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Erschienen in: Journal of Economic Interaction and Coordination 2/2019

10.01.2019 | Regular Article

Partnership duration and concurrent partnering: implications for models of HIV prevalence

verfasst von: Alan G. Isaac, Larry Sawers

Erschienen in: Journal of Economic Interaction and Coordination | Ausgabe 2/2019

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Abstract

Researchers and policy makers have argued that long-duration concurrent relationships promote the spread of HIV. The concurrency hypothesis proposes that concurrent partnering, particularly as manifested in formal and informal polygyny, is a primary contributor to the spread of HIV in sub-Saharan Africa. We investigate claims that agent-based models of concurrent partnering support this hypothesis. Specifically, we explore how assumptions about the duration and network structure of sexual partnerships affect the results of agent-based models of HIV propagation. We offer new support for the contention that long-duration concurrent partnering can be protective against HIV transmission rather than promoting it. Additionally, we argue that the focus on concurrency has misdirected attention away from the key role of exclusivity.

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1
For a detailed discussion, see Sawers and Stillwaggon (2010).
 
2
From the EHG2011 model, we incorporate the improved transmission parameterization, vital dynamics (discussed below), and longer simulation period. At the level of code, we adopt a discrete time-to-event implementation that was inspired by their publicly available C++ code. Our Python implementation is available upon request.
 
3
They are also appropriately staged (i.e., they vary during the course of the infection.) As explained by Eaton (2013), “[w]ith constant infectiousness, the overall spread of the virus is less dependent on onward transmission within the first few months of infection.”
 
4
There is only one primary partner, while there may be multiple secondary partners.
 
5
This heuristic schematic is essentially a simplified UML class box (Bersini 2012), but that is not meant to imply any particular approach to implementation. It documents only key public features, specifies only the types of operation (e.g., method) arguments, and omits constructors. Conventionally a frozen property (in braces) indicates immutability, but this is omitted to reduce diagram clutter. Operations specify no return type because they are called only for their side effects.
 
6
The [*] annotation conventionally indicates that there can be zero or more partnerships. (We use an ordered collection to ensure replicability.) Partnering is dynamic: an individual may add or remove a partnership. (To avoid clutter, we do not list the associated operations.) Partnership formation and dissolution is stochastic, as specified below.
 
7
This simplifying assumption is standard in HIV modeling. In fact there are two main types of HIV (and numerous strains), and individuals can be infected by more than one type or strain.
 
8
Partnerships are therefore the undirected edges in a dynamic bipartite graph.
 
9
The fixed multiplicity of 2 is indicated in brackets, following a UML convention. The pair of partners and the ptype are immutable attributes of a partnership.
 
10
One is reminded of a description in Binmore (2007, p. 536): “One may imagine that Alice knocks on doors at random if unmatched. When Bob or Chris answers the door, she bargains with him until agreement is reached or their unpredictable wives grow tired and run her off the property.”
 
11
Following Eaton et al. (2011), we do not impose a maximum number of partners for each individual. Other approaches are common in the literature. For example, Morris and Kretzschmar (1997) impose a maximum of 4 partners per individual. Morris and Kretzschmar (2000) report Ugandan survey data that suggests that having even as many as 3 partners is rare, and their associated simulation model correspondingly imposes a maximum of 3 partners. Caraëel et al. (2004, p. 65) report that more than 8 partners in a year is very rare, with nearly half of respondents reporting 0 partners and almost all the rest 5 or fewer. Although we do not impose an exogenous maximum, individuals with more than a few partners are extremely rare, even when there is no concurrency resistance whatsoever.
 
12
See the “Appendix” for a detailed parameterization. See Kretzschmar and Morris (1996, p. 181) and Eaton (2013, p. 48) for a detailed discussion and corresponding pseudocode, or Eaton et al. (2011) for a complete C++ implementation. This approach is very common in the literature, but variations exist. For example, the MK2000 model instead sets a ceiling on total partnerships equal to the maximum that is possible given their ceiling on the number of partnerships per person. However, that model is applied to a different question (the consequences of the mean degree of the population in various scenarios).
 
13
In an agent-based model, one might expect to work with a per-act risk of infection, possibly deriving a daily risk of infection as the product of a per-act transmission rate and coital frequency. However, Hollingsworth et al. (2008) argue that measuring the number of sex acts is subject to substantial error, which produces a corresponding error in the per-act transmission rate. In contrast, there is substantial evidence from seroconversion data concerning annual transmission risks. Working directly with daily risk of infection allows less problematic calibration to this evidence. We therefore adopt this approach, which has remained fairly standard in the literature since the MK1997 model. Specifically, we follow the EHG2011 model in calibrating the daily transmission risk to the stage-specific annual risk of infection documented by Hollingsworth et al. (2008).
 
14
Following Eaton et al. (2011) and Sawers et al. (2011), our individuals do not die of any other causes. (Contrast with McCreesh et al. (2012), who remove individuals from the model at age 55.) Allowing individuals to die of old age is largely irrelevant for our research questions, although it would very slightly reduce transmission likelihood (since in principle an infected partner could die of old age before transmitting the disease).
Additionally, as noted by two referees, our baseline model does not include mother-to-child transmission. In a scenario contrast experiment (not shown), we allow seropositive mothers to produce seropositive offspring who survive to adolescence. In comparison with our baseline results, the duration results with seropositive births are qualitatively similar. As expected, this change boosts prevalence at every duration combination.
 
15
These models determine mean duration by drawing each partnership’s duration from a (shifted) geometric distribution with parameter \(\sigma =0.005\), the daily risk of dissolution. In contrast, we will consider 21 different values of \(\sigma \) for each partnership type, allowing that primary partnerships may be longer or shorter in duration than secondary partnerships. (Our distinction between primary and secondary partnerships therefore does not correspond to the distinction between long-duration and short-duration partnerships in Morris and Kretzschmar (2000) or McCreesh et al. (2012), although it encompasses it.)
 
16
Results for the full EHG2011 range of concurrency resistances are available upon request.
 
17
A single experiment comprises 441 distinct scenarios (i.e., combinations of primary-partnership mean duration and secondary-partnership mean duration). Our focal experiment includes 100 replicates of each scenario, which—for this focal experiment alone—implies more than 40, 000 simulations of daily actions over our time horizon of 250 years.
 
18
Recall that EHG2011 has a single partnership duration for all partnerships, which is an unrealistically short 200 days. This constrains the possible levels of concurrency prevalence. With more plausible (much longer) partnership durations, we naturally see higher concurrency prevalence.
 
19
For example, the Partners Demonstration Project found that integrated ART and PrEP delivery to serodiscordant couple drastically lowered HIV transmission (Baeten et al. 2016).
 
20
We do not illustrate concurrency prevalence since (as expected) the outcomes are not changed.
 
21
For additional evidence of coital dilution, see Gaydosh et al. (2013), Reniers and Tfaily (2010), Reniers and Tfaily (2012), and Reniers and Watkins (2010).
 
22
Primary partnerships have the highest frequency of sex but need not have the longest duration. As a concrete example, the post-war partnership between Sartre and de Beauvoir might be classified both as long-duration and as secondary.
 
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Metadaten
Titel
Partnership duration and concurrent partnering: implications for models of HIV prevalence
verfasst von
Alan G. Isaac
Larry Sawers
Publikationsdatum
10.01.2019
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Economic Interaction and Coordination / Ausgabe 2/2019
Print ISSN: 1860-711X
Elektronische ISSN: 1860-7128
DOI
https://doi.org/10.1007/s11403-018-00234-1

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