^{1}

^{*}

^{2}

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Conceived and designed the experiments: FL SA. Performed the experiments: FL SA. Analyzed the data: FL SA. Contributed reagents/materials/analysis tools: FL SA. Wrote the paper: FL SA.

The authors have declared that no competing interests exist.

Many pathogens associated with chronic infections evolve so rapidly that strains found late in an infection have little in common with the initial strain. This raises questions at different levels of analysis because rapid within-host evolution affects the course of an infection, but it can also affect the possibility for natural selection to act at the between-host level. We present a nested approach that incorporates within-host evolutionary dynamics of a rapidly mutating virus (hepatitis C virus) targeted by a cellular cross-reactive immune response, into an epidemiological perspective. The viral trait we follow is the replication rate of the strain initiating the infection. We find that, even for rapidly evolving viruses, the replication rate of the initial strain has a strong effect on the fitness of an infection. Moreover, infections caused by slowly replicating viruses have the highest infection fitness (i.e., lead to more secondary infections), but strains with higher replication rates tend to dominate within a host in the long-term. We also study the effect of cross-reactive immunity and viral mutation rate on infection life history traits. For instance, because of the stochastic nature of our approach, we can identify factors affecting the outcome of the infection (acute or chronic infections). Finally, we show that anti-viral treatments modify the value of the optimal initial replication rate and that the timing of the treatment administration can have public health consequences due to within-host evolution. Our results support the idea that natural selection can act on the replication rate of rapidly evolving viruses at the between-host level. It also provides a mechanistic description of within-host constraints, such as cross-reactive immunity, and shows how these constraints affect the infection fitness. This model raises questions that can be tested experimentally and underlines the necessity to consider the evolution of quantitative traits to understand the outcome and the fitness of an infection.

Rapidly mutating viruses, such as hepatitis C virus, can escape host immunity by generating new strains that avoid the immune system. Existing data support the idea that such within-host evolution affects the outcome of the infection. Few theoretical models address this question and most follow viral diversity or qualitative traits, such as drug resistance. Here, we study the evolution of two virus quantitative traits—the replication rate and the ability to be recognised by the immune response—during an infection. We develop an epidemiological framework where transmission events are driven by within-host dynamics. We find that the replication rate of the virus that initially infects the host has a strong influence on the epidemiological success of the disease. Furthermore, we show that the cross-reactive immune response is key to determining the outcome of the infection (acute or chronic). Finally, we show that the timing of the start of an anti-viral treatment has a strong effect on viral evolution, which impacts the efficiency of the treatment. Our analysis suggests a new mechanism to explain infection outcomes and proposes testable predictions that can drive future experimental approaches.

Rapidly mutating viruses, such as hepatitis C (HCV) and Human immunodeficiency virus (HIV), are very successful at surviving in their hosts because of their rapid evolutionary dynamics, which allow them to evade the immune response. Models have been developed in evolutionary epidemiology that link within- and between-host dynamics

Most theoretical and experimental studies focus on the dynamics of viral diversity during an infection (see e.g.,

Infections caused by a rapidly mutating virus exhibit high levels of genetic diversity. Classical theory predicts that, in such a case, faster replicating strains have the highest infection fitness because they gather more resources before the end of the infection

Some within-host models study the evolutionary dynamics of the replication rate during the course of an infection. A common finding of such models is that the replication rate increases during the course of an infection, either because of resource competition or because of apparent competition through the immune system

Here, we focus on the fitness of a viral strategy at the between-host level (i.e., how many new infections an infection can cause). Bonhoeffer and Nowak

The immune system is known to be a major constraint on viral evolution

This assumption echoes the immunogenicity criterion formalised by Pradeu and Carosella

Here, we develop a nested model that links within-host evolutionary dynamics to the epidemiology. By explicitly describing the immune dynamics, the model takes into account the fact that a viral strategy dominant early in an infection (e.g., replicating slowly to escape the immune system) may be rare later in the infection.

