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Effects of contact structure on the transient evolution of HIV virulence

View Article: PubMed Central - PubMed

ABSTRACT

Early in an epidemic, high densities of susceptible hosts select for relatively high parasite virulence; later in the epidemic, lower susceptible densities select for lower virulence. Thus over the course of a typical epidemic the average virulence of parasite strains increases initially, peaks partway through the epidemic, then declines again. However, precise quantitative outcomes, such as the peak virulence reached and its timing, may depend sensitively on epidemiological details. Fraser et al. proposed a model for the eco-evolutionary dynamics of HIV that incorporates the tradeoffs between transmission and virulence (mediated by set-point viral load, SPVL) and their heritability between hosts. Their model used implicit equations to capture the effects of partnership dynamics that are at the core of epidemics of sexually transmitted diseases. Our models combine HIV virulence tradeoffs with a range of contact models, explicitly modeling partnership formation and dissolution and allowing for individuals to transmit disease outside of partnerships. We assess summary statistics such as the peak virulence (corresponding to the maximum value of population mean log10 SPVL achieved throughout the epidemic) across models for a range of parameters applicable to the HIV epidemic in sub-Saharan Africa. Although virulence trajectories are broadly similar across models, the timing and magnitude of the virulence peak vary considerably. Previously developed implicit models predicted lower virulence and slower progression at the peak (a maximum of 3.5 log10 SPVL) compared both to more realistic models and to simple random-mixing models with no partnership structure at all (both with a maximum of ≈ 4.7 log10 SPVL). In this range of models, the simplest random-mixing structure best approximates the most realistic model; this surprising outcome occurs because the dominance of extra-pair contact in the realistic model swamps the effects of partnership structure.

No MeSH data available.


Pairs plot: bivariate relationships among summary statistics for each model structure.The three summary statistics for each simulation are plotted against each other in order to visualize the relationship among the summary statistics and to help compare models. Surprisingly, the implicit model, an approximation for instantaneous partnership formation model (instswitch), shows an almost identical trend with a model that has pair formation dynamics (pairform). The dashed line in the equilibrium vs. peak virulence plot (lower left) shows the 1:1 line, where equilibrium and peak virulence are equal. To avoid too much overplotting, only 10% of the parameter sets (randomly sampled) are shown here.
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pcbi.1005453.g005: Pairs plot: bivariate relationships among summary statistics for each model structure.The three summary statistics for each simulation are plotted against each other in order to visualize the relationship among the summary statistics and to help compare models. Surprisingly, the implicit model, an approximation for instantaneous partnership formation model (instswitch), shows an almost identical trend with a model that has pair formation dynamics (pairform). The dashed line in the equilibrium vs. peak virulence plot (lower left) shows the 1:1 line, where equilibrium and peak virulence are equal. To avoid too much overplotting, only 10% of the parameter sets (randomly sampled) are shown here.

Mentions: Our chosen summary statistics (peak time, maximum mean log10 SPVL, equilibrium mean log10 SPVL, and minimum mean progression time) all vary considerably across models (Fig 4). We first consider the models of intermediate realism: implicit, instantaneous-switching with and without extra-pair contact, and pair formation without extra-pair contact. Some parameter sets for these models lead to low equilibrium virulence (2.3-3 log10 SPVL). For these data sets, virulence may either increase from its initial value, reaching an early peak (≈ 200 years) between 3 and 4 log10 SPVL and then declining to a lower equilibrium value, or in extreme cases virulence may decline immediately, leading to a peak virulence (as we have defined it) equal to the starting value of α(0) = 3 log10 SPVL at t = 0 (Fig 5). At the opposite extreme, parameter sets that produce high equilibrium virulence (4.7 log10 SPVL) also produce late peaks (> 200 years) and high peak virulence (5.6 log10 SPVL).


Effects of contact structure on the transient evolution of HIV virulence
Pairs plot: bivariate relationships among summary statistics for each model structure.The three summary statistics for each simulation are plotted against each other in order to visualize the relationship among the summary statistics and to help compare models. Surprisingly, the implicit model, an approximation for instantaneous partnership formation model (instswitch), shows an almost identical trend with a model that has pair formation dynamics (pairform). The dashed line in the equilibrium vs. peak virulence plot (lower left) shows the 1:1 line, where equilibrium and peak virulence are equal. To avoid too much overplotting, only 10% of the parameter sets (randomly sampled) are shown here.
© Copyright Policy
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC5391972&req=5

pcbi.1005453.g005: Pairs plot: bivariate relationships among summary statistics for each model structure.The three summary statistics for each simulation are plotted against each other in order to visualize the relationship among the summary statistics and to help compare models. Surprisingly, the implicit model, an approximation for instantaneous partnership formation model (instswitch), shows an almost identical trend with a model that has pair formation dynamics (pairform). The dashed line in the equilibrium vs. peak virulence plot (lower left) shows the 1:1 line, where equilibrium and peak virulence are equal. To avoid too much overplotting, only 10% of the parameter sets (randomly sampled) are shown here.
Mentions: Our chosen summary statistics (peak time, maximum mean log10 SPVL, equilibrium mean log10 SPVL, and minimum mean progression time) all vary considerably across models (Fig 4). We first consider the models of intermediate realism: implicit, instantaneous-switching with and without extra-pair contact, and pair formation without extra-pair contact. Some parameter sets for these models lead to low equilibrium virulence (2.3-3 log10 SPVL). For these data sets, virulence may either increase from its initial value, reaching an early peak (≈ 200 years) between 3 and 4 log10 SPVL and then declining to a lower equilibrium value, or in extreme cases virulence may decline immediately, leading to a peak virulence (as we have defined it) equal to the starting value of α(0) = 3 log10 SPVL at t = 0 (Fig 5). At the opposite extreme, parameter sets that produce high equilibrium virulence (4.7 log10 SPVL) also produce late peaks (> 200 years) and high peak virulence (5.6 log10 SPVL).

View Article: PubMed Central - PubMed

ABSTRACT

Early in an epidemic, high densities of susceptible hosts select for relatively high parasite virulence; later in the epidemic, lower susceptible densities select for lower virulence. Thus over the course of a typical epidemic the average virulence of parasite strains increases initially, peaks partway through the epidemic, then declines again. However, precise quantitative outcomes, such as the peak virulence reached and its timing, may depend sensitively on epidemiological details. Fraser et al. proposed a model for the eco-evolutionary dynamics of HIV that incorporates the tradeoffs between transmission and virulence (mediated by set-point viral load, SPVL) and their heritability between hosts. Their model used implicit equations to capture the effects of partnership dynamics that are at the core of epidemics of sexually transmitted diseases. Our models combine HIV virulence tradeoffs with a range of contact models, explicitly modeling partnership formation and dissolution and allowing for individuals to transmit disease outside of partnerships. We assess summary statistics such as the peak virulence (corresponding to the maximum value of population mean log10 SPVL achieved throughout the epidemic) across models for a range of parameters applicable to the HIV epidemic in sub-Saharan Africa. Although virulence trajectories are broadly similar across models, the timing and magnitude of the virulence peak vary considerably. Previously developed implicit models predicted lower virulence and slower progression at the peak (a maximum of 3.5 log10 SPVL) compared both to more realistic models and to simple random-mixing models with no partnership structure at all (both with a maximum of ≈ 4.7 log10 SPVL). In this range of models, the simplest random-mixing structure best approximates the most realistic model; this surprising outcome occurs because the dominance of extra-pair contact in the realistic model swamps the effects of partnership structure.

No MeSH data available.