Factors leading to strong primary immune responses.

<p>Values of the parameters are as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0002306#pone-0002306-g002" target="_blank">Fig. 2c</a> (basic: τ<i>_ae⁰</i> = 10⁴, λ<i>_r⁰</i> = 10⁴, τ<i>_r⁰</i> = 10 and see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0002306#pone-0002306-t001" target="_blank">Table 1</a>) so that we are in the bi-stability region (regime 3). Initially, there are no effector T cells. At time <i>t</i> = 0, one (i.e. the maximum quantity) antigen is introduced (<i>X⁰</i> = 1): we neglect the growing phase of the antigen. Grey zones correspond to tolerance, i.e. the system falls into the strongly regulated state. White zones correspond to the development of a strong immune response, i.e. the system falls into the weakly regulated state. (a) Effect of the the effector and regulatory T cells turnover rates (<i>m_e</i> and <i>m_r</i>, respectively), with τ<i>_ap</i> = 10⁻²; (b) effect of the pre-existing number of regulatory T cells (<i>T_r⁰</i>) and the regulatory T cells turnover rate (<i>m_r</i>), with τ<i>_ap</i> = 10⁻²; and (c) impact of an inflammatory burst on the development of an immune response, depending on its duration (<i>D</i>) and intensity (τ<i>_ap^inf</i>), with τ<i>_ap^rest</i> = 10⁻² and <i>T_r⁰</i> = 1. Note that in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0002306#pone-0002306-g004" target="_blank">Fig. 4a </a><i>T_r⁰</i> = 0.</p

Basic value of the parameters (time unit is the day).

<p>Basic value of the parameters (time unit is the day).</p

Stability of the strongly regulated equilibrium.

<p>It is characterized by the mean period of time (<i>D</i>) during which inflammation must be maintained to induce a long lasting immune response. Again values of the parameters are as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0002306#pone-0002306-g002" target="_blank">Fig. 2c</a> (basic: τ<i>_ae⁰</i> = 10⁴, λ<i>_r⁰</i> = 10⁴, τ<i>_r⁰</i> = 10 and see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0002306#pone-0002306-t001" target="_blank">Table 1</a>). (a) Effect of the duration (<i>D</i>) and intensity (τ<i>_ap^inf</i>) of the inflammatory burst. The threshold line obtained with the same parameters but for an introduced antigen is reported on the graph as a dashed line (with <i>T_r⁰</i> = 1, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0002306#pone-0002306-g004" target="_blank">Fig. 4d</a>); and (b) Effect of the duration of the inflammatory burst (<i>D</i>) and the regulatory T cells turnover rate (<i>m_r</i>), with τ<i>_ap^inf</i> = 10³. As in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0002306#pone-0002306-g004" target="_blank">Fig. 4</a> grey zones correspond to tolerance and white zones correspond to the development of a strong immune response. In (a) and (b), τ<i>_ap^rest</i> = 10⁻².</p

Impact of the parameters on the nature of the equilibrium regime.

<p>Situations are divided into the 3 regimes described in the main text (see also <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0002306#pone-0002306-g002" target="_blank">Fig. 2</a>). (a) For different values of the activation rate of APCs by effector cells (τ<i>_ae⁰</i>) and different rates of regression of APCs by regulatory T cells (τ<i>_r⁰</i>), with λ<i>_r⁰</i> = 10⁴; (b) for different values of the activation rate of APCs by effector T cells (τ<i>_ae⁰</i>) and different rates of inhibition of effector cells by regulatory T cells (λ<i>_r⁰</i>), with τ<i>_r⁰</i> = 1; (c) same as (b) but with τ<i>_r⁰</i> = 10; (d) same as (b) but with τ<i>_r⁰</i> = 0.1.</p

Effect of the parameters on the model where the infection rate depends on the number of infected individuals in the population.

<p>(A) Regime followed according to the basic reproductive number of normal individuals () and duration of immunity (); (B) same as (A) but with (<i>q</i> = ρ = 1). The bold lines represent the threshold value at equilibrium, where the number of infected individuals is the same in a population consisting only of “avoiders” and in a population exclusively composed of “normal” individuals.</p

Detrimental effect of pathogen avoidance for non-lethal diseases.

<p>It is represented by the relative frequency (<i>r</i>, Y-axis) at which “avoider” individuals suffer classical infections compared to “normal” ones (when values are below one, avoiding the pathogenic agent is beneficial), according to the rate of infection by a pathogenic agent (X-axis). (A) For total immune periods of one year, avoiding the pathogenic agent is beneficial only for low infection rates. For high infection rates, both strategies tend to become equivalent since boosts to the immune system are almost systematic; (B) for lifelong immunity, avoiding the pathogenic agent is always a good strategy; and (C) considering a continuum in the total duration of immunity (in years) shows that “avoiders” can be more than six times more at risk of becoming sick compared to “normal” individuals. The threshold where both strategies are equivalent (<i>r</i> = 1) is represented with a dashed line (A) or with a bold red line (C).</p

Impact of pathogen avoidance when the infection rate depends on the number of infected individuals in the population.

<p>We plot here the equilibrium proportion of infected individuals in the host population (Y-axis) according to the proportion of “avoiders” (<i>p_A</i>, X-axis). Note that here the transmission rate of the pathogen can be derived from the value of through the formula . (A) An example of a situation where the system follows regime A (, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0002299#s3" target="_blank">Results</a>: Model where exposure depends on infected individuals, for description of regimes); (B) an example of a situation where the system follows regime A-n (); (C) an example of a situation where the system follows regime N-a () and (D) an example of a situation where the system follows regime N ().</p

Flow diagram of the five classes of the modified <i>SIR</i> model.

<p>Arrows represent the transitions, with their associated rates. Transition rates in red are the only ones that differ between “avoiders” and “normal” individuals.</p

The average times of appearance of successive accumulations of escape mutations.

<p>In both panels the time of emergence of mutants with a given number of escape mutations is shown. Orange and blue bars correspond to runs with and without recombination, respectively. A shows the time of appearance of E escapes (escapes at the escape locus). Panel B shows the time of appearance of EC escapes (escapes at the escape and compensatory locus). The simulations show that recombination accelerates the emergence of escape mutations. Parameters used: , ; the others are defined in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0016052#pone-0016052-t001" target="_blank">Table 1</a>. The plot shows an average of 10000 simulation runs.</p

CTL dynamics and the impact of recombination.

<p>Figures are plotted as a function of mean avidity and variance of avidity of the CTL response. Panel A shows the mean diversity of the CTL population which decreases with increasing mean (except for an initial increase in avidity) and decreasing variance in avidity. Panel B shows the mean number of escapes during infection without recombination after 1 yr. of infection, which has an optimum for a given mean avidity of response and correlates well with the diversity of the CTL response in panel A. Panel C shows the factor of increase in the number of escapes after one year (cf. panel B) due to recombination, which is the strongest for broad and even responses. Panels D and E show the time of appearance (days) of the full escape variant without and with recombination, respectively. The hatched areas show runs in which the full escape mutant did not appear within the time of 1000 days. The impact of recombination on the time of emergence of the full escape mutant, shown in panel F, corresponds well to the impact of recombination on the number of escape mutations after one year, shown in panel C. The mean and variance of log avidities ( and , respectively) plotted in all panels are defined in each simulation, and the distribution of avidity values is drawn from a uniform distribution in each simulation run between and . The parameters used: , , . All other parameters are given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0016052#pone-0016052-t001" target="_blank">Table 1</a>. Each point in the plot shows an average of 5000 simulation runs.</p