic>k</italic>
+ </sub>
+ <italic>i</italic>,<italic>j</italic>,<italic>k</italic> reflecting
+ the different rates at which persons progress through different
+ stages of disease by genotype, gender, and disease stage.</p>
+ </fn>
+ </table-wrap-foot>
+ </table-wrap>
+ <table-wrap id="T4">
+ <label>Table 4</label>
+ <caption>
+ <p>Parameter values</p>
+ </caption>
+ <table>
+ <tr>
+ <th>Parameter</th>
+ <th>Definition</th>
+ <th>Value</th>
+ </tr>
+ <tr>
+ <td colspan="3">
+ <hr/>
+ </td>
+ </tr>
+ <tr>
+ <td>μ<sub>
+ <italic>F</italic>
+ </sub>
+ <italic>F</italic>, μ<sub>
+ <italic>M</italic>
+ </sub>
+ <italic>M</italic>
+ </td>
+ <td align="left">All-cause mortality for adult females (males)</td>
+ <td align="left">0.015 (0.016) per year</td>
+ </tr>
+ <tr>
+ <td>μ<sub>χ</sub>χ</td>
+ <td align="left">All-cause childhood mortality (<15 years of
+ age)</td>
+ <td align="left">0.01 per year</td>
+ </tr>
+ <tr>
+ <td>
+ <italic>B</italic>
+ <sub>
+ <italic>r</italic>
+ </sub>
+ <italic>r</italic>
+ </td>
+ <td align="left">Birthrate</td>
+ <td align="left">0.25 per woman per year</td>
+ </tr>
+ <tr>
+ <td>
+ <italic>SA</italic>
+ <sub>
+ <italic>F</italic>
+ </sub>
+ <italic>F</italic>
+ </td>
+ <td align="left">Percent females acquiring new partners (sexual
+ activity)</td>
+ <td align="left">10%</td>
+ </tr>
+ <tr>
+ <td>
+ <italic>SA</italic>
+ <sub>
+ <italic>M</italic>
+ </sub>
+ <italic>M</italic>
+ </td>
+ <td align="left">Percent males acquiring new partners (sexual
+ activity)</td>
+ <td align="left">25%</td>
+ </tr>
+ <tr>
+ <td>
+ <italic>m</italic>
+ <sub>
+ <italic>F</italic>
+ </sub>
+ <italic>F</italic>(ς<inline-formula>
+ <tex-math id="M5">\documentclass[12pt]{minimal}
+ \usepackage{wasysym} \usepackage[substack]{amsmath}
+ \usepackage{amsfonts} \usepackage{amssymb}
+ \usepackage{amsbsy} \usepackage[mathscr]{eucal}
+ \usepackage{mathrsfs} \DeclareFontFamily{T1}{linotext}{}
+ \DeclareFontShape{T1}{linotext}{m}{n} { <->
+ linotext }{}
+ \DeclareSymbolFont{linotext}{T1}{linotext}{m}{n}
+ \DeclareSymbolFontAlphabet{\mathLINOTEXT}{linotext}
+ \begin{document} $$ {\mathrm{_{{F}}^{{2}}}} $$
+ \end{document} </tex-math>
+ </inline-formula>)</td>
+ <td align="left">Mean (variance) no. of new partners for females</td>
+ <td align="left">1.8 (1.2) per year</td>
+ </tr>
+ <tr>
+ <td>ς<inline-formula>
+ <tex-math id="M6">\documentclass[12pt]{minimal}
+ \usepackage{wasysym} \usepackage[substack]{amsmath}
+ \usepackage{amsfonts} \usepackage{amssymb}
+ \usepackage{amsbsy} \usepackage[mathscr]{eucal}
+ \usepackage{mathrsfs} \DeclareFontFamily{T1}{linotext}{}
+ \DeclareFontShape{T1}{linotext}{m}{n} { <->
+ linotext }{}
+ \DeclareSymbolFont{linotext}{T1}{linotext}{m}{n}
+ \DeclareSymbolFontAlphabet{\mathLINOTEXT}{linotext}
+ \begin{document} $$ {\mathrm{_{{M}}^{{2}}}} $$
+ \end{document} </tex-math>
+ </inline-formula>
+ </td>
+ <td align="left">Variance in no. of new partners for males</td>
+ <td align="left">5.5 per year </td>
+ </tr>
+ <tr>
+ <td>1 − <italic>p</italic>
+ <sub>
+ <italic>v</italic>
+ </sub>
+ <italic>v</italic>
+ </td>
+ <td align="left">Probability of vertical transmission</td>
+ <td align="left">0.30 per birth</td>
+ </tr>
+ <tr>
+ <td>
+ <italic>I</italic>
+ <sub>
+ <italic>i</italic>,<italic>j</italic>,<italic>k</italic>
+ </sub>
+ <italic>i</italic>,<italic>j</italic>,<italic>k</italic>(0)</td>
+ <td align="left">Initial total population HIV-positive</td>
+ <td align="left">0.50% </td>
