From: Theoretical analysis of the evolution of immune memory
Parameter | Value | Biological Relevance |
---|---|---|
pathogen pool | ||
n p | pathogen pool size, 50 | This value is small in comparison to findings in [44, 45] (1399-1415 human pathogens) but large in comparison to other theoretical studies, e.g. [18]. |
p occ,j | occurrence probability of pathogen j | depends on the pathogen environment |
p surv,j | basic survival probability for pathogen j | depends on the pathogen environment |
λ | reproduction probability, 0.2 | probability that one individual reproduces per year; an individual living until age 40 produces on average 5 offspring. |
p inf | probability of infection, 0.1 and 0.5 | not experimentally determined yet; might vary between pathogens and depend on the route of trans mission |
individuals | ||
n mp,i | memory pool size of individual i, maximally 50 | the maximal value of 50 memory units guarantees that an individual could theoretically generate one memory unit specific for each pathogen |
n rep, i | number of newly generated memory cells of individual i | maximally 50 |
ζ | probability to survive until the reproductive age; 0.5 and 0.75 | childhood mortality differs from country to country; high in non-developed countries and lower in developed countries [59] |
Ï„ i | type of replacement of individual i | one of the traits studied; 'random' correspond to homeostasis model [37], 'age-dependent' correspond to attrition model [34, 35] |
m i (j) | number of memory cells of individual i against pathogen j | Â |
Θ k (t) | number of individuals of type k at time t |  |
w | fitness difference | Â |
 | number of pathogen exposures per year, 3 | arbitrarily defined |
 | survival curve, concave down- ward | The relation between the number of memory cells and the level of protection has not yet been determined quantitatively; our definition guarantees a fast increase with few memory cells, but also the possibility of leaky protection (see also Discussion). |