article: The existence of long-lived reservoirs of latently infected CD4+ T cells is the major barrier to curing HIV, and has been extensively studied in this light. However, the effect of these reservoirs on the evolutionary dynamics of the virus has received little attention. Here, we present a within-host quasispecies model that incorporates a long-lived reservoir, which we then nest into an epidemiological model of HIV dynamics. For biologically plausible parameter values, we find that the presence of a latent reservoir can severely delay evolutionary dynamics within a single host, with longer delays associated with larger relative reservoir sizes and/or homeostatic proliferation of cells within the reservoir. These delays can fundamentally change the dynamics of the virus at the epidemiological scale. In particular, the delay in within-host evolutionary dynamics can be sufficient for the virus to evolve intermediate viral loads consistent with maximising transmission, as is observed, and not the very high viral loads that previous models have predicted, an effect that can be further enhanced if viruses similar to those that initiate infection are preferentially transmitted. These results depend strongly on within-host characteristics such as the relative reservoir size, with the evolution of intermediate viral loads observed only when the within-host dynamics are sufficiently delayed. In conclusion, we argue that the latent reservoir has important, and hitherto under-appreciated, roles in both within- and between-host viral evolution.
  Shortly after the introduction of anti-retroviral therapy (ART) to treat HIV infected individuals, viral reservoirs, in the form of long-lived CD4+ T cells containing integrated proviral DNA, were identified in infected patients [1,2]. These reservoirs are established soon after infection [3,4], are long-lived [5], and virus can re-emerge from the reservoirs after months or even years of latency [6]. As such, latent reservoirs represent the major barrier to curing HIV [7,8]. Although reservoirs of latent viruses have been extensively studied in the light of treatment and viral eradication, including several modelling studies (see [9] and [10] for recent reviews), we have little understanding of how latent reservoirs influence viral dynamics during untreated infection, and in turn how this might affect viral evolution at the epidemiological scale. Viral lineages in the reservoir are expected to be evolutionarily very stable because proviruses only replicate when the host cell divides, and since this uses the host-cell replication machinery, mutation rates are extremely low. The reservoir is therefore likely to provide an archive of “ancestral” viral strains that were circulating earlier during the infection. If these archived viruses are reactivated months, or even years, after infection, their presence might have a profound influence on within- and between-host dynamics. Using a population-genetic modelling approach Kelly et al. showed that cycling through the reservoir can lower the within-host neutral rate of HIV evolution [11,12]. In a model of drug resistance, Ward et al. furthermore showed that a latent reservoir can provide memory of non-resistant viral strains for up to several years after treatment is started [13], and recently, Immonen et al. showed that substitution rates among within-host HIV lineages are overdispersed, which is consistent with the circulating of virus through a reservoir [14]. Using a simulation model of within-host dynamics, it has also been predicted that due to recombination a significant fraction of circulating viral strains will have fragments of their genome that have been latent for some time during infection [15]. Moreover, there has been speculation that the transmission of ancestral strains could explain the lower rates of HIV evolution observed at the epidemiological scale compared to within individuals [16–19], and the unexpectedly high heritability of HIV set-point viral load despite considerable within-host evolution between transmission events [20,21]. Here, we present a quasispecies model of within-host HIV evolutionary dynamics that incorporates a latently infected reservoir. Of note, we find that the presence of a latent reservoir can severely delay the within-host evolution of the virus. The extent of this delay is primarily determined by the replication rates of competing strains, the activation rate of latently infected cells, the relative size of the reservoir compared to the number of active infected cells (which we estimate from published data [1,22–26] to be between 0. 