+ </tr>
+ <tr>
+ <td>χ<sub>
+ <italic>i</italic>,<italic>j</italic>
+ </sub>
+ <italic>i</italic>,<italic>j</italic>(0)</td>
+ <td align="left">Initial total children in population (<15 years
+ of age)</td>
+ <td align="left">45%</td>
+ </tr>
+ <tr>
+ <td>
+ <italic>W</italic>/<italic>W</italic> (0)</td>
+ <td align="left">Initial total wild types
+ (<italic>W</italic>/<italic>W</italic>) in
+ population</td>
+ <td align="left">80% </td>
+ </tr>
+ <tr>
+ <td>
+ <italic>W</italic>/Δ32(0)</td>
+ <td align="left">Initial total heterozygotes
+ (<italic>W</italic>/Δ32) in population</td>
+ <td align="left">19%</td>
+ </tr>
+ <tr>
+ <td>Δ32/Δ32(0)</td>
+ <td align="left">Initial total homozygotes
+ (Δ32/Δ32) in population</td>
+ <td align="left">1%</td>
+ </tr>
+ <tr>
+ <td>
+ <italic>r</italic>
+ <sub>
+ <italic>M</italic>
+ </sub>
+ <italic>M</italic>(<italic>r</italic>
+ <sub>
+ <italic>F</italic>
+ </sub>
+ <italic>F</italic>)</td>
+ <td align="left">Initial percent males (females) in total
+ population</td>
+ <td align="left">49% (51%)</td>
+ </tr>
+ <tr>
+ <td>ϕ<sub>
+ <italic>F</italic>
+ </sub>
+ <italic>F</italic>, ϕ<sub>
+ <italic>M</italic>
+ </sub>
+ <italic>M</italic>
+ </td>
+ <td align="left">Number of sexual contacts a female (male) has</td>
+ <td align="left">30 (24) per partner</td>
+ </tr>
+ <tr>
+ <td>ɛ<sub>
+ <italic>i</italic>,<italic>j</italic>,<italic>k</italic>
+ </sub>
+ <italic>i</italic>,<italic>j</italic>,<italic>k</italic>
+ </td>
+ <td align="left">% effect of mutation on transmission rates (see
+ Table <xref ref-type="table" rid="T2">2</xref>)</td>
+ <td align="left">0 < ɛ<sub>
+ <italic>i</italic>,<italic>j</italic>,<italic>k</italic>
+ </sub>
+ <italic>i</italic>,<italic>j</italic>,<italic>k</italic> <
+ 1</td>
+ </tr>
+ <tr>
+ <td>δ</td>
+ <td align="left">Death rate for AIDS population</td>
+ <td align="left">1.0 per year </td>
+ </tr>
+ <tr>
+ <td>
+ <italic>q</italic>
+ </td>
+ <td align="left">Allelic frequency of Δ32 allele</td>
+ <td align="left">0.105573</td>
+ </tr>
+ </table>
+ <table-wrap-foot>
+ <fn>
+ <p>Shown are the parameter values for parameters other than the
+ transmission probabilities (Table <xref ref-type="table" rid="T2"
+ >2</xref>) and the progression rates (Table <xref
+ ref-type="table" rid="T3">3</xref>). Each were estimated from
+ data as described in text.</p>
+ </fn>
+ </table-wrap-foot>
+ </table-wrap>
+ <p>The effects of the CCR5 W/Δ32 and CCR5 Δ32/Δ32 genotypes are
+ included in our model through both the per-capita probabilities of infection, λ<sub>
+ <italic>î</italic>,<italic></italic>,<italic></italic>→<italic>i</italic>,<italic>j</italic>
+ </sub>, and the progression rates, γ<sub>
+ <italic>i</italic>
+ </sub>
+ <sub>,</sub>
+ <sub>
+ <italic>j</italic>
+ </sub>
+ <sub>,</sub>
+ <sub>
+ <italic>k</italic>
+ </sub>. The infectivity coefficients, λ<sub>
+ <italic>î</italic>,<italic></italic>,<italic></italic>→<italic>i</italic>,<italic>j</italic>
+ </sub>, are calculated for each population subgroup based on the following:
+ likelihood of HIV transmission in a sexual encounter between a susceptible and
+ an infected
+ (β<sub>îıı^^,<italic>j</italic>,<italic>k</italic>
+ <italic>k</italic>^^→<italic>i</italic>,<italic>j</italic>
+ </sub>) person; formation of new partnerships (<italic>c</italic>
+ <sub>
+ <italic>j</italic>
+ </sub>
+ <italic>j</italic>); number of contacts in a given partnership (ϕ<sub>
+ <italic>j</italic>
