Skip to main content


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
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]
τ 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).