06 and 3. 1), and the extent to which cells within the reservoir proliferate. Since it is reasonable to speculate that all of these factors vary considerably among infected individuals, the influence of the reservoir in different individuals is likely to be very heterogeneous, and, if recombination is pervasive and selection pressures differ across the HIV genome, might also vary among sites [15]. Next, we nest the within-host model into a standard model of HIV epidemiological dynamics, enabling us to determine the effects of within-host evolution, and importantly the reservoir, on between-host evolutionary dynamics. If viral strains differ in their within-host fitness, variants with a higher in vivo replication rate will be favoured within a given host. Indeed, the replicative capacity of viral populations (as measured by in vitro competition assays) has been found to increase over the course of an HIV infection, albeit slowly [27,28]. It was also shown that individuals infected with a virus with a high replicative capacity tend to have a high viral load and vice versa [28,29], with the replicative capacity either predicted from the Pol sequence of the circulating virus [28] or measured by an in vitro competition assay [29]. Furthermore, in a study of 149 transmission pairs a weak positive correlation was found between the replicative capacity conferred by the Gag sequence of the virus that initiated an infection and the set-point viral load (spVL) [30], the relatively stable concentration of viral particles in the blood during the chronic phase of HIV infection. The spVL, in turn, is a predictor of the severity of infection, or virulence, since individuals with a high set-point tend to progress to AIDS faster [31,32]. As well as being a predictor for the duration of infection, set-point viral load is also correlated with the transmission rate [33,34]. Hence, infected individuals with a low set-point viral load (who, because of the correlations described above, are likely infected with a strain that has a low replicative capacity) will live long but will infect few other individuals because their transmission rate is low, while individuals with a high viral load will have a high transmission rate during the infection but will also cause few new infections because progression to AIDS is fast. Under this trade-off between duration of the infection and the transmission rate, it has been calculated that the transmission potential (defined as the number of new infections caused by an infected individual over the entire infectious period) is maximised when set-point viral loads are intermediate, i. e. log (spVL) ≈ 4. 5 [35,36]. The distribution of set-point viral loads found in populations of infected individuals is centered around these intermediate values, suggesting that HIV virulence might have evolved to maximise between-host transmission [35–37]. This is surprising, since HIV evolves rapidly within hosts and durations of infections are long, and so the virus should be expected to evolve to maximise within-host fitness (e. g. replication rate) at the expense of between-host fitness, an outcome known as ‘short-sighted’ evolution [38]. Previous mathematical and computational studies have explored this interplay between within- and between-host selection, either by including within-host selection for high replication rate, which was in turn directly coupled to higher virulence as described above [20], or by including within-host selection for immune escape mutations in a heterogeneous host population and hence allowing the virus to adapt to each new host [39]. In both cases, for realistic within-host selection pressures and mutation rates, the within-host selection process was found to dominate between-host selection, and hence between-host level adaptation was not predicted to occur [20,39]. Here, we find that delays in within-host dynamics caused by the presence of a reservoir can have a large impact on how the virus evolves at the epidemiological level, and can, under certain parameter conditions, be substantial enough to explain evolution towards intermediate levels of virulence that maximise transmission. We therefore contend that it is important to consider reservoir dynamics not only in patients on antiretroviral therapy, but also in untreated individuals with ongoing active viral replication. Understanding how the virus evolves under different levels of selection is crucial if we want to better describe the course of epidemics, and predict the evolutionary impacts of potential intervention measures.
