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Table 1 Parameter values

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

 

Θ k (t)

number of individuals of type k at time t

 

w

fitness difference

 
 

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).