+ </sub>); and probability of encountering an infected individual
+ (<italic>I</italic>
+ <sub>
+ <italic>î</italic>,<italic></italic>,<italic></italic>
+ </sub>/<italic>N</italic>
+ <sub>
+ <italic></italic>
+ </sub>). The formula representing this probability of infection is <disp-formula>
+ <tex-math id="M7">\documentclass[12pt]{minimal} \usepackage{wasysym}
+ \usepackage[substack]{amsmath} \usepackage{amsfonts}
+ \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal}
+ \usepackage{mathrsfs} \DeclareFontFamily{T1}{linotext}{}
+ \DeclareFontShape{T1}{linotext}{m}{n} { <-> linotext }{}
+ \DeclareSymbolFont{linotext}{T1}{linotext}{m}{n}
+ \DeclareSymbolFontAlphabet{\mathLINOTEXT}{linotext} \begin{document} $$
+ {\lambda}_{\hat {i},\hat {j},\hat
+ {k}{\rightarrow}i,j}=\frac{C_{j}{\cdot}{\phi}_{j}}{N_{\hat
+ {j}}}\hspace{.167em} \left[ { \,\substack{ \\ {\sum} \\ _{\hat {i},\hat
+ {k}} }\, }{\beta}_{\hat {i},\hat {j},\hat
+ {k}{\rightarrow}i,j}{\cdot}I_{\hat {i},\hat {j},\hat {k}} \right] , $$
+ \end{document} </tex-math>
+ </disp-formula> where <italic>j</italic> ≠ <italic></italic> is
+ either male or female. <italic>N</italic>
+ <sub>
+ <italic></italic>
+ </sub> represents the total population of gender <italic></italic> (this
+ does not include those with AIDS in the simulations).</p>
+ <p>The average rate of partner acquisition, <italic>c<sub>j</sub>
+ </italic>, includes the mean plus the variance to mean ratio of the relevant
+ distribution of partner-change rates to capture the small number of high-risk
+ people: <italic>c<sub>j</sub>
+ </italic> = <italic>m<sub>j</sub>
+ </italic> + (ς<inline-formula>
+ <tex-math id="M8">\documentclass[12pt]{minimal} \usepackage{wasysym}
+ \usepackage[substack]{amsmath} \usepackage{amsfonts}
+ \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal}
+ \usepackage{mathrsfs} \DeclareFontFamily{T1}{linotext}{}
+ \DeclareFontShape{T1}{linotext}{m}{n} { <-> linotext }{}
+ \DeclareSymbolFont{linotext}{T1}{linotext}{m}{n}
+ \DeclareSymbolFontAlphabet{\mathLINOTEXT}{linotext} \begin{document} $$
+ {\mathrm{_{{\mathit{j}}}^{2}}} $$ \end{document} </tex-math>
+ </inline-formula>/<italic>m</italic>
+ <sub>j</sub>) where the mean (<italic>m<sub>j</sub>
+ </italic>) and variance (ς<inline-formula>
+ <tex-math id="M9">\documentclass[12pt]{minimal} \usepackage{wasysym}
+ \usepackage[substack]{amsmath} \usepackage{amsfonts}
+ \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal}
+ \usepackage{mathrsfs} \DeclareFontFamily{T1}{linotext}{}
+ \DeclareFontShape{T1}{linotext}{m}{n} { <-> linotext }{}
+ \DeclareSymbolFont{linotext}{T1}{linotext}{m}{n}
+ \DeclareSymbolFontAlphabet{\mathLINOTEXT}{linotext} \begin{document} $$
+ {\mathrm{_{{\mathit{j}}}^{2}}} $$ \end{document} </tex-math>
+ </inline-formula>) are annual figures for new partnerships only (<xref
+ ref-type="bibr" rid="B32">32</xref>). These means are estimated from Ugandan
+ data for the number of heterosexual partners in the past year (<xref
+ ref-type="bibr" rid="B33">33</xref>) and the number of nonregular
+ heterosexual partners (i.e., spouses or long-term partners) in the past year
+ (<xref ref-type="bibr" rid="B34">34</xref>). In these sexual activity
+ surveys, men invariably have more new partnerships; thus, we assumed that they
+ would have fewer average contacts per partnership than women (a higher rate of
+ new partner acquisition means fewer sexual contacts with a given partner; ref.