We perform stochastic simulations with a model that describes the within-host evolution of a viral strain undergoing mutation. In our model, the immune response is assumed to be strain specific and we account for cross-reactive immunity, i.e., the fact that strains are recognised by more than one clone of lymphocytes. Viral strains are identified by their replication rate and their antigen value, the latter defining the extent to which the strain is recognised by a given T-cell clone. We introduce between-host dynamics by adding transmission events whose probabilities depend on the viral load at a given time (see the

Notation | Description | Value |

Number of cells infected with viruses of strain |
variable | |

Number of immune cells specific to strains with antigen |
variable | |

Number of viral strains | variable | |

Number of lymphocyte clones | 20 | |

Replication rate of viral strain ^{−1}) |
||

Maximum replication rate (day |
4 | |

Antigen value of viruses of strain |
variable | |

Receptor value of lymphocytes of clone |
variable | |

Maximum killing rate (day^{−1} lymphocyte^{−1}) |
||

Maximum activation rate of lymphocytes (infected cells^{−1}) |
||

Breadth of immune cells specificity | ||

Virus mutation rate (per generation) | ||

Width of the distribution of replication rates | ||

death rate of infected cells (day^{−1}) |
||

death rate of lymphocytes (day^{−1}) |
||

Probability of transmission to another host (per generation) | ||

Probability of virulence, i.e. host death (per generation) | 0 | |

Intensity of a virus-clearance treatment (day^{−1}) |
0 | |

Intensity of a replication-blocking treatment (day^{−1}) |
0 |

Ranges for parameter values for the death rates and for the killing rate are taken from a

With identical parameter values, we can observe a chronic (A,C,E) or an acute (B, D, F) infection. A) and B) Population dynamics of infected cells (in black) and immune cells (in red). C) and D) Diversity dynamics (Shannon index). E) and F) Evolutionary dynamics of the replication rate. Black dots indicate the replication rates present at any time, the red line is the average replication rate for each time t, and the large blue dots show the replication rates of the strains that are transmitted to another host after a transmission event. Here

Within-host evolutionary dynamics are expected to affect the dynamics of disease transmission. On panels E and F, large blue dots indicate strains that are transmitted following a stochastic transmission event (see the

To get a more accurate picture of the evolutionary dynamics, we performed multiple runs of simulations with different parameter values.

A) Number of transmission events (i.e. infection fitness), B) Duration of the infection, C) Average replication rate of transmitted strains, and D) Viral diversity (Shannon index) near the end of the infection. Curves with different colour symbols represent simulations performed with different values of

Parameters ----------- Traits | Initial replication rate ( |
Cross-reactive immunity ( |
Maximum immune activation rate ( |
Mutation rate ( |
Mutation width of |
Maximum killing rate ( |
Treatment intensity ( |

Infection fitness | |||||||

Duration of the infection (Log) | |||||||

Mean replication rate of transmitted strains | |||||||

Final viral diversity | |||||||

Final number of immune cells (Log) | |||||||

Final number of infected cells (Log) |

We performed linear fits based on a multivariate linear model on the mean values of the traits as a function of 12 factors: 9 model parameters (

Significance test codes: ‘^{***}’: ^{**}’: 0.01; ‘^{*}’: 0.05; ‘^{n.s.}

As described in the

We find that the initial replication rate (

We model the variation in the breadth of the immune response by varying the width (

In the case of infections caused by a rapidly replicating strain (high

We model viral mutation as a stochastic process (see the

Effect of the initial replication rate (x-axis) on the infection fitness for different values of A) the mutation rate

Increasing the width (

Increasing the maximum T-cell activation rate (

Increasing the maximum T-cell killing rate (

We also studied the effect of the initial population sizes of infected cells and of lymphocytes (precursor frequency), the possibility of host death (i.e., virulence) and of saturation in the lymphocyte proliferation function in equation 1. These results are shown in

