Model results for the system with stable (blue) and unstable (red) vaccine, the latter having a decay rate roughly twice that of the former (see Table 2).

<p>The benefits of stability are not fully realised until a booster dose is applied (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030435#pone-0030435-g005" target="_blank">Figure 5</a>).</p

<i>In-vivo</i> experimental results for cattle inoculated with a regular dose of vaccine at 0 and 29 days, giving the resultant IgM (left) and IgG (right) levels recorded: (top: blue) normal vaccine producing a regular immune response; (bottom: green) vac

<p>Plots give the median value (central bar), 25th–75th percentile (box) and extreme values (whiskers) unless considered outliers, in which case they are plotted separately (cross) for four (bottom: T-cell independent) or five (top: T-cell dependent) replicates (individual cattle). Data from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030435#pone.0030435-Grant1" target="_blank">[9]</a>. Note the significant differences in magnitude between the T-cell dependent and T-cell independent cases. Results presented on a log-scale.</p

Parameters.

<p>Definitions of system parameters and values used in simulations (with justification and/or reference source). Here generally refers to production rates, to conversion rates, to decay rates and to temporal delays. For simulations we consider .</p>†<p>wk: week; c: particle (vaccine, complex or cell) concentration.</p

Experimental and simulation results for IgM () and IgG () for the full system (blue) and for the system with a reduced T-cell dependent response only (green).

<p>Here the mean and range of each of the datasets from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030435#pone-0030435-g006" target="_blank">Figure 6</a> are plotted, together with the simulation results from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030435#pone-0030435-g007" target="_blank">Figure 7</a>, with the model outputs suitably scaled (the peak of the experimental mean for each of the two immunoglobulins matched by the peak of the full T-dependent system).</p

Variables.

<p>Definitions of system variables.</p

Model results for the system with different initial doses of (stable) vaccine: (solid), (dashed), (dot-dashed) and (dotted).

<p>Model results for the system with different initial doses of (stable) vaccine: (solid), (dashed), (dot-dashed) and (dotted).</p

Model results for the system with stable (blue) and unstable (red) vaccine, in response to a second (booster) vaccine dose administered approximately 4 weeks after the initial one.

<p>Model results for the system with stable (blue) and unstable (red) vaccine, in response to a second (booster) vaccine dose administered approximately 4 weeks after the initial one.</p

Schematic of the short-term and long-term dynamics of the immune response, as stimulated by vaccine antigen.

<p>For variable definitions see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030435#pone-0030435-t001" target="_blank">Table 1</a>; for parameter definitions and values see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030435#pone-0030435-t002" target="_blank">Table 2</a>.</p

LHS applied to the immunological model with parameter ranging from to 4 times the nominal values shows that qualitative behaviour is maintained.

<p>Here the median (solid line) is plotted together with the range of possible results, in 5 percentile steps (shaded) from 410 replicates (axes upper bound set at maximum of 95^th percentile range) on a log scale.</p

Model results for the full system (blue) and for the system with a reduced T-cell dependent response only (green), where and have been reduced to 1% of their original values.

<p>All figures present variables on a log scale as percentages of their peak value.</p