+ <xref ref-type="bibr" rid="B35">35</xref>). To incorporate this assumption
+ in our model, the male contacts/partnership, ϕ<sub>
+ <italic>M</italic>
+ </sub>, was reduced by 20%. In a given population, the numbers of
+ heterosexual interactions must equate between males and females. The balancing
+ equation applied here is <italic>SA</italic>
+ <sub>F</sub>·<italic>m</italic>
+ <sub>F</sub>·<italic>N</italic>
+ <sub>F</sub> = <italic>SA</italic>
+ <sub>M</sub>·<italic>m</italic>
+ <sub>M</sub>·<italic>N</italic>
+ <sub>M</sub>, where <italic>SA<sub>j</sub>
+ </italic> are the percent sexually active and <italic>N<sub>j</sub>
+ </italic> are the total in the populations for gender <italic>j</italic>. To
+ specify changes in partner acquisition, we apply a male flexibility mechanism,
+ holding the female rate of acquisition constant and allowing the male rates to
+ vary (<xref ref-type="bibr" rid="B36">36</xref>, <xref ref-type="bibr" rid="B37"
+ >37</xref>).</p>
+ <sec>
+ <title>Transmission probabilities.</title>
+ <p>The effect of a genetic factor in a model of HIV transmission can be included
+ by reducing the transmission coefficient. The probabilities of transmission
+ per contact with an infected partner,
+ β<sub>îıı^^,^^,<italic>k</italic>
+ <italic>k</italic>^^→<italic>i</italic>,<italic>j</italic>
+ </sub>, have been estimated in the literature (see ref. <xref
+ ref-type="bibr" rid="B38">38</xref> for estimates in minimally treated
+ groups). We want to capture a decreased risk in transmission based on
+ genotype (ref. <xref ref-type="bibr" rid="B39">39</xref>, Table <xref
+ ref-type="table" rid="T2">2</xref>). No studies have directly evaluated
+ differences in infectivity between HIV-infected CCR5 W/Δ32
+ heterozygotes and HIV-infected CCR5 wild types. Thus, we base estimates for
+ reduced transmission on studies of groups with various HIV serum viral loads
+ (<xref ref-type="bibr" rid="B40">40</xref>), HTLV-I/II viral loads
+ (<xref ref-type="bibr" rid="B41">41</xref>), and a study of the effect
+ of AZT treatment on transmission (<xref ref-type="bibr" rid="B29"
+ >29</xref>). We decrease transmission probabilities for infecting
+ CCR5Δ32/Δ32 persons by 100-fold to reflect the rarity of
+ infections in these persons. However, we assume that infected
+ CCR5Δ32/Δ32 homozygotes can infect susceptibles at a rate
+ similar to CCR5W/W homozygotes, as the former generally have high viremias
+ (ref. <xref ref-type="bibr" rid="B30">30</xref>, Table <xref
+ ref-type="table" rid="T2">2</xref>). We also assume that male-to-female
+ transmission is twice as efficient as female-to-male transmission (up to a
+ 9-fold difference has been reported; ref. <xref ref-type="bibr" rid="B42"
+ >42</xref>) (ref. <xref ref-type="bibr" rid="B43">43</xref>, Table <xref
+ ref-type="table" rid="T2">2</xref>).</p>
+ <p>Given the assumption of no treatment, the high burden of disease in people
+ with AIDS is assumed to greatly limit their sexual activity. Our initial
+ model excludes people with AIDS from the sexually active groups.
+ Subsequently, we allow persons with AIDS to be sexually active, fixing their
+ transmission rates (β<sub>AIDS</sub>) to be the same across all CCR5
+ genotypes, and lower than transmission rates for primary-stage infection (as
+ the viral burden on average is not as high as during the acute phase), and
+ larger than transmission rates for asymptomatic-stage infection (as the
+ viral burden characteristically increases during the end stage of
+ disease).</p>
+ </sec>
+ <sec>
+ <title>Disease progression.</title>
+ <p>We assume three stages of HIV infection: primary (acute, stage A),
+ asymptomatic HIV (stage B), and AIDS. The rates of transition through the
+ first two stages are denoted by γ<sub>
+ <italic>i</italic>,<italic>j</italic>,<italic>k</italic>
+ </sub>
+ <italic>i</italic>,<italic>j</italic>,<italic>k</italic>, where
+ <italic>i</italic> represents genotype, <italic>j</italic> is
+ male/female, and <italic>k</italic> represents either stage A or stage B.
+ Transition rates through each of these stages are assumed to be inversely
+ proportional to the duration of that stage; however, other distributions are
+ possible (<xref ref-type="bibr" rid="B31">31</xref>, <xref ref-type="bibr"
+ rid="B44">44</xref>, <xref ref-type="bibr" rid="B45">45</xref>).