In the absence of within-host evolution,

This figure is obtained by combining

In our model, each one of the transmitted strains potentially has a different infection fitness based on its replication rate. We therefore combine differential fitness (

We simulate two types of treatments: the first type improves the killing of infected cells and is modelled with an additional killing term of infected cells, the second type blocks viral replication and is modelled with a limitation term on viral replication. Current treatments of HCV use

In

In panels A, and B the treatment starts at the time of the infection, in panels C, and D the treatment starts 30 days after the beginning of the infection. Finally in panels E and F treatment starts 180 days after the infection. Panels A, C, and E show the average infection fitness (IF). Panels B, D, and F show the average duration of the infections (DoI). The latter is calculated by excluding simulation runs that result in host before the beginning of the treatment (this is done to highlight the effect of the treatment at the within-host level). Different colours correspond to different treatment intensities (

The timing of the treatment also affects the course of an infection. When the treatment is initiated at the onset of an infection (which would be the case if hosts are treated following exposure), we see a shift of the curves to the right (

In order to investigate the effect of treatment at the host level rather than at the host population level, we focussed on the duration of the infection and removed from the analysis hosts who had cleared the infection before the beginning of the treatment (

We developed a nested model that incorporates within-host evolutionary dynamics into an epidemiological perspective to study the evolution of viral traits, such as the replication rate. This approach raises an important issue in that viral traits evolve within the host during the course of an infection and at the between-host level. In other words, what infects a host (a strain with its initial replication rate) differs from what is transmitted (a distribution of replication rates). We show that the replication rate of the strain that initiates the infection has a strong effect on the course and on the fitness of an infection. On average, the initial replication rate tends to be heritable from one infection to the next. These two results (heritability and fitness effect) combined with the known variability in replication rates indicate that, in our model, natural selection acts on viral replication at the between-host level.

We find that infection fitness (measured as the number of transmission events per infection) is maximised for infections initiated by slow-replicating strains. This is partly due to the assumption we make on the immune proliferation function, which allows slow-replicating strains to have the most efficient resource exploitation (by escaping from the immune response). Escaping from the immune response has a second advantage because it gives more opportunities to these strains to generate escape mutants. We are not aware of studies on the evolution of HCV replication rate at the between-host level. In the case of HIV, the subtype C of HIV-1 has been shown to be spreading more rapidly than other subtypes

In epidemiology, the idea that low replication rates can be optimal is not new; it is present in the transmission-virulence trade-off theory

Our model also illustrates the conflict between levels of selection

Our model allows us to study the evolutionary consequences of anti-viral treatments on infection life-history traits. Increasing the efficiency with which a treatment blocks viral replication decreases viral fitness, but also increases the evolutionarily optimal replication rate of the virus. This is consistent with theoretical

Most epidemiological models find a host ‘selfish’ strategy, which consists in increasing its own protection at the expenses of the community

Few studies have attempted to model HCV disease outcomes. Wodarz

A key feature of our model is that for the exact same parameter values, we can observe chronic or acute infections (for a review on this topic, see

We show that replication rate of the initial strain and the parameters describing the immune response alter the probability that one of the two outcomes (chronic or acute infection) is reached. The few observations on the correlations between the outcome of HCV infections and the viral replication rate tend to support our results. Data on the growth of HCV in sera suggest that slow replicating viral populations are common in HCV cases with viral persistence

The immune response against HCV is puzzling. The mechanisms responsible for the high rate of viral persistence are thought to be the result of complex early host-virus interactions that involve immune system heterogeneity, viral diversity and cross-reactive immunity

The between-host dynamics of our model could be extended in several ways. We used an invasion fitness analysis (with

Modelling the between-host dynamics more explicitly would allow one to take into account the age of the infection. Day

Another extension would be to include several transmission routes for the virus. The model we use here assumes that infections are initiated by a unique viral strain, which is known to be the case for sexual transmission of HIV

Regarding the selective forces involved in the evolution of HCV at a population level, there is evidence that the major histocompatibility complex (MHC) allele diversity among the population is a major force driving the evolution of the virus