  We have investigated how the presence of a latent reservoir affects the evolutionary dynamics of HIV within individuals and at the population level. Surprisingly, we find that the latent reservoir can cause a significant delay to the within-host evolutionary process. Furthermore, if within-host evolution is sufficiently delayed the virus can evolve intermediate levels of virulence which optimise transmission at the population level. This is in contrast to the situation in which a within-host reservoir is absent and where high virulence strains are expected to dominate. Hence, the delay in within-host evolution can prevent the short-sighted evolution of very high levels of virulence. It is important to note that these between-host effects only occur if the latent reservoir is relatively large compared to the active compartment. In the lower ranges of our estimates for the relative reservoir size (e. g. rL ≈ 0. 1), almost no effect of the reservoir on within-host evolutionary dynamics was found. For these conditions, the preferential transmission of strains similar to the ancestral virus, stored in long-lived memory cells, might provide an alternative explanation to the observed population level adaptation of virulence [21]. This is not an unreasonable hypothesis: ancestral strains are, by definition, transmissible, and during the course of a single infection there will not be selection to maintain transmissibility per se. There is now a growing body of indirect evidence that ancestral virus might be preferentially transmitted, including work on individual transmission pairs [51,52], a large cohort study [53], and phylogenetic studies [16,18,19]. Our model can be extended to investigate the population level effects of preferential transmission of ancestral virus. As a case study, we incorporated this mechanism into our model by assuming that, during the course of an infection, the virus acquires additional mutations that lower its relative transmissibility per transmission event compared to strains carrying fewer of these mutations, but which are neutral at the within-host level and do not affect virulence (S2 Text). We then find that inclusion of preferential transmission of ancestral virus can result in the dominance of strains with intermediate virulence that maximise the population level reproduction number, R0, of the infection, even for cases where high virulence strains dominate in the absence of preferential transmission (S7 Fig). As might be expected, however, the effect of this preferential transmission depends on the strength of the preference and the rate at which transmissibility-lowering mutations are acquired, and we only find population level adaptation of the virus if preferential transmission is sufficiently strong (S8 Fig). Although this model provides a proof of concept that preferential transmission of ancestral virus can lead to population level adaptation of the virulence, more biologically realistic models should be developed to further study this mechanism. Because both our within-host and between-host results are very sensitive to the relative size of the reservoir compared to the number of infected actively replicating cells, our model produces testable predictions for the effect of the relative reservoir size on the within-host evolutionary dynamics of the virus. The larger the reservoir compared to the active compartment, the more delayed within-host evolutionary dynamics are expected to be, ranging from almost no delay in individuals with a small relative reservoir size (lower bounds of our rL estimates) to a delay of multiple years in individuals in whom the reservoir is large relative to the number of actively infected cells (higher bounds of our rL estimates). In particular, this might explain the low rates of evolution in natural controllers of HIV infection who maintain very low plasma HIV RNA levels, and in whom we therefore speculate that the relative size of the reservoir compared to the active compartment is large. In these patients there is growing evidence for low levels of ongoing viral replication [54–56] and the evolutionary rate has been estimated to be 3–4 times lower than in non-controllers [55]. Furthermore, in another study a negative correlation between set-point viral load and evolutionary rate has been described [57], a trend that we would predict if a high set point viral load is indicative of a small relative reservoir size. Although these data support the hypothesis that a relatively large latent reservoir delays within-host evolutionary dynamics, caution is needed in interpreting these and other results since confounding factors, such as APOBEC induced mutations, also affect both set-point viral load and rates of evolution [58]. Quantifying the number of latently infected cells containing viable provirus in HIV patients is a major challenge. Empirical estimates of the size of the latent reservoir within patients on ART can vary 2 logs in magnitude depending on the experimental method used [59]. Viral outgrowth assays tend to underestimate the reservoir size, while PCR based methods tend to lead to an overestimation [60]. We have hoped to avoid some of these biases by estimating a relative reservoir size compared to the number of actively infected cells, which should be relatively insensitive to errors in estimates of the absolute number of infected active and latent cells, as long as both are biased in the same way. Using both direct and indirect methods we found that the relative size of the latent reservoir can vary enormously among patients, ranging from 0. 