+ Although viral loads generally peak in the first 2 months of infection,
+ steady-state viral loads are established several months beyond this (<xref
+ ref-type="bibr" rid="B46">46</xref>). For group A, the primary
+ HIV-infecteds, duration is assumed to be 3.5 months. Based on results from
+ European cohort studies (<xref ref-type="bibr" rid="B7"
+ >7</xref>–<xref ref-type="bibr" rid="B10">10</xref>), the
+ beneficial effects of the CCR5 W/Δ32 genotype are observed mainly in
+ the asymptomatic years of HIV infection; ≈7 years after
+ seroconversion survival rates appear to be quite similar between
+ heterozygous and homozygous individuals. We also assume that
+ CCR5Δ32/Δ32-infected individuals and wild-type individuals
+ progress similarly, and that men and women progress through each disease
+ stage at the same rate. Given these observations, and that survival after
+ infection may be shorter in untreated populations, we choose the duration
+ time in stage B to be 6 years for wild-type individuals and 8 years for
+ heterozygous individuals. Transition through AIDS, δ<sub>AIDS</sub>,
+ is inversely proportional to the duration of AIDS. We estimate this value to
+ be 1 year for the time from onset of AIDS to death. The progression rates
+ are summarized in Table <xref ref-type="table" rid="T3">3</xref>.</p>
+ </sec>
+ </sec>
+ <sec>
+ <title>Demographic Setting.</title>
+ <p>Demographic parameters are based on data from Malawi, Zimbabwe, and Botswana
+ (<xref ref-type="bibr" rid="B3">3</xref>, <xref ref-type="bibr" rid="B47"
+ >47</xref>). Estimated birth and child mortality rates are used to calculate
+ the annual numbers of children (χ<sub>
+ <italic>i</italic>,<italic>j</italic>
+ </sub>
+ <italic>i</italic>,<italic>j</italic>) maturing into the potentially sexually
+ active, susceptible group at the age of 15 years (<xref ref-type="bibr" rid="B3"
+ >3</xref>). For example, in the case where the mother is CCR5 wild type and
+ the father is CCR5 wild type or heterozygous, the number of CCR5 W/W children is
+ calculated as follows [<italic>s</italic>uppressing (<italic>t</italic>)
+ notation]: χ<sub>1,<italic>j</italic>
+ </sub>1,<italic>j</italic> = <disp-formula>
+ <tex-math id="M10">\documentclass[12pt]{minimal} \usepackage{wasysym}
+ \usepackage[substack]{amsmath} \usepackage{amsfonts}
+ \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal}
+ \usepackage{mathrsfs} \DeclareFontFamily{T1}{linotext}{}
+ \DeclareFontShape{T1}{linotext}{m}{n} { <-> linotext }{}
+ \DeclareSymbolFont{linotext}{T1}{linotext}{m}{n}
+ \DeclareSymbolFontAlphabet{\mathLINOTEXT}{linotext} \begin{document} $$
+ B_{r}\hspace{.167em}{ \,\substack{ \\ {\sum} \\ _{k} }\, } \left[
+ S_{1,F}\frac{(S_{1,M}+I_{1,M,k})}{N_{M}}+ \left[
+ (0.5)S_{1,F}\frac{(S_{2,M}+I_{2,M,k})}{N_{M}} \right] + \right $$
+ \end{document} </tex-math>
+ </disp-formula>
+ <disp-formula>
+ <tex-math id="M11">\documentclass[12pt]{minimal} \usepackage{wasysym}
+ \usepackage[substack]{amsmath} \usepackage{amsfonts}
+ \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal}
+ \usepackage{mathrsfs} \DeclareFontFamily{T1}{linotext}{}
+ \DeclareFontShape{T1}{linotext}{m}{n} { <-> linotext }{}
+ \DeclareSymbolFont{linotext}{T1}{linotext}{m}{n}
+ \DeclareSymbolFontAlphabet{\mathLINOTEXT}{linotext} \begin{document} $$
+ p_{v} \left \left( \frac{(I_{1,F,k}(S_{1,M}+I_{1,M,k}))}{N_{M}}+ \left[
+ (0.5)I_{1,F,k}\frac{(S_{2,M}+I_{2,M,k})}{N_{M}} \right] \right) \right]
+ ,\hspace{.167em} $$ \end{document} </tex-math>
+ </disp-formula> where the probability of HIV vertical transmission, 1 −
+ <italic>p<sub>v</sub>
+ </italic>, and the birthrate, <italic>B<sub>r</sub>
+ </italic>, are both included in the equations together with the Mendelian
+ inheritance values as presented in Table <xref ref-type="table" rid="T1"
+ >1</xref>. The generalized version of this equation (i.e., χ<sub>
+ <italic>i</italic>,<italic>j</italic>
+ </sub>
+ <italic>i</italic>,<italic>j</italic>) can account for six categories of
+ children (including gender and genotype). We assume that all children of all
+ genotypes are at risk, although we can relax this condition if data become
+ available to support vertical protection (e.g., ref. <xref ref-type="bibr"
+ rid="B48">48</xref>). All infected children are assumed to die before age
+ 15. Before entering the susceptible group at age 15, there is additional loss
+ because of mortality from all non-AIDS causes occurring less than 15 years of
+ age at a rate of μ<sub>χ</sub>χ × χ<sub>
+ <italic>i</italic>,<italic>j</italic>
+ </sub>
+ <italic>i</italic>,<italic>j</italic> (where μ<sub>χ</sub> is the
+ mortality under 15 years of age). Children then enter the population as
+ susceptibles at an annual rate, ς<sub>
+ <italic>j</italic>
+ </sub>
+ <italic>j</italic> × χ<sub>
+ <italic>i</italic>,<italic>j</italic>
+ </sub>
+ <italic>i</italic>,<italic>j</italic>/15, where ς<sub>
+ <italic>j</italic>
+ </sub> distributes the children 51% females and 49% males. All
+ parameters and their values are summarized in Table <xref ref-type="table"
+ rid="T4">4</xref>.</p>
+ </sec>
+ </sec>
+ <sec>
+ <title>Prevalence of HIV</title>
+ <sec>
+ <title>Demographics and Model Validation.</title>
