Immune Response to a Variable Pathogen: A Stochastic Model with Two Interlocked Darwinian Entities

<table>Sketch of how convolution of a binomial distribution is applied to probability distribution. (a) multiplication phase <svg height="11.175" id="M87" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 17.475 11.175" width="17.475" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>, (<a href="https://static.hindawi.com/articles/cmmm/volume-2012/784512/figures/#EEq3">3</a>). (b) Selection phase <svg height="11.75" id="M88" style="vertical-align:-0.23206pt" version="1.1" viewbox="0 0 8.2875004 11.75" width="8.2875004" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>, (<a href="https://static.hindawi.com/articles/cmmm/volume-2012/784512/figures/#EEq4">4</a>). <svg height="16.625" id="M89" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 53.712502 16.625" width="53.712502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg> Maximal possible number of copies. (<svg height="11.375" id="M90" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 41.5625 11.375" width="41.5625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M509 373q0 -52 -42.5 -118.5t-124.5 -159.5l-94 -107h-27q-22 209 -78 342q-21 48 -41 48q-18 0 -63 -62l-22 21q77 111 125 111q30 0 52 -21.5t38 -75.5q37 -130 52 -285q48 62 74.5 99.5t53.5 87t27 76.5q0 43 -17 60q-5 5 -5 15q0 17 12.5 30.5t28.5 13.5
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</svg>) Number of copies.</table>

Computational and Mathematical Methods in Medicine

fig2

Figure 2

Figure 2: Immune Response to a Variable Pathogen: A Stochastic Model with Two Interlocked Darwinian Entities 