06 to 3. 1 latently infected cells per infected active cell. At this moment it is unclear to what extent this variation is caused by differences in the experimental methods used or is true variation between the patients themselves. Other studies have suggested that the relative size of the reservoir is much smaller than we have estimated here because most viral DNA in the reservoir is not viable (e. g. [15]). However, recent evidence suggests that the same is true of viral DNA in actively replicating cells [58], leading us to conclude that our estimates of the relative reservoir size are probably in the right ball park. Furthermore, although at first sight our estimates for the relative reservoir size might appear high, it is important to recognise that they represent a “snapshot” of viral dynamics. Although many active CD4+ T cells are infected over the course of an HIV infection, the total number of actively infected cells at any given point is small [1]. Thus, the ratio between the numbers of latently and actively infected cells at any given time point might be larger than intuitively expected. As well as relative reservoir size, the rate at which the reservoir is replenished and depleted, and hence the (assumed) homeostatic proliferation rate in the reservoir, is another important determinant of within-host dynamics. There is a growing body of evidence suggesting that latent reservoirs are maintained by homeostatic proliferation in patients on antiretroviral therapy. Modelling studies have suggested that homeostatic proliferation must occur to maintain stable reservoir sizes under therapy [61,62], and in support of this Chomont et al. [26] found direct evidence of ongoing homeostatic proliferation in a subset of infected memory CD4+ T cells. More recent studies of HIV DNA integration sites at single-cell level [63,64] found that multiple cells carry identical proviral sequences at the same integration site, suggesting that up to 40% of cells in the latent reservoir have arisen from clonal expansion [63]. We should however be careful in interpreting these results, since the clonally expanded proviruses were not tested for replication competency. In a different study Cohn et al. [65] found that although the majority of integrated proviruses resided in clonally expanded T cells, all of the 75 proviruses found in these clones were defective. However, since in our model we only assume a very low level of proliferation of latently infected cells, if at all, these results do not directly contradict our assumptions. We find that the within-host evolutionary dynamics of HIV can be severely delayed by the presence of a latent reservoir if mutations are neutral within-host or have a small within-host fitness effect. Some mutations might however confer a larger within-host fitness benefit, as has been suggested for some immune escape mutations [66–68], although other studies have found that immune escape might be relatively slow, especially during the chronic phase of infection [66,69,70]. For mutations that have a large effect on within-host fitness, we predict that the presence of the reservoir will have very little effect on within-host evolutionary dynamics because the fittest variant will quickly sweep the active compartment and the reservoir. However, since recombination happens very frequently during HIV replication [48,71,72] we still expect to see the predicted effect of the latent reservoir when considering neutral mutations or mutations with small within-host fitness effects. When modelling the evolution of virulence at the population level, we have confined ourselves to considering viral factors, and not host factors or host-virus interactions, which are likely to be mediated through the host immune response. The high heritability of HIV set-point viral load [21] suggests that viral factors are important determinants of virulence, although as yet we do not know what these factors are, and this is the subject of ongoing research. Since the human population is very heterogeneous (e. g. with regard to immune responses) and this might impact epidemiological and evolutionary dynamics [39], an important next step will be to determine how the incorporation of host heterogeneity affects our conclusions. Because of the problems they pose to eradication of viral infection, latent HIV reservoirs have mainly been studied in the context of antiretroviral treatment [7,8]. Here, however, we have investigated how reservoir dynamics influence the evolutionary dynamics of HIV in untreated individuals with ongoing active viral replication. Overall, our models have shown that latently infected cells can have a major impact on the evolution of the virus. The latent reservoir plays a role in the determination of the within-host evolutionary rate and the outcome of population level evolution of virulence. Therefore, latently infected cells should be considered if we want to understand the evolutionary dynamics of HIV at the within- and between-host levels.