Our work leads to predictions that can be tested experimentally: strains that dominate early in the infection and those that dominate later have different replication rates; and the replication rate of the initial strain and the mutation rate affect the duration and/or the fitness of an infection (see

This study stresses the key role played by the cross-reactive immune response in controlling the duration and the fitness of an infection. In addition to the theoretical challenge described above, an experimental validation of this study could be to measure

We model viral dynamics with an immune control model based on a predator-prey-like interaction, where lymphocytes are predators. We assume a finite number of T-cell clones per host,

Following previous models, we simplify the virus life cycle by focusing on infected cells only

T-cells of clone

Equation system 1 only describes within-host dynamics, but nothing is specified concerning evolutionary processes. Here, the number of viral strains

In this model, viruses of strain

We analyse the effect of escape mutants with a hybrid stochastic-deterministic approach (see

We wish to stress that our model allows for backwards mutation. By this we mean that a mutant can be identical to another strain in the infection or to a strain that was present earlier in the infection. This approach provides a realistic representation of the quasi-species characteristics of HCV evolution and frees us from potential biases due to infinite allele model assumptions.

The number of strains is not constant in these simulations. We follow the evolution of strain diversity by measuring the Shannon index,

We extended the model to study the effect of two types of treatments. The first type of treatment directly increases the killing of infected cells. It is obtained by adding a death term (

We do not introduce host death in the default case of the model. The main justification for this assumption is that, from the point of view of the virus, host recovery or host death are very similar, the only difference lies at the epidemiological level that is outside the scope of this study. The effect of virulence is shown in

Having a nested model requires a careful definition of the viral trait that evolves at the between-host level. Here, we follow the replication rate of the strain that causes an infection (or ‘initial replication rate’). Can this trait evolve under natural selection at the between-host level? For this, three conditions must be fulfilled

Now that we have specified our trait of interest, we need to introduce a fitness measure for the infection bearing the trait. The ‘fitness’ of an infection can be expressed through the basic reproduction ratio (

To estimate the infection fitness, we introduce a random transmission event in the simulation. At each time step, this event occurs with a probability proportional to the log of the total density of infected cells at this time, thus reflecting recent data showing that the transmission rate during primary infections with HIV increases linearly or more than linearly with the viral load

In addition to the infection fitness, we investigate the effect of parameter values and initial values on several life-history traits of the infection: the duration of the infection, the final viral diversity (measured near the end of the infection), the final total immune cell density, and the final total viral load. The analysis is performed by varying one of the parameters at the time and running simulations for 22 different initial replication rates (ranging from

Finally, we introduce a

Dynamics of the average replication rate of transmitted strains and of the total number of strains transmitted per day We show the results obtained for 200 simulation runs for low, average, and high cross-reactive immune responses, respectively (^{2} = 0.902, B) ^{2} = 0.883, C) ^{2} = 0.810). Bottom panels show the number of transmission events over time. Increasing cross-reactive immunity (from left to right) decreases the average replication rate of transmitted strains.

(0.16 MB TIF)

Effects of parameter variations on the replication rate of transmitted strains. Effect of the initial replication rate _{0} (x-axis) on the average transmitted replication rate for different values of A) mutation rate _{max}, and D) maximum killing rate of immune cells _{max}. Different parameter values are shown using different colour symbols (see the box in each panel) and the default case is in black.

(0.52 MB EPS)

Details about the simulations. This text file gives further details about the simulations and the statistical tests used in

(0.08 MB PDF)

Additional results. We discuss the effect on life-history traits of variations of the initial value of immune cells and infected cells, of the probability of virulence and of the effect of a saturation term for the description of lymphocyte proliferation rate function.

(0.08 MB PDF)

We thank T. Day, A. Lloyd, N. Mideo, S. Lion, S. Gandon, A. Zecry, and two anonymous reviewers for helpful comments.

^{+}-T-lymphocyte responses.