Text S1: Details about the simulations

We describe the within-host evolutionary dynamics with a hybrid stochastic-deterministic model. Similar approaches have been proposed to model within-host evolutionary dynamics in HIV, showing that one can assume a deterministic behaviour for the population of infected and immune cells whilst keeping a stochastic description of the viral evolution [1,2]. Here, contrary to previous models, we track the dynamics of two viral traits: the replication rate and the antigen characteristic of each viral strain present in the host (for a similar approach with only two strains per host, see [3]). Due to the complexity of the model, numerical simulations are performed with a code written in C that is available upon request to the authors. In the model, at each time step, the population size of each viral strain and each lymphocyte clone are updated using the system of differential equation 1 given in the main text. This system is solved numerically with a fourth order RungeKutta algorithm [4]. A viral strain is removed from the system if the number of cells infected by this strain falls below 1. Each viral strain is characterised by a replication rate and an antigenic value (see the Model section in the main text). The immune cells are described as a population of a finite number of T-cell clones m each with a receptor that recognises antigens within a range of values defined by the function given in Eq. 2 of the main text. In the simulations we assume m = 20. We assume that infections are generated by a single strain with an initial replication rate φ0 and an antigen value A0. This assumption is supported by recent data for HIV infections [5]; little is know about HCV transmission dynamics. Simulations are ended when the maximum time (Tmax = 800 days) is reached or when the total numbers of infected cells and immune cells both reach a threshold value of 1012 that we assume a large value that correspond to the death of the host.