  Within a host we consider two compartments: an active compartment and a latent reservoir. The active compartment describes the infection of active CD4+ T cells. In this compartment, viral replication (i. e. new infections) and mutation take place. A small fraction, k, of the newly infected cells enter the reservoir compartment as long-lived latently infected cells. These cells are reactivated at a rate a per day. An overview of the model structure is shown in Fig 1. Consider n different viral strains that can differ in their replication rate, γi (i = 1,2, …, n). Let xi be the frequency of strain i in the active compartment, and yi its frequency in the latent reservoir. Mutations are described by a mutation matrix M = (mij), where mij is the probability that strain j mutates into strain i during replication. The dynamics of the system are described by the following differential equations: {dxidt= (1−k) ∑j=1nmijγjxj+arLyi−xi ( (1−k) ∑j=1nγjxj+arL∑j=1nyj) dyidt=krL∑j=1nmijγjxj−ayi−yi (krL∑j=1nγjxj−a∑j=1nyj), (1) or in matrix-vector notation {dxdt= (1−k) Qx+arLy−x ( (1−k) γ−+arL) dydt=krLQx−ay−y (krLγ−−a), (2) where x = (x1, x2, …, xn) T, y = (y1, y2, …, yn) T, Q = (qij) = (mij γj) is the replication-mutation matrix, and γ−=∑j=1nγjxj is the total replication rate of the virus. The last term in all of these equations represents a chemostat-assumption, which assures that the frequencies xj and yj add up to one at all times [40]. This chemostat-assumption is equivalent to assuming that the death rate of cells within a given compartment is the same for all strains. Note that Eq 1 introduces an additional parameter, the relative reservoir size rL. Since we describe strain frequencies, rather than absolute numbers of infected cells, this parameter is needed to account for a potential difference in size between the two connected compartments. Let A be the total number of infected active CD4+ T cells, and L the total number of latently infected memory CD4+ T cells. Then, the number of memory CD4+ T cells latently infected with strain i is given by yi L. Since these cells are reactivated at a rate a per day, the total rate of re-entry of strain i into the active compartment is ayiL cells per day. The contribution of these reactivated cells to the change in frequency of strain i in the active compartment is given by Δxi (a) =ayiLA (3) since the size of the active compartment is A cells. A similar argument can be made to describe the contribution of newly latently infected cells to the strain distribution in the reservoir, which is given by Δyi (k) =k∑j=1nmijγjxjAL=ALk∑j=1nmijγjxj. (4) In both cases we see that if the reservoir and the active compartment are of unequal size, this size difference has to be accounted for. Hence, we define rL=LA (5) as the relative size of the reservoir. The use of this parameter rL is also illustrated in Fig 1. Note that our model implicitly includes the possibility of homeostatic proliferation of latently infected cells. Viral load stays approximately constant during chronic infection, and therefore we can expect the number of actively infected cells (i. e. the absolute size of the active compartment) to be relatively constant as well, as is also predicted by models of within-host infection dynamics (see [9] and [10] for recent reviews). In the model, we make the additional assumption that the relative size of the reservoir compared to the active compartment remains constant during chronic infection. This means that the absolute size of the reservoir must also remain the same (see Eq 5). Using the notation of Eq 5, let A and L be the absolute size of the active compartment and the reservoir, respectively. Since ∑j=1nγjxj≈1 (see Table 1 for parameter values) the total entry rate of cells entering the reservoir is approximately k ∙ A, while the total outflow rate of cells leaving the reservoir is a ∙ L. To maintain a constant reservoir size in the absence of homeostatic proliferation these entry and outflow rates must be equal, i. e. k=a⋅LA=a⋅rL. If however the outflow is greater than the inflow (i. e. a>krL), then homeostatic proliferation of latently infected cells is implicitly assumed to take place so as to maintain the reservoir size, at a rate ρ=a−krL. (6) Since new HIV infections are generally established by a single viral genotype [45–47], we assume that all within-host processes are started with only a single strain present at time τ = 0. It has been shown that the reservoir of latently infected cells is established very quickly, as early as 10 days after infection [3,4]. We incorporate this into our model by assuming that the initial strain is immediately present in both the active compartment and the latent reservoir. From these initial conditions, Eq 2 is