Stochastic Approach in the modelling of ISFabio Luciani 
The first model is a stochastic dynamic system for the CD8+ T naive lymphocytes (CD8+ CD95) dynamics on the long time scale of the human life span. The purpose is to test the recent hypothesis that the depletion of virgin CD8+ T lymphocytes can be considered a likely marker of mortality. The model is capable of fitting the experimental data concerning the changes of virgin T cell concentration over age, and at the same time to reproduce survival curves similar to the demographic ones. It confirms the finite probability of having individuals with a life span much longer than the average (centenarians) and that the stochastic process is responsible of the peculiar shape of survival curves, strikingly similar from worms to humans and in outbred and inbred populations (see figure 1). The second model emphasizes the role of chronic antigenic stimuli in the clonal expansion of T and B cells over a long time scale and their role on the Immunosenescence. This is particularly relevant since the study of the chronic stimulations is quite neglected even if they are fundamental for the vaccine effectiveness.
The stochastic approach is innovative in the population dynamics of Immune Cells
The stochastic approach introduce new insights in Immunology. The first model confirms our hypotesis based on experimental data: CD8+ T Cells depletion is a likely Mortality Marker. Moreover the comparison with demographic curves was successful.
The second model emphasizes the role of chronic antigenic stimuli in the clonal expansion over a long time scale. This is particularly relevant since the study of the chronic stimulations is quite neglected also from an experimental point of view.
The stochastic approach is a mathematical tool for the introduction of a phenomenon over a microscopical scale (molecular dimensions) in population dynamics over a long time scale
Even if a mean genetically capability of responding antigens has been taken into account the stochastic effects allow to reproduce heterogeneity of the cell populations coming from different individuals.
In comparison with other studies on longevity (C. Elegans) we have found that the shape of survival curves is not dependent from the genetics but only from the fluctuation of antigenic load. (human in the last decades)
Figure 1: Distribution of v(t) and survival curves
Top: Black Central curve is v(t), blue external curves v(t)±σ(t) with v_{∞}=0.4 ; γ=0.1 (right) v_{∞}=0.4 ; γ=0.15 (left). Bottom: Corresponding survival curves for different values of the parameters v_{∞} , γ. 
Figure 2: Theoretical curves with demographic data represented by dots (top). Human Male (top left) and Human Females (top right). The same demographic data (down) 1994.

The stochastic approach is innovative in the population dynamics of Immune Cells.
The stochastic approach introduce new insights in Immunology. The first model confirms our hypotesis based on experimental data: CD8+ T Cells depletion is a likely Mortality Marker. Moreover the comparison with demographic curves was successful.
The second model emphasizes the role of chronic antigenic stimuli in the clonal expansion over a long time scale. This is particularly relevant since the study of the chronic stimulations is quite neglected also from an experimental point of view.
The stochastic approach is a mathematical tool for the introduction of a phenomenon over a microscopical scale (molecular dimensions) in population dynamics over a long time scale.
Even if a mean genetically capability of responding antigens has been taken into account the stochastic effects allow to reproduce heterogeneity of the cell populations coming from different individuals.
In comparison with other studies on longevity (C. Elegans) we have found that the shape of survival curves is not dependent from the genetics but only from the fluctuation of antigenic load. (human in the last decades)
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