Schematic representation of the pathogen life cycle.

<p>In our model we assume that hosts can either be uninfected or infected by the wild type (in green) or a mutant genotype (in red). Transmission can take two different routes. Horizontal transmission occurs between a susceptible host and an infected host with genotype <i>i</i> with rate <i>β</i>_<i>i</i>[<i>I</i>|<i>S</i>] (see supporting information Theory in <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1004810#ppat.1004810.s001" target="_blank">S1 Text</a>). Vertical transmission occurs when and infected host reproduces in an empty site with rate <i>b</i>_<i>I</i><i>δq</i>_<i>0/i</i>, where <i>b</i>_<i>I</i> is the reproduction rate of infected hosts, <i>δ</i> is the fidelity of vertical transmission and <i>q</i>_<i>0/i</i> measures the average local density of empty sites around hosts infected with genotype <i>i</i>. Among hosts infected by the same genotype we distinguish hosts that got infected horizontally (noted </p><p></p><p></p><p></p><p><mi>I</mi><mi>i</mi><mi>H</mi></p><p></p><p></p><p></p>) or vertically (noted <p></p><p></p><p></p><p><mi>I</mi><mi>i</mi><mi>V</mi></p><p></p><p></p><p></p>). Both types of hosts can reproduce and have an increased mortality rate <i>α</i>_<i>i</i> (i.e. virulence) due to the infection with genotype <i>i</i>.<p>