numerically integrated to calculate xij (τ) and yij (τ), the frequency of strain i in the active compartment and the reservoir at time τ after infection in an individual originally infected with strain j at time τ = 0. Note that a constraint of using the time-since-infection framework is the assumption that no superinfection takes place. Numerical integration was done with Matlab’s built-in differential equation solver ode45, using default settings. Then, following Lythgoe et al. [20] we define the strain specific infectivity profile βij (τ) =αj (τ) xij (τ). (7) Here, αj (τ) is a predefined overall infectivity profile of infections established by strain j. We assume that the infectivity profile αj (τ) consists of three stages: acute infection, a chronic phase and a late phase. The durations of the acute and late phases are assumed to be equal for all infections, as is the infectivity during these phases. The duration and infectivity of the chronic phase, however, are assumed to be functions of spVL: infections with higher spVLs have shorter chronic phases, and higher infectivities during this chronic phase, than infections with lower spVLs (illustrated in S3 Fig, see [20,35,36] for details and parameter estimates). Because the duration of the chronic phase depends on the spVL, the total duration of the infection, Tj, will also be shorter for more virulent strains (i. e. those with a higher spVL) [20,35]. Viral load is relatively stable during chronic infection, even though a large amount of within-host evolution takes place during this period. We therefore assume that the spVL in turn is determined by the infecting strain. Since spVL correlates with replicative capacity of the virus [28–30], we furthermore assume that strains with higher replication rates result in infections with higher spVLs [20]. Following Lythgoe et al. [20], we use the strain specific infectivity profiles described by Eq 7 to nest the within-host dynamics into a multitype epidemiological model to describe the between-host dynamics [49]. Here we will provide a short description of the model, see [20] and [49] for the full derivation. We use a susceptible-infected model with demography. Let S (t) and I (t) be the number of susceptible and infected individuals at time t, respectively, and let N (t) = S (t) + I (t) be the total number of individuals in the population. Let Ii (t) be the number of type-i infected individuals, i. e. individuals initially infected with strain i. Then, I (t) =∑i=1nIi. Assume that all individuals die at a natural death rate ν, and furthermore that type-i infected individuals die at time Ti after initial infection if they have not succumbed to natural mortality. Let B be the rate at which new susceptible individuals enter the population. Finally, let Hi (t) denote the incidence of type-i infections, i. e. the rate at which new type-i infections occur. Assuming random mixing of the population, the epidemiological dynamics are then described by Hi (t) =S (t) N (t) ∑j=1n∫0Tjβij (τ) Hj (t−τ) e−ντdτ, (8) S (t) =N (t) −∑i=1n∫0TiHi (t−τ) e−ντdτ, (9) dNdt=B−νN (t) −∑i=1nHi (t−Ti) e−νTi, (10) Ii (t) =∫0TiHi (t−τ) e−ντdτ. (11) These equations were numerically integrated using Matlab, using Matlab’s function trapz to numerically solve the integrals and the forward Euler method to solve the differential equations (timestep dt = 0. 01 year). The next-generation matrix K= (kij) = (∫0Tjβij (τ) e−ντdτ) can also easily be calculated. This next-generation matrix can be used to quickly find the equilibrium of the model without numerically solving Eqs 8–11. Namely, at equilibrium the basic reproduction number R0 of the infection is equal to the dominant eigenvalue of the next-generation matrix K, while the corresponding eigenvector (normalised to have components summing up to one) gives the relative incidence (H−i*) [20,49]. R0 represents the average number of new infections one infected individual would cause in a fully susceptible population during its lifetime. At equilibrium, however, the number of infected individuals is constant over time and hence the number of new cases arising from a single infection should be equal to one. Therefore, at equilibrium S*N*=1R0 (12) where the star denotes equilibrium values. Setting Eqs 8–11 to equilibrium and using Eq 12 we can now directly derive Ii*=B (R0−1) H−i* (1−e−νTi) ν (R0−∑j=1nH−i*e−νTi), (13) and similar expressions for Hi*, S* and N* (see [20]). Since R0 and (H−i*) can be found from the next-generation matrix K, all equilibrium values can thus be directly calculated from the next-generation matrix. To estimate the relative reservoir size rL, two data sources were used: (i) a direct report on the number of active and latent CD4+ T cells with integrated HIV-1 DNA