+ <p>The model was validated by using parameters estimated from available demographic
+ data. Simulations were run in the absence of HIV infection to compare the model
+ with known population growth rates. Infection was subsequently introduced with
+ an initial low HIV prevalence of 0.5% to capture early epidemic
+ behavior.</p>
+ <p>In deciding on our initial values for parameters during infection, we use Joint
+ United Nations Programme on HIV/AIDS national prevalence data for Malawi,
+ Zimbabwe, and Botswana. Nationwide seroprevalence of HIV in these countries
+ varies from ≈11% to over 20% (<xref ref-type="bibr"
+ rid="B3">3</xref>), although there may be considerable variation within
+ given subpopulations (<xref ref-type="bibr" rid="B2">2</xref>, <xref
+ ref-type="bibr" rid="B49">49</xref>).</p>
+ <p>In the absence of HIV infection, the annual percent population growth rate in the
+ model is ≈2.5%, predicting the present-day values for an average
+ of sub-Saharan African cities (data not shown). To validate the model with HIV
+ infection, we compare our simulation of the HIV epidemic to existing prevalence
+ data for Kenya and Mozambique (<ext-link ext-link-type="url"
+ xmlns:xlink="http://www.w3.org/1999/xlink"
+ xlink:href="http://www.who.int/emc-hiv/fact-sheets/pdfs/kenya.pdf"
+ >http://www.who.int/emc-hiv/fact-sheets/pdfs/kenya.pdf</ext-link> and ref.
+ <xref ref-type="bibr" rid="B51">51</xref>). Prevalence data collected from
+ these countries follow similar trajectories to those predicted by our model
+ (Fig. <xref ref-type="fig" rid="F2">2</xref>). </p>
+ <fig id="F2">
+ <label>Figure 2</label>
+ <caption>
+ <p>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. <xref ref-type="bibr"
+ rid="B17">17</xref>). 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.</p>
+ </caption>
+ <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="pq1813251002"
+ > </graphic>
+ </fig>
+ </sec>
+ <sec>
+ <title>Effects of the Allele on Prevalence.</title>
+ <p>After validating the model in the wild type-only population, both CCR5Δ32
+ heterozygous and homozygous people are included. Parameter values for HIV
+ transmission, duration of illness, and numbers of contacts per partner are
+ assumed to be the same within both settings. We then calculate HIV/AIDS
+ prevalence among adults for total HIV/AIDS cases.</p>
+ <p>Although CCR5Δ32/Δ32 homozygosity is rarely seen in HIV-positive
+ populations (prevalence ranges between 0 and 0.004%), 1–20%
+ of people in HIV-negative populations of European descent are homozygous. Thus,
+ to evaluate the potential impact of CCR5Δ32, we estimate there are
+ 19% CCR5 W/Δ32 heterozygous and 1% CCR5
+ Δ32/Δ32 homozygous people in our population. These values are in
+ Hardy-Weinberg equilibrium with an allelic frequency of the mutation as
+ 0.105573.</p>
+ <p>Fig. <xref ref-type="fig" rid="F3">3</xref> shows the prevalence of HIV in two
+ populations: one lacking the mutant CCR5 allele and another carrying that
+ allele. In the population lacking the protective mutation, prevalence increases
+ logarithmically for the first 35 years of the epidemic, reaching 18%
+ before leveling off. </p>
+ <fig id="F3">
+ <label>Figure 3</label>
+ <caption>
+ <p>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.</p>
+ </caption>
+ <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="pq1813251003"
+ > </graphic>
+ </fig>
+ <p>In contrast, when a proportion of the population carries the CCR5Δ32
+ allele, the epidemic increases more slowly, but still logarithmically, for the
+ first 50 years, and HIV/AIDS prevalence reaches ≈12% (Fig. <xref
+ ref-type="fig" rid="F3">3</xref>). Prevalence begins to decline slowly after
+ 70 years.</p>
+ <p>In the above simulations we assume that people with AIDS are not sexually active.
+ However, when these individuals are included in the sexually active population
+ the severity of the epidemic increases considerably (data not shown). Consistent
+ with our initial simulations, prevalences are still relatively lower in the
+ presence of the CCR5 mutation.</p>
+ <p>Because some parameters (e.g., rate constants) are difficult to estimate based on
+ available data, we implement an uncertainty analysis to assess the variability
+ in the model outcomes caused by any inaccuracies in estimates of the parameter
+ values with regard to the effect of the allelic mutation. For these analyses we
+ use Latin hypercube sampling, as described in refs. <xref ref-type="bibr"
+ rid="B52">52</xref>–<xref ref-type="bibr" rid="B56">56</xref>, Our
+ uncertainty and sensitivity analyses focus on infectivity vs. duration of
+ infectiousness. To this end, we assess the effects on the dynamics of the
+ epidemic for a range of values of the parameters governing transmission and
+ progression rates:
+ β<sub>îıı^^,^^,<italic>k</italic>
+ <italic>k</italic>^^→<italic>i</italic>,<italic>j</italic>
+ </sub> and γ<sub>
+ <italic>i</italic>,<italic>j</italic>,<italic>k</italic>
+ </sub>
+ <italic>i</italic>,<italic>j</italic>,<italic>k</italic>. All other parameters
+ are held constant. These results are presented as an interval band about the
+ average simulation for the population carrying the CCR5Δ32 allele (Fig.
