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

Figure 5

Sketch for (9), (10), and (12) of how convolution of a binomial distribution is applied to probability distribution. (a) Multiplication phase 𝑀, (9), (10): 𝜇_𝐴−𝑁_𝐴−𝑘_𝐴 total copies of initial form 𝐴 (and 𝜇_𝐵−𝑁_𝐵−𝑘_𝐵 total copies of mutant 𝐵); 𝜇_𝐴−𝑁_𝐴 maximal possible copies according to the multiplication factors 𝜌_𝐴 of initial form 𝐴 (and 𝜇_𝐵−𝑁_𝐵 maximal possible copies according to the multiplication factors 𝜌_𝐵 of mutant 𝐵); 𝑘_𝐴𝐵 (and 𝑘_𝐵𝐴) number of copies transforming from initial form 𝐴 to mutant 𝐵 (and vice versa resp.). (b) Selection phase 𝑆, (12).