in several chronic phase patients [1], and (ii) several studies reporting HIV-1 DNA levels pre- and during anti-retroviral treatment in patients starting treatment during chronic phase [22–26]. Chun et al. [1] report the concentration of cells with integrated HIV-1 DNA and the percentage of total cells that are latent. Then, the relative reservoir size can be directly calculated as rL=[HIVDNA]l (1−Pa) [HIVDNA]aPa (14) Here, Pa denotes the percentage of CD4+ T cells that are activated (HLA DR+), and [HIVDNA]a and [HIVDNA]l are the concentrations of HIV DNA positive active and latent cells (per 106 active/latent cells), respectively. For the second set of studies, note that if treatment is effective, all HIV DNA measured during treatment can be assumed to be integrated in long-lived memory CD4+ cells [26]. If we furthermore assume that reservoir size does not decrease drastically with treatment (which is in agreement with the very long half-lives found for the reservoir [5]), the HIV DNA levels during treatment represent the size of the reservoir before treatment was initiated. Pre-treatment HIV DNA levels, however, represent the size of the total infected population (i. e. actively and latently infected cells). Using these proxies we can calculate the relative reservoir size as rL=[HIVDNA]t[HIVDNA]n−[HIVDNA]t, (15) where [HIVDNA]t and [HIVDNA]n denote the HIV DNA-level during treatment and pre-treatment (naive), respectively. Note that we do not incorporate the fraction of defective integrated proviruses into our indirect method. Approximately 88% of integrated proviruses in resting CD4+ T cells in patients on ART are completely replication incompetent because of genetic defects [60]. However, since most of these mutations are induced pre-integration (either due to reverse transcriptase infidelity or host cell APOBEC activity), we should expect to find defective integrated proviruses in activated CD4+ T cells as well. Indeed, it was recently shown that a substantial proportion of HIV DNA sequences isolated from peripheral blood mononuclear cells from treatment-naïve patients contain premature stop codons [58]. If mutations in the HIV sequence happen at equal rate during infection of activated and resting CD4+ T cells, and if resting CD4+ cells infected with defective virus live the same amount of time and proliferate at the same rate as those latently infected with non-defective virus (an assumption that has however recently been challenged [65]), the fraction of cells infected with replication competent proviruses should be similar in both compartments. Hence, the ratio of replication competent HIV DNA levels does not change and our estimate for the relative reservoir size is unaffected.
summary: During HIV infection, a small proportion of infected cells containing integrated proviral DNA enter a long-lived resting phase, thus creating latent reservoirs of virus. These reservoirs are a major barrier to curing HIV and have been studied intensively in this light. Latent reservoirs might also affect viral dynamics during untreated infection, because they provide an archive of old viral variants that can re-enter circulation at a later time upon activation of latently infected cells. We developed a mathematical model to investigate how reservoir dynamics affect the evolution of the virus within single hosts, and find that the presence of a latent reservoir can severely delay within-host evolutionary dynamics. This delay increases with the relative size of the reservoir and the rate at which latently infected cells proliferate. By nesting this within-host model into an epidemiological model of host population dynamics, we show that the presence of latent reservoirs can also influence the population-level evolution of the virus. In contrast to predictions made by previous models we find that population-level adaptation to maximise transmission between hosts, rather than within-host fitness, can occur, but only if adaptation of the virus within hosts is sufficiently slowed down by the presence of latent reservoirs.
keywords: organismal evolution
  medicine and health sciences
  microbial mutation
  pathology and laboratory medicine
  viral transmission and infection
  pathogens
  microbiology
  retroviruses
  viruses
  immunodeficiency viruses
  physiological processes
  homeostasis
  rna viruses
  microbial evolution
  viral load
  hiv epidemiology
  lentivirus
  medical microbiology
  hiv
  epidemiology
  microbial pathogens
  viral replication
  evolutionary immunology
  viral evolution
  virology
  physiology
  viral pathogens
  biology and life sciences
  evolutionary biology
  organisms
title: Effect of the Latent Reservoir on the Evolution of HIV at the Within- and Between-Host Levels