+ <xref ref-type="fig" rid="F3">3</xref>). Although there is variability in
+ the model outcomes, the analysis indicates that the overall model predictions
+ are consistent for a wide range of transmission and progression rates. Further,
+ most of the variation observed in the outcome is because of the transmission
+ rates for both heterosexual males and females in the primary stage of infection
+ (β<sub>2,M,A</sub>
+ <sub>→</sub>
+ <sub>
+ <italic>i</italic>
+ </sub>
+ <sub>,F</sub>, β<sub>2,F,A</sub>
+ <sub>→</sub>
+ <sub>
+ <italic>i</italic>
+ </sub>
+ <sub>,M</sub>). As mentioned above, we assume lower viral loads correlate with
+ reduced infectivity; thus, the reduction in viral load in heterozygotes has a
+ major influence on disease spread.</p>
+ </sec>
+ </sec>
+ <sec>
+ <title>HIV Induces Selective Pressure on Genotype Frequency</title>
+ <p>To observe changes in the frequency of the CCR5Δ32 allele in a setting with
+ HIV infection as compared with the Hardy-Weinberg equilibrium in the absence of HIV,
+ we follow changes in the total number of CCR5Δ32 heterozygotes and
+ homozygotes over 1,000 years (Fig. <xref ref-type="fig" rid="F4">4</xref>). We
+ initially perform simulations in the absence of HIV infection as a negative control
+ to show there is not significant selection of the allele in the absence of
+ infection. To determine how long it would take for the allelic frequency to reach
+ present-day levels (e.g., <italic>q</italic> = 0.105573), we initiate this
+ simulation for 1,000 years with a very small allelic frequency (<italic>q</italic> =
+ 0.00105). In the absence of HIV, the allelic frequency is maintained in equilibrium
+ as shown by the constant proportions of CCR5Δ32 heterozygotes and homozygotes
+ (Fig. <xref ref-type="fig" rid="F4">4</xref>, solid lines). The selection for
+ CCR5Δ32 in the presence of HIV is seen in comparison (Fig. <xref
+ ref-type="fig" rid="F4">4</xref>, dashed lines). We expand the time frame of
+ this simulation to 2,000 years to view the point at which the frequency reaches
+ present levels (where <italic>q</italic> ∼0.105573 at year = 1200). Note that
+ the allelic frequency increases for ≈1,600 years before leveling off. </p>
+ <fig id="F4">
+ <label>Figure 4</label>
+ <caption>
+ <p>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: (<italic>A</italic>) wild types (W/W), (<italic>B</italic>)
+ heterozygotes (W/Δ32), and (<italic>C</italic>) 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.
+ (<italic>D</italic>) The allelic selection effect over a 2,000-year time
+ scale.</p>
+ </caption>
+ <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="pq1813251004"
+ > </graphic>
+ </fig>
+ </sec>
+ <sec sec-type="discussion">
+ <title>Discussion</title>
+ <p>This study illustrates how populations can differ in susceptibility to epidemic
+ HIV/AIDS depending on a ubiquitous attribute such as a prevailing genotype. We have
+ examined heterosexual HIV epidemics by using mathematical models to assess HIV
+ transmission in dynamic populations either with or without CCR5Δ32
+ heterozygous and homozygous persons. The most susceptible population lacks the
+ protective mutation in CCR5. In less susceptible populations, the majority of
+ persons carrying the CCR5Δ32 allele are heterozygotes. We explore the
+ hypothesis that lower viral loads (CCR5Δ32 heterozygotes) or resistance to
+ infection (CCR5Δ32 homozygotes) observed in persons with this coreceptor
+ mutation ultimately can influence HIV epidemic trends. Two contrasting influences of
+ the protective CCR5 allele are conceivable: it may limit the epidemic by decreasing
+ the probability of infection because of lower viral loads in infected heterozygotes,
+ or it may exacerbate the epidemic by extending the time that infectious individuals
+ remain in the sexually active population. Our results strongly suggest the former.
+ Thus, the absence of this allele in Africa could explain the severity of HIV disease
+ as compared with populations where the allele is present.</p>
+ <p>We also observed that HIV can provide selective pressure for the CCR5Δ32
+ allele within a population, increasing the allelic frequency. Other influences may
+ have additionally selected for this allele. Infectious diseases such as plague and
+ small pox have been postulated to select for CCR5Δ32 (<xref ref-type="bibr"
+ rid="B57">57</xref>, <xref ref-type="bibr" rid="B58">58</xref>). For plague,
+ relatively high levels of CCR5Δ32 are believed to have arisen within
+ ≈4,000 years, accounting for the prevalence of the mutation only in
+ populations of European descent. Smallpox virus uses the CC-coreceptor, indicating
+ that direct selection for mutations in CCR5 may have offered resistance to smallpox.
+ Given the differences in the epidemic rates of plague (<xref ref-type="bibr"
+ rid="B59">59</xref>), smallpox, and HIV, it is difficult to directly compare our
+ results to these findings. However, our model suggests that the CCR5Δ32
+ mutation could have reached its present allelic frequency in Northern Europe within
+ this time frame if selected for by a disease with virulence patterns similar to HIV.
+ Our results further support the idea that HIV has been only recently introduced as a
+ pathogen into African populations, as the frequency of the protective allele is
+ almost zero, and our model predicts that selection of the mutant allele in this
+ population by HIV alone takes at least 1,000 years. This prediction is distinct from
+ the frequency of the CCR5Δ32 allele in European populations, where pathogens
+ that may have influenced its frequency (e.g., <italic>Yersinia pestis</italic>) have
+ been present for much longer.</p>
+ <p>Two mathematical models have considered the role of parasite and host genetic
+ heterogeneity with regard to susceptibility to another pathogen, namely malaria
+ (<xref ref-type="bibr" rid="B60">60</xref>, <xref ref-type="bibr" rid="B61"
+ >61</xref>). In each it was determined that heterogeneity of host resistance
+ facilitates the maintenance of diversity in parasite virulence. Given our underlying
+ interest in the coevolution of pathogen and host, we focus on changes in a host
+ protective mutation, holding the virulence of the pathogen constant over time.</p>
+ <p>Even within our focus on host protective mutations, numerous genetic factors,
+ beneficial or detrimental, could potentially influence epidemics. Other genetically
+ determined host factors affecting HIV susceptibility and disease progression include
+ a CCR5 A/A to G/G promoter polymorphism (<xref ref-type="bibr" rid="B62">62</xref>),
+ a CCR2 point mutation (<xref ref-type="bibr" rid="B11">11</xref>, <xref
+ ref-type="bibr" rid="B63">63</xref>), and a mutation in the CXCR4 ligand (<xref
+ ref-type="bibr" rid="B64">64</xref>). The CCR2b mutation, CCR264I, is found in
+ linkage with at least one CCR5 promoter polymorphism (<xref ref-type="bibr"
+ rid="B65">65</xref>) and is prevalent in populations where CCR5Δ32 is
+ nonexistent, such as sub-Saharan Africa (<xref ref-type="bibr" rid="B63">63</xref>).
+ However, as none of these mutations have been consistently shown to be as protective
+ as the CCR5Δ32 allele, we simplified our model to incorporate only the effect
+ of CCR5Δ32. Subsequent models could be constructed from our model to account
+ for the complexity of multiple protective alleles. It is interesting to note that
+ our model predicts that even if CCR264I is present at high frequencies in Africa,
+ its protective effects may not augment the lack of a protective allele such as
+ CCR5Δ32.</p>
+ <p>Although our models demonstrate that genetic factors can contribute to the high
+ prevalence of HIV in sub-Saharan Africa, demographic factors are also clearly
+ important in this region. Our models explicitly incorporated such factors, for
+ example, lack of treatment availability. Additional factors were implicitly
+ controlled for by varying only the presence of the CCR5Δ32 allele. More
+ complex models eventually could include interactions with infectious diseases that
+ serve as cofactors in HIV transmission. The role of high sexually transmitted
+ disease prevalences in HIV infection has long been discussed, especially in relation
+ to core populations (<xref ref-type="bibr" rid="B15">15</xref>, <xref
+ ref-type="bibr" rid="B50">50</xref>, <xref ref-type="bibr" rid="B66">66</xref>).
+ Malaria, too, might influence HIV transmission, as it is associated with transient
+ increases in semen HIV viral loads and thus could increase the susceptibility of the
+ population to epidemic HIV (<xref ref-type="bibr" rid="B16">16</xref>).</p>
+ <p>In assessing the HIV/AIDS epidemic, considerable attention has been paid to the
+ influence of core groups in driving sexually transmitted disease epidemics. Our
+ results also highlight how characteristics more uniformly distributed in a
+ population can affect susceptibility. We observed that the genotypic profile of a
+ population affects its susceptibility to epidemic HIV/AIDS. Additional studies are
+ needed to better characterize the influence of these genetic determinants on HIV
+ transmission, as they may be crucial in estimating the severity of the epidemic in
+ some populations. This information can influence the design of treatment strategies
+ as well as point to the urgency for education and prevention programs.</p>
+ </sec>
+ </body>
+ <back>
+ <ack>
+ <p>We thank Mark Krosky, Katia Koelle, and Kevin Chung for programming and technical
+ assistance. We also thank Drs. V. J. DiRita, P. Kazanjian, and S. M. Blower for
+ helpful comments and discussions. We thank the reviewers for extremely insightful